An International Journal of the Polish Statistical Association

Transcription

1 STATISTICS IN TRANSITION nw sris An Intrnational Journal of th Polish Statistical Association CONTENTS From th Editor... Submission information for authors... 5 Sampling mthods and stimation CIEPIELA P., GNIADO M., WESOŁOWSKI J., WOJTYŚ M., Dynamic K-Composit stimator for an arbitrary rotation schm... 7 SHUKLA D., PATHAK SH., THAKUR N.S., Estimation of population man using two auxiliary sourcs in sampl survys... TAILOR R., SHARMA B., Modifid stimators of population varianc in prsnc of auxiliary information TIKKIWAL G.C., Khandlwal A., Crop acrag and crop production stimats for small domains rvisitd ONYEKA A.C., Estimation of population man in post-stratifid sampling using known valu of som population paramtr(s Othr articls CASTELLANOS E. M., Nonrspons bias in th Survy of Youth Undrstanding of Scinc and Tchnology in Bogotá SANKLE R., SINGH J.R., MANGAL I.K., Cumulativ sum control charts for truncatd normal distribution undr masurmnt rror GOŁATA E., Data intgration and small domain stimation in Poland xprincs and problms Comparativ Survys TARKA P., Customrs rsarch and quivalnc masurmnt in factor analysis Congrss of Polish Statistics: Th 00th Annivrsary of th Polish Statistical Association Editor s not on th Statistical Congrss Sction CZEKANOWSKI J. ( Biographical not... 6 NEYMAN J. ( Biographical not DOMAŃSKI CZ., 00 yars of th Polish Statistical Association ŁAGODZIŃSKI W., Th Polish Statistical Association (PTS R-stablishing SZREDER M., Nw conomy nw challngs for statistics... 9 KORDOS J., "Statistics in Transition" and "Statistics in Transition - nw sris" - First Fiftn Yars Editorial Offic. Statistics in Transition nw sris today... 0 Congrss Information Congrss Announcmnt Congrss Agnda Volum 3, Numbr, March 0 SPECIAL ISSUE

2 STATISTICS IN TRANSITION-nw sris, March 0 STATISTICS IN TRANSITION-nw sris, March 0 Vol. 3, No., pp. 4 FROM THE EDITOR Th Spring 0 issus of th Statistics in Transition nw sris is bing rlasd somwhat arlir than usually in ordr to contribut in this way to th upcoming Congrss of Polish Statistics, which is undr prparation to clbrat th hundrdth annivrsary of stablishing of th Polish Statistical Association. Accordingly, in addition to Journal s rgular sctions on stimation and sampling issus and othr articls, and also on comparativ survys a spcial congrssional sction is includd in this volum, containing voics ( occasional statmnts of svral mmbrs of th Journal s Editorial Board, and of important Congrss information matrials. Th first part starts with papr by Przmysław Cipila, Małgorzata Gniado, Jack Wsołowski and Małgorzata Wojtyś on Dynamic K-composit stimator for an arbitrary rotation schm. Authors bgin with an ovrviw of th proprtis of classical K-composit stimator proposd by Hansn, Hurwitz, Nisslson and Stinbrg (955 and intnsivly studid in Rao and Graham (964. It givs an altrnativ solution to quasi-optimal stimation undr rotation sampling whn it is allowd that units lav th sampl for svral occasions and thn com back. Sinc th K-composit stimator suffrs from crtain disadvantags as bing dsignd for a stabl situation in th sns that its basic paramtr is kpt constant on all occasions and rstrictd only to a crtain family of rotation dsigns authors propos a dynamic vrsion of th K-composit stimator (DK-composit stimator, without any rstrictions on th rotation pattrn. Although th proposd algorithm is simplr than th on for th classical K-composit stimator with optimal wights, it is prcis, in th sns that it dos not us any approximat or asymptotic approach. Diwakar Shukla, Sharad Pathak and Narndra Singh Thakur in papr ntitld Estimation of Population Man Using Two Auxiliary Sourcs in Sampl Survys propos familis for stimation of population man of th main variabl using th information on two diffrnt auxiliary variabls, undr simpl random sampling without rplacmnt (SRSWOR schm. Thr diffrnt classs of stimators ar constructd and xamind with a compltiv study with othr xisting stimators. Th xprssion for bias and man squard rror of th proposd familis ar obtaind up to first ordr of approximation. Usual ratio

3 W.Okrasa: From th Editor... stimator, product stimator, dual to ratio stimator, ratio-cum-product typ stimator and many mor stimators ar idntifid as particular cass of th suggstd family; thortical rsults ar supportd by numrical xampls. In th nxt papr, Modifid Estimators of Population Varianc in Prsnc of Auxiliary Information by Rajsh Tailor and Balkishan Sharma proposd is an stimator of population varianc using information on known paramtrs of auxiliary variabl. It has bn shown that using modifid sampling fraction th proposd stimators ar mor fficint than th usual unbiasd stimator of population varianc and usual ratio stimator for population varianc undr crtain givn conditions. Empirical study is also carrid out to dmonstrat th mrits of th proposd stimators of population varianc ovr othr stimators considrd in this papr. G. C. Tikkiwal and Alka Khandlwal in papr Crop Acrag and Crop Production Estimats for Small Domains Rvisitd discuss th problm of advanc and final stimats of yild of principal crops, at national and rgional (Stat lvls, which ar of grat importanc for country s macro lvl planning. For dcntralizd planning and for othr purposs lik crop insuranc, loan to farmrs, tc., th rliabl stimats of crop production for small domains ar also in grat dmand. This papr, thrfor, discusss and rviw critically th mthodology usd to provid crop acrag and crop production stimats for small domains, basd on indirct mthods of stimation, including th SICURE modl approach. Th indirct mthods of stimation so dvlopd us data obtaind ithr through traditional survys, lik Gnral Crop Estimation Survys (GCES data, or a combination of th survys and satllit data. In papr Estimation of Population Man in Post-Stratifid Sampling Using Known Valu of Som Population Paramtr(s by A.C. Onyka a gnral family of combind stimators of th population man in post-stratifid sampling (PSS schm is prsntd, following Khoshnvisan t.al. (007 and Koyuncu and Kadilar (009, and using known valus of som population paramtrs of an auxiliary variabl. Proprtis of th proposd family of stimators, including conditions for optimal fficincy, ar obtaind up to first ordr approximations, and th rsults ar illustratd mpirically. Th scond group of articls ( othr articls is opnd by papr of Edgar Mauricio Buno Castllanos on Nonrspons Bias in Th Survy of Youth Undrstanding of Scinc and Tchnology in Bogotá. Th Colombian Obsrvatory of Scinc and Tchnology OCyT dvlopd in 009 a survy about undrstanding of Scinc and Tchnology in studnts of high school in

4 STATISTICS IN TRANSITION-nw sris, March 0 3 Bogotá, Colombia. Th sampling dsign was stratifid according to th natur of school (public or privat. Two sourcs of unit nonrspons wr dtctd. Th first on corrsponds to schools that did not allowd to collct information. Th scond sourc corrsponds to studnts who did not assist during th days whn survy was applid. Estimats wr obtaind through two diffrnt approachs. Rsults obtaind in both cass do not show visibl diffrncs whn stimating ratios; vn though, som grat diffrncs wr obsrvd whn stimating totals. Rsults obtaind using th scond approach ar blivd to b mor rliabl bcaus of th mthodology usd to handl itm nonrspons. R. Sankl, J.R. Singh and I.K. Mangal in papr Cumulativ Sum Control Charts For Truncatd Normal Distribution undr Masurmnt Error constructd Cumulativ Sum (CUSUM Control Charts for man undr truncatd normal distribution and masurmnt rror. For diffrnt truncation points and diffrnt sizs of masurmnt rror tabls hav bn prpard for th avrag run lngth, lad distanc and th angl of mask. Thy analyz th snsitivity of th paramtrs of th V-Mask and th Avrag Run Lngth (ARL through numrical valuation for diffrnt valus of r. Elżbita Gołata s papr Data Intgration and Small Domain Estimation in Poland Exprincs and Problms has twofold objctiv, ncompassing, on th on hand, a prsntation of Polish xprincs with th mthodological issus considrd currntly as on of th most important i.., data intgration (DI and statistical stimation for small domains (SDE; and, on th othr hand, it attmpts to dtrmin rlationship btwn ths two typs of mthods. Givn convrgnc of th goals of both mthods, SDE and DI (i.., to incras fficincy of th us of xisting sourcs of information, simulation study was conductd in ordr to vrify th hypothsis of synrgis rfrring to combind application of both groups of mthods: SDE and DI. Th third sction, comparativ survys, is rprsntd in this volum by on itm, by Piotr Tarka s papr on Customrs Rsarch and Equivalnc Masurmnt in Factor Analysis. Author discusss th problm of btwn population validity of th masurmnt, whn xtractd factors may hard to b qually compard on th rflctiv basic lvl (unlss all conditions of invarianc masurmnt ar mt. Hnc, implmntation of customrs rsarch and any intr-cultural studis rquir a multi-cultural modl dscribing statistical diffrncs in both culturs with invarianc as undrlying assumption. In th articl mployd was a modl for analysis of customrs prsonal valus prtaining to hdonic consumption aspcts in two culturally opposit populations.

5 4 W.Okrasa: From th Editor... Data wr gnratd through survy conductd in two countris, in th following citis: Poland (Poznan and Th Nthrlands (Rottrdam and Tilburg, using probability sampls of youth. This modl mad it possibl to tst invarianc masurmnt undr cross-group constraints and thus xamining structural quivalnc of latnt variabls valus. Th sction dvotd to th Congrss of Polish Statistics, concluds this volum. Włodzimirz OKRASA Editor-in-Chif

6 STATISTICS IN TRANSITION-nw sris, March 0 5 STATISTICS IN TRANSITION-nw sris, March 0 Vol. 3, No., pp. 5 SUBMISSION INFORMATION FOR AUTHORS Statistics in Transition nw sris (SiT is an intrnational journal publishd jointly by th Polish Statistical Association (PTS and th Cntral Statistical Offic of Poland, on a quartrly basis (during it was issud twic and sinc 006 thr tims a yar. Also, it has xtndd its scop of intrst byond its originally primary focus on statistical issus prtinnt to transition from cntrally plannd to a markt-orintd conomy through mbracing qustions rlatd to systmic transformations of and within th national statistical systms, world-wid. Th SiT-ns sks contributors that addrss th full rang of problms involvd in data production, data dissmination and utilization, providing intrnational community of statisticians and usrs including rsarchrs, tachrs, policy makrs and th gnral public with a platform for xchang of idas and for sharing bst practics in all aras of th dvlopmnt of statistics. Accordingly, articls daling with any topics of statistics and its advancmnt as ithr a scintific domain (nw rsarch and data analysis mthods or as a domain of informational infrastructur of th conomy, socity and th stat ar appropriat for Statistics in Transition nw sris. Dmonstration of th rol playd by statistical rsarch and data in conomic growth and social progrss (both locally and globally, including bttr-informd dcisions and gratr participation of citizns, ar of particular intrst. Each papr submittd by prospctiv authors ar pr rviwd by intrnationally rcognizd xprts, who ar guidd in thir dcisions about th publication by critria of originality and ovrall quality, including its contnt and form, and of potntial intrst to radrs (sp. profssionals. Manuscript should b submittd lctronically to th Editor: [email protected]., followd by a hard copy addrssd to Prof. Wlodzimirz Okrasa, GUS / Cntral Statistical Offic Al. Nipodlgłości 08, R. 87, Warsaw, Poland It is assumd, that th submittd manuscript has not bn publishd prviously and that it is not undr rviw lswhr. It should includ an abstract (of not mor than 600 charactrs, including spacs. Inquiris concrning th submittd manuscript, its currnt status tc., should b dirctd to th Editor by mail, addrss abov, or [email protected]. For othr aspcts of ditorial policis and procdurs s th SiT Guidlins on its Wb sit:

7

8 STATISTICS IN TRANSITION nw sris, March 0 7 STATISTICS IN TRANSITION nw sris, March 0 Vol. 3, No., pp. 7-0 DYNAMIC K-COMPOSITE ESTIMATOR FOR AN ARBITRARY ROTATION SCHEME Przmysław Cipila, Małgorzata Gniado, Jack Wsołowski 3 and Małgorzata Wojtyś 4 ABSTRACT Classical K-composit stimator was proposd in Hansn t al. (955. Its optimality proprtis wr dvlopd in Rao and Graham (964. This stimator givs an altrnativ solution to quasi-optimal stimation undr rotation sampling whn it is allowd that units lav th sampl for svral occasions and thn com back. Such situations happn frquntly in ral survys and ar not covrd by th rcursiv optimal stimator introducd by Pattrson (955. Howvr th K-composit stimator suffrs from crtain disadvantags. It is dsignd for a stabl situation in th sns that its basic paramtr is kpt constant on all occasions. Additionally it is rstrictd only to a crtain family of rotation dsigns. Hr w propos a dynamic vrsion of th K-composit stimator (DK-composit stimator without any rstrictions on th rotation pattrn. Mathmatically, th algorithm, w dvlop, is much simplr than th on for th classical K-composit stimator with optimal wights. Morovr, it is prcis, in th sns that it dos not us any approximat or asymptotic approach (opposd to th mthod usd in Rao and Graham (964 for computing optimal wights.. Introduction It is wll known that, whil looking for optimal stimators in survys which rpat in tim with th sam tim spacing, taking undr account obsrvations not only from th prsnt dition of th survy (occasion but also from prvious occasions may significantly improv th quality of stimation. Bank PEKAO, Warszawa, POLAND Towarzystwo Ubzpiczń na Życi "Warta", Warszawa, POLAND 3 Główny Urząd Statystyczny and Wydział Matmatyki i Nauk Informacyjnych, Politchnika Warszawska, Warszawa, POLAND, -mail: [email protected] 4 Wydział Matmatyki i Nauk Informacyjnych, Politchnika Warszawska, Warszawa, POLAND, -mail: [email protected]

9 8 P. Cipila, M. Gniado, J. Wsołowski, M. Wojtyś: Dynamic K-composit... For th bst linar unbiasd stimators (BLUEs of th man on a givn occasion, to rduc tim and mmory rquirmnts, it is dsirabl to hav a rcursiv form for such an stimator which rfrs only to crtain (possibly, small numbr of optimal stimators from rcnt occasions and, additionally, obsrvations from thos occasions. Such a problm was compltly solvd in a sminal papr by Pattrson (950 for a family of rotation pattrns which do not allow for a com-back of a unit to th sampl, aftr laving it for som occasions. Th solution givs a formula for th BLUE of μ h, th man on th hth occasion, as a linar combination of th BLUE of μ h and obsrvations from (h th and hth occasions. Howvr, in many practical survys, th rotation pattrn allows hols, i.. som units stay in a sampl for a numbr of occasions, lav it for a numbr of occasions, thn rturn to th survy for a numbr of occasions. Important xampls includ th Currnt Population Survy (CPS in th US, whr th units follow th pattrn (a unit is in th sampl for subsqunt 4 occasions, lavs it for subsqunt 8 occasions, is again in th sampl for subsqunt 4 occasions and thn nvr rturns to th sampl, or polish Labour Forc Survy with th pattrn 00 (s Szarkowski and Witkowski (994 or Popiński (006. Unfortunatly th rcurrnt form of th BLUE in such situations of rotation pattrns with hols is not known in gnral, s for instanc Yansanh and Fullr (998. (Actually, th rcurrnt form of th optimal stimators for any rotation pattrn with hols of siz has bn drivd only rcntly in Kowalski (009 and for th Szarkowski schm 00 vn mor rcntly in Wsołowski (00. A widly accptd solution in th gnral situation is th K-composit stimator introducd in Hansn t al. (955. Its optimality proprtis wr studid for svral modls in Rao and Graham (964 (shortnd to RG in th rst of this papr. By dfinition K-composit stimator maks us only of th most rcnt past composit stimator and obsrvations from th prsnt and th most rcnt past occasions. Mor prcisly K-composit stimator on hth occasion, ˆμ h, has th following form ( ˆμ h = Q ˆμ h X (h h,h (h X h,h ( Q X h, ( whr ˆμ h is th K-composit stimator on (h th occasion, X(h h,h is th sampl man for th units common to both (h th and hth occasions calculatd for th hth occasion, X(h h,h is th sampl man of for th units common to both (h th and hth occasions calculatd for th (h th occasion, Xh is th sampl man for all th units on hth occasion and Q [0, is a numrical paramtr which dos not dpnd on h(!. Additionally in RG only a rstrictd though natural family of rotation pattrns is invstigatd:

10 STATISTICS IN TRANSITION nw sris, March 0 9 a group of units rmains in th sampl for r occasions, thn lavs it for m occasions, coms back to th sampl for r occasions, lavs it for m occasions, and so on. In such a stting strngthnd by assuming xponntial (Modl or arithmtic (Modl corrlation pattrn th optimal choic of Q is considrd in that papr (in passing, lt us not that Modl 3 for corrlation pattrn is impossibl sinc th rsulting covarianc matrix may not b positiv dfinit. To attain this goal in RG it is takn h, sinc othrwis, apparntly, th optimal Q has to dpnd on h. Numrical solutions ar thn obtaind sinc th rsulting formula ((4 in RG for th varianc of th stimator is analytically non-tratabl. As it alrady has b mntiond K-composit stimator has bn usd for yars with som adjustmnts in th CPS - s for instanc Bailar (975, Brau and Ernst (983 or Lnt t al. (994. A complt dscription can b found for instanc in Currnt Population Survy (00. Th adjustmnts known as AK-composit stimator introducd in Gurny and Daly (965 has bn furthr dvlopd,.g. in Cantwll (988 and Cantwll and Caldwll (998. A mor rcnt approach through rgrssion composit stimator has bn considrd in Bll (00, Fullr and Rao (00, Singh t al. (00 (with implications for Canadian Labour Forc Survy. It is basd on modifid rgrssion mthod proposd in Singh (996. Th difficulty in rcursiv stimation in rpatd survys for pattrns with hols was raisd in Yansanh and Fullr (998, who analyzd variancs of composit stimators in svral rotation schms. For a rlativly currnt dscription of th stat of art in th ara on can consult Stl and McLarn (008, in particular Sc. IV on diffrnt rotation pattrns and Sc. V on composit stimators. A vry rcnt papr on optimal stimation undr rotation is by Towhidi and Namazi-Rad (00. In th prsnt papr w dvlop th ida of K-composit stimator in two nw dirctions. First, Q = Q h is allowd to dpnd on th numbr of occasion. Thn it appars that th optimal solution for Q h is vry simpl: it is attaind through minimizing crtain quadratic function F h (which has to b dtrmind on ach occasion. Scond, any rotation pattrn is allowd. Th pric for such a dvlopmnt is surprisingly chap: w only hav to kp track of subsqunt Q h s (to b abl to dtrmin F h s.. Dynamic K-composit stimator W considr a doubl array of random variabls (X i,j which may b column-wis or row-wis infinit or finit, whr th rows ar for valus of th variabl of intrst for diffrnt units on th sam occasion, whil columns ar for valus of th variabl for th sam unit on diffrnt occasions. Thus X i,j rprsnts th valu of th variabl on ith occasion for th jth unit of

11 0 P. Cipila, M. Gniado, J. Wsołowski, M. Wojtyś: Dynamic K-composit... th population. W assum that on a givn occasion all th variabls hav th sam man, which is th paramtr w want to stimat, i.. E X i,j = μ i, i,j =,,... Also it is assumd that thr is no corrlation btwn diffrnt units, i.. Cov(X i,j,x l,k =0 for j = k, i, j, k, l =,,... Ths two assumptions ar crucial for furthr dvlopmnt of our rsult. Th rmaining two ar not important for th drivation w propos but, first, mak formulas somwhat simplr, scond, sinc thy includ som paramtrs which ar assumd to b known, it is dsirabl to hav as fw such paramtrs as possibl. Thus, additionally w assum th xponntial corrlation pattrn btwn th valus of th variabl for th sam unit on diffrnt occasions (which, whil not so important hr, is a crucial condition for th Pattrson schm, i.. Corr(X i,j,x ik,j =ρ k, for any k =0,,..., i,j =,,..., for som ρ [, ]. Finally it is assumd that th variancs of all variabls ar constant, i.. Var X i,j = σ > 0, i,j =,,... Th dynamic vrsion of K-composit stimator, which calld hr DKcomposit stimator, has th form ˆμ h = Q h ( ˆμ h X (h h,h (h X h,h ( Q h X h, h =, 3,... ( whil ˆμ = X, whr all th symbols whr introducd in ( xcpt of Q h which plays th rol of th formr Q. Lt us point out th w do not impos any a priori rstrictions on th rang of (Q h (rstriction imposd in RG on th rang of Q, Q (0,, mad it possibl to pass to th limit with h in th xprssion for th varianc of ˆμ h. Our goal is to choos Q h in a dynamic way, i.. on ach occasion h, th valu Q h has to minimiz th varianc of ˆμ h. Th rotation schm is dscribd by th rotation matrix R =(r i,j, whr r i,j =if th jth unit is in th sampl on th ith occasion, othrwis r i,j =0. Thr is absolutly no rstriction on th rotation pattrn. By n i w dnot th sampl siz on th ith occasion, and m i dnots th siz of ovrlap btwn sampls on occasions (i th and ith. Dnot also for k =, 3,...

12 STATISTICS IN TRANSITION nw sris, March 0 Q i Q i... Q k, for i =,...,k, D i,k =, i = k. Thn w dfin wights which will b rsponsibl for th form of quadratic functions (F k to b minimizd: w ( i,j = n (3 and for any i =,...,k > and any j =,,... [ ( w (k i,j = r ri,j i,j D i,k ( D i,k r ] i,j m i n i n i m i, (4 whr in th last xprssion w adopt th rul that r k,j = r 0,j =0. Not that with such a littl abus of notation th formula for w ( i,j agrs with ( (4. Lt us mphasiz that to find th wights for a givn occasion k w (k i,j nothing mor is ndd but k numbrs Q,...,Q k (not that Q =0,by th dfinition of ˆμ. Now w ar rady to prsnt our main rsult which xplains how to choos, occasion by occasion, th valus (Q h which mak th stimator ˆμ h optimal in th modl w considr hr. Though th formulas, in particular (6, do not look vry frindly, it has to b mphasizd that actually to find Q h on nds just Q,...,Q h to calculat w (h i,j and consquntly, A h, B h and C h. Thorm. In th modl dscribd abov th optimal valu of Q h which minimizs th varianc of DK-composit stimator ˆμ h, h, is C h B h Q h = (5 A h B h C h with C = B and A h B h C h > 0, whr for h A h = σ j h ( i= w (h i,j ( ρσ m h B h = σ n h ri,j j h i= ρ j i <i h w (h i,j h i= w (h i,j w (h i,j r i,jr i,jρ i i r h,j r h,j r i,j ρ h i, (6 w (h i,j r i,j r h,j ρ h i, (7

13 P. Cipila, M. Gniado, J. Wsołowski, M. Wojtyś: Dynamic K-composit... Morovr, ˆμ h = C h = σ n h. (8 h i= j w (h i,j r i,jx i,j with th wights (w (h i,j dfind in (4. Actually, as it will b obsrvd during th proof, which is givn in Sction 3, ( A h B h C h = Var ˆμ h which is always positiv sinc σ > 0. (h (h X h,h X h,h X h 3. Proof Th proof is by induction with rspct to h. For h =th rsult holds tru sinc thn C = B yilds Q =0. Morovr, (4 for k =agrs with th formula for w ( i,j. W assum that it holds for h and w will prov it for h. Comput th varianc of ˆμ h : Var ˆμ h = Q h [ Var ˆμ h Var ( Cov ˆμ h, ( (h (h X h,h Var X h,h Cov ˆμ h, ( ] (h X h,h Cov X(h (h h,h, X h,h (h X h,h [ Q h ( Q h Cov (ˆμ h, X ( h Cov X(h h,h, X ( h Cov X(h h,h, X ] h ( Q h Var X h = Q h A h Q h ( Q h B h ( Q h C h, whr th last quality dfins th quantitis A h, B h and C h. By th induction assumption h ˆμ h = i= j w (h i,j r i,j X i,j. Thn a dirct computation givs

14 STATISTICS IN TRANSITION nw sris, March 0 3 Var ˆμ h = σ j h ( i= w (h i,j ri,j i <i h w (h i,j w (h i,j r i,jr i,jρ i i, Var (h (h X h,h = Var X h,h = σ, m h ( Cov ˆμ h, ( Cov ˆμ h, (h X h,h = σ m h j (h X h,h = σ m h j h i= h i= w (h i,j r i,j r h,j r h,j ρ h i, w (h i,j r i,j r h,j r h,j ρ h i, ( Cov X(h (h h,h, X h,h = σ ρ. m h Combining th last fiv formulas w obsrv that th dfinition of A h agrs with th xprssion (6. Similarly to chck if (7 holds w hav to comput Cov (ˆμ h, X h = σ n h j h i= ( Cov X(h h,h, X h = σ, n h ( Cov X(h h,h, X h = σ ρ. n h Finally, (8 follows sinc Minimizing Var X h = σ n h. w (h i,j r i,j r h,j ρ h i, w gt th solution (5. F h (x =(A h B h C h x (B h C h x C h Th DK-composit stimator is a linar stimator so in gnral it has a form

15 4 P. Cipila, M. Gniado, J. Wsołowski, M. Wojtyś: Dynamic K-composit... ˆμ h = h v i,j r i,j X i,j i= j with som wights (v i,j. To finish th proof w hav to show that v i,j r i,j = w (h i,j r i,j as dfind in (4 for any i =,...,h and any j =,,... Not that by th dfinition of ˆμ h givn in ( w hav ˆμ h = Q h j h i= w (h i,j r i,j X i,j m h j r h,j r h,j X h,j r h,j r h,j X h,j ( Q h r h,j X h,j. m h n h j Comparing th cofficints of X i,j in th last two xprssions w gt for i = h j for i = h v h,j r h,j = Q h r h,j r h,j Q h m h n h ] nh n h = r h,j [ D h,h ( rh,j m h r h,j = w (h h,j r h,j, v h,j r h,j = Q h ( w (h h,j r h,j m h r h,j r hj = Q h r h,j [ D h,h ( rh,j m h = r h,j [ D h,h ( rh,j m h n h and for any i<h [ ( = Q h w (h ri,j i,j r i,j D i,h m i sinc Q h D k,h = D k,h for k = i, i. Thus th proof is compltd. n h ] Q h r h,j r h,j n h m h ] D h,h ( n h r h,j m h v i,j r i,j ( D i,h r ] i,j n i n i m i = w (h h,j r h,j, = w (h i,j r i,j

16 STATISTICS IN TRANSITION nw sris, March Numrical xampls Blow, similarly to numrical comparisons in RG, w considr prcntag gain in fficincy for th DK-composit stimator compard to th man of th obsrvations from th last hth occasion. It is dfind as g h = Var X h Var ˆμ h Var ˆμ h 00. (9 W took h =0, sinc th paramtr Q h bhavs quit stabl with rspct to occasion numbr h. In Tabls and w giv th optimal wight Q h, th varianc of μ h and g h for diffrnt valus of corrlation ρ in two schms: Szarkowski s 00 (Tabl and CPS (Tabl. W can asily s that th largst gain is achivd for strong corrlations and th smallst whn thr is no corrlation btwn occasions for th sam unit. Tabl. Szarkowski schm Tabl. CPS schm ρ Q 0 Var ˆμ 0 g 0 ρ Q 0 Var ˆμ 0 g Sourc: own calculations Considr now a cascad rotation schm which is dfind through a rotation pattrn (,ε,...,ε k,, ε l {0, }, l =,...,k, which movs on unit down th rotation matrix with subsqunt occasions, that is (r i,i,...,r i,ik =(,ε,...,ε k,

17 6 P. Cipila, M. Gniado, J. Wsołowski, M. Wojtyś: Dynamic K-composit... for any i =,,..., othrwis r i,j =0. Th numbr k is calld th rotation pattrn lngth. Taking th advantag of th fact that th DK-composit stimator allows for any rotation schm, w calculatd prcntag gain (as dfind in (9 in fficincy for all possibl cascad schms with rotation pattrns of lngth up to 0. Tabl 3 contains 0 schms with th smallst and 0 with th largst gain among such 8 = 56 schms. Hr, again, th rsults for h =0 ar prsntd. Th largst gain is achivd for "spars" schms with small numbr of lmnts in th rotation pattrn (and strong corrlations whil th lowst gain is obsrvd for schms with complt or almost complt rotation pattrns (and for wak corrlations. Similar comparisons of variancs for particular rotation cascad pattrns in th tim sris framwork can b found in McLarn and Stl (000 (s also Stl and McLarn (00. Tabl 3. Th worst and th bst rotation pattrns worst pattrns ρ g 0 bst pattrns ρ g Sourc: own calculations

18 STATISTICS IN TRANSITION nw sris, March 0 7 Tabl 4. Comparison btwn K-composit and DK-composit stimators ρ Q 0 g 0 diff Q 0 g 0 diff Q 0 g 0 diff m r = m r = m r = m r = m r = Sourc: own calculations

19 8 P. Cipila, M. Gniado, J. Wsołowski, M. Wojtyś: Dynamic K-composit... Tabl 4. Comparison btwn K-composit and DK-composit stimators, continuation Sourc: own calculations ρ Q 0 g 0 diff Q 0 g 0 diff m r = m r = m r = m r = m r = Tabl 4 shows Q h, g h and th diffrnc (diff = g g h btwn th gains obtaind in two ways: g for th K-composit stimator as computd in Tabl ofrgandg h for th DK-composit stimator as proposd in th prsnt papr. W took h = 00 though in many particular cass th valus for Q h and g h stabilizd much arlir. Th numbrs r and m ar rsponsibl for th rotation pattrn, i.. a unit stays in th sampl for r occasions, lavs th sampl for m occasions, coms back into th sampl for r occasions, and so on. Tabl 4 is namd "comparison" nvrthlss w cannot actually in strictly mathmatical sns compar ths two valus of g and g h bcaus th two mthods involv diffrnt modls: RG considrd a finit population cas in which a givn unit rturns to th survy infinitly oftn whras in th prsnt papr an infinit population modl is invstigatd and a unit rturns to th survy aftr a gap of m occasions for anothr squnc of r occasions and

20 STATISTICS IN TRANSITION nw sris, March 0 9 thn lavs th survy. In th cours of simulations w notd that Q h for th DK-composit stimator ar quit stabl, vn for rlativly small valus of h. Morovr, thir valus obsrvd in simulations wr quit similar to thos of Q, obtaind in Tabl of RG. In our Tabl 4 it is visibl that diffrncs in gains of fficincy ar rmarkabl for strong corrlations and small gaps m, whil for small corrlations and larg gaps m thy ar insignificant. Small ngativ valus which appar in som cass ar du to th fact that th two mthods ar not prcisly quivalnt, othrwis ngativ valus would not b possibl sinc th mthod w prsnt hr is optimal within considrd class of stimators. REFERENCES BAILAR, B. (975. Th ffcts of rotation group bias on stimats from panl survys. J. Amr. Statist. Assoc. 70, BELL, P. (00. Comparison of altrnativ Labour Forc Survy stimators. Survy Mth. 7(, BREAU, P., ERNST, L. (983. Altrnativ stimators to th currnt composit stimator. Proc. Sc. Survy Rs. Mth., Amr. Statist. Assoc., CANTWELL, P.J. (988. Varianc formula for th gnralizd composit stimator undr balancd on-lvl rotation plan. SRD Rsarch Rport Cnsus/SRD/88/6, Burau of th Cnsus, Statistical Rsarch Division, -6. CANTWELL, P.J., CALDWELL, C.V. (998. Examining th rvisions in monthly rtail and wholsal trad survys undr a rotation panl dsign. J. Offic. Statist. 4, Currnt Population Survy (00. Dsign and Mthodology, Tchnical Papr 63RV, Burau of Labour Statistics, U.S. Cnsus Burau. FULLER, W., RAO, J.N.K. (00. A rgrssion composit stimator with application to th Canadian Labour Forc Survy. Survy Mth. 7(, GURNEY, M., DALY, J.F. (965. A multivariat approach to stimation in priodic sampl survys. Proc. Amr. Statist. Assoc., Sct. Soc. Statist., HANSEN, M.H., HURWITZ, W.N., NISSELSON, H., STEINBERG, J. (955. Th rdsign of th cnsus currnt population survy. J. Amr. Math. Assoc. 50,

21 0 P. Cipila, M. Gniado, J. Wsołowski, M. Wojtyś: Dynamic K-composit... KOWALSKI, J. (009. Optimal stimation in rotation pattrns. J. Statist. Plan. Infr. 39(4, LENT, J., MILLER, S., CANTWELL, P. (994. Composit wights for th Currnt Population Survy. Proc. Sc. Survy Rs. Mth., Amr. Statist. Assoc., MCLAREN, C.H., STEEL, D.G. (000. Th impact of diffrnt rotation pattrns on th sampling varianc of sasonally adjustd and trnd stimats. Survy Mth. 6(, PATTERSON, H.D. (950. Sampling on succssiv occasions with partial rplacmnt of units. J. Royal Statist. Soc., Sr. B, POPIŃSKI, W. (006. Dvlopmnt of th Polish Labour Forc Survy. Statist. Transit. 7(5, RAO, J.N.K., GRAHAM, J.E. (964. Rotation dsigns for sampling on rpatd occasions. Ann. Math. Statist. 35, SINGH, A.C. (996. Combining information in survy sampling by modifid rgrssion. Proc. Sct. Survy Rs. Mth., Amr. Statist. Assoc., 0-9. SINGH, A.C., KENNEDY, B., WU, S. (00. Rgrssion composit stimation for th Canadian Labour Forc Survy with a rotating panl dsign. Survy Mth. 7, STEEL, D., MCLAREN, C. (00, In sarch of a good rotation pattrn. In: Advancs in Statistics, Combinatorics and Rlatd Aras. Singapor, World Scintific, STEEL, D., MCLAREN, C. (008. Dsign and analysis of rpatd survys. Cntr for Statist. Survy Mth., Univ. Wollonong, Working Papr -08, -3, SZARKOWSKI, A., WITKOWSKI, J. (994, Th Polish labour forc survy. Statist. Transit. (4, TOWHIDI, M., NAMAZI-RAD, M.-R. (00. An optimal mthod of stimation in rotation sampling. Adv. Appl. Statist. 5(, WESOŁOWSKI, J. (00. Rcursiv optimal stimation in Szarkowski rotation schm. Statist. Transit. (, YANSANEH, I.S., FULLER, W. (998. Optimal rcursiv stimation for rpatd survys. Survy Mth. 4, 3-40.

22 STATISTICS IN TRANSITION-nw sris, March 0 STATISTICS IN TRANSITION-nw sris, March 0 Vol. 3, No., pp. 36 ESTIMATION OF POPULATION MEAN USING TWO AUXILIARY SOURCES IN SAMPLE SURVEYS Diwakar Shukla, Sharad Pathak and Narndra Singh Thakur ABSTRACT This papr proposs familis for stimation of population man of th main variabl undr study using th information on two diffrnt auxiliary variabls undr simpl random sampling without rplacmnt (SRSWOR schm. Thr diffrnt classs of stimators ar constructd, xamind with a complt study with othr xisting stimators. Th xprssion for bias and man squard rror of th proposd familis ar obtaind up to first ordr of approximation. Usual ratio stimator, product stimator, dual to ratio stimator, ratio-cum-product typ stimator and many mor stimators ar idntifid as particular mmbrs of th suggstd family. Exprssions of optimization ar drivd and thortical rsults ar supportd by numrical xampls. Ky words: Family of stimators, SRSWOR, Bias and Man squard rror. AMS Subjct Classification: 94A0, 6D05. Introduction To improv th xactitud in sampl survys thory th us of two auxiliary variabls for stimation of population man of a variabl undr study has playd an influntial rol. A numbr of stimators ar accssibl in th litratur of sampl survys whr supporting information is th contributor to improv th mthodology. Out of all ratio and product stimators ar good xampls as vidnc to stat this. Th ratio stimation mthod is practical whn th corrlation cofficint btwn th study and auxiliary variabl is positiv [Cochran (940, 4]. If th corrlation cofficint btwn th study and auxiliary variabl is ngativ thn th us of product stimation will mak th study valuabl [Robson (957 and Murthy (964]. Dpartmnt of Mathmatics and Statistics. Dr. Hari Singh Gour Cntral Univrsity, Sagar, M.P., India [email protected], [email protected]. Cntr for Mathmatical Scincs, Banasthali Univrsity, Rajasthan, India.

23 D. Shukla, Sh. Pathak, N. Singh Thakur: Estimation of Thr ar so many situations in survy sampling whr th rcord of mor auxiliary variabl is availabl for th invstigators (at last for two variabls. Thr ar so many rsarchrs who usd th information of mor than two auxiliary variabls to contribut in th fild. Dalabhara and Sahoo (994 prsntd a class of stimators in stratifid sampling with two auxiliary variabls for stimation of man. In anothr contribution Dalabhara and Sahoo (000 proposd an unbiasd stimator in two-phas sampling using two auxiliary variabls. Abu-Dayyh t al. (003 usd auxiliary variabls to show stimators of finit population man. Sahoo and Sahoo (993 suggstd a class of stimators in two-phas sampling using two auxiliary variabls. In anothr work Sahoo and Sahoo (00 discussd about prdictiv stimation of finit population man in two-phas sampling using two auxiliary variabls. Singh and Shukla (987 hav a discussion on on paramtr family of factor typ ratio stimator. In a study Shukla t al. (99 transformd factor typ stimator to mak th stimation mor ffctiv. Shukla (00 Studid F-T stimator and sampling procdur undrtakn was two-phas sampling. In this squnc Singh and Singh (99 providd Chain typ stimator with two auxiliary variabls undr doubl sampling schm. In anothr study Singh t al. (994 suggstd a class of chainratio stimator with two auxiliary variabls and th study compltd undr doubl sampling schm. Kadilar and Cingi (004 took two auxiliary variabls in simpl random sampling to find population man. Morovr, Kadilar and Cingi (005 drivd a nw stimator using two auxiliary variabls. Prri (007 analysd th work of Singh (965, 967b and suggstd a nw improvd work on ratio-cumproduct typ stimators with th application of Srivnkataramana, T. (980 stimator on prvious proposd work of Singh (967b. Many authors including Srivastava (97, Srivastava and Jhajj (983, Ray and Sahai (980, Khar and Srivastava (98, Hansn t al.(953 and Dsraj (965 usd mor than on supporting information to mak th study mor imprssiv. Som othr usful contributions ovr applications of auxiliary information ar du to Mukhopadhyay (000, Cochran (005, Murthy (976, Sukhatm t al. (984, Naik and Gupta (99, Singh and Shukla (993 and Shukla t al (009 tc.. Notations and Assumptions Notations for th study ar: Y, X, and X : Population Paramtrs y, x and x : Man pr unit stimats for a simpl random sampl of siz n. n : Sampl siz f : Sampling friction (f = n/n N : Population siz

24 STATISTICS IN TRANSITION-nw sris, March 0 3 ρ 0 : Corrlation btwn variabl Y and X ρ : Corrlation btwn variabl Y and X 0 ρ : Corrlation btwn variabl X and X C SY Y = Y : Cofficint of variation for variabl Y C 0 S X C X = : Cofficint of variation for variabl X C X X X ( S C X = : Cofficint of variation for variabl X C ( 3. Som Estimators In th litratur of survy sampling so many stimators and stimation procdurs xist. This litratur is th basic motivation to work in this dirction and contribution in this ara. Lt Y is th main variabl and X, X ar two auxiliary variabl thn som wll known stimators ar as follows. 3.. Ratio stimator X y R = y (3.a x R R Y = YM[ C X ρ CY C X ] [ C C ρ C C ] Bias( y = E( y (3.b MSE( y R = Y M Y X Y X ; M = (3.c n N 3.. Product stimator x y P = y (3.a X Bias( y = E( y Y = YM ρ C C (3.b P MSE( y R P [ C C ρ C C ] Y X = Y M Y X Y X ; M = (3.c n N 3.3. Dual to ratio stimator [By Srivnkataramana, T. (980] NX nx y VR = y (3.3a ( N n X

25 4 D. Shukla, Sh. Pathak, N. Singh Thakur: Estimation of Y Bias( yvr = E( yvr Y = ρ CY C X (3.3b N MSE( yvr = Y M[ CY α CX αρ CYC X ] ; M =, α = n /( N n n N (3.3c 3.4. Ratio-cum-product typ stimator Singh (965, 967b proposd som ratio-cum-product typ stimators as X x y R = y (3.4a x X R E( yr Y = YM[ C ρ0 C0C ρ0 C0C ρ C ] [ C C C ρ C C ρ C C C ] Bias( y = C (3.4b = Y M MSE( y R ρ C (3.4c X X y R = y (3.5a x x R = E( yr Y [ C C ρ C C ρ C C ρ C ] Bias( y = YM C 0 [ C C C ρ C C ρ C C C ] = Y M MSE( y R ρ C (3.5b (3.5c x x y P = y X X (3.6a P E( yp Y [ ρ C C ρ C C ρ C ] Bias( y = = YM C (3.6b [ C C C ρ C C ρ C C C ] = Y M MSE( y P ρ C (3.6c x X y P = y (3.7a X x P = E( yp Y 0 [ C ρ C C ρ C C ρ C ] Bias( y = YM C 0 0 [ C C C ρ C C ρ C C C ] 0 0 (3.7b MSE( y P = Y M ρ C (3.7c whr M = n N

26 STATISTICS IN TRANSITION-nw sris, March Proposd Estimator(s Singh and Shukla (987 discussd a family of factor-typ (F-T ratio stimator for stimating population man. In anothr contribution Singh and Shukla (993 drivd fficint factor-typ stimator for stimating th sam population paramtr. Driving motivation from both som proposd stimators ar givn blow. ( yf T = ytt T ( yf T = y (4. T T ( yf T 3 = y T ( Ai Ci X i fb xi Whr Ti = (4. ( Ai fbi X i Ci xi A i = ( Ki ( Ki ; Bi = ( Ki ( Ki 4; Ci = ( Ki ( Ki 3( Ki 4 (4.3 Rmark 4. Hr w hav a combination of K i whr i = (,. Som of th factors ar shown in th following tabl whr ( K = K. As abov concrnd K i whr i = (, is constant to choos suitably so that th rsulting man squard rror of proposd stimators may bcom last. For xampl lt K i = X X thn th valus of T and T will b and rspctivly and so on. x x Rmark 4. By proposd stimator w can obtain so many diffrnt stimators. For ach combination of K, an stimator xists. ( K Tabl 4.. Som Mmbrs of th proposd stimation. X t = y x X x = K = (At K x t 5 = y X X x =, K = (At K X t = y x x X =, K = (At K x t 6 = y X x X = K = (At K t t 3 X = y x NX nx ( N n X = (At K =, K 3 7 x = y X NX ( N n X nx = (At K =, K 3 X 4 y x =, K = t = (At K 4 x 8 y X =, K = t = (At K 4

27 6 D. Shukla, Sh. Pathak, N. Singh Thakur: Estimation of Tabl 4.. Som Mmbrs of th proposd stimation (cont.. t 9 NX nx X = y ( N n X x t 0 NX nx x = y ( N n X X t NX nx NX nx = y ( N n X ( N n X t NX nx = y ( N n X (At K =, K 3 = X 3 y x = 4, K = t = (At K At K =, K 3 = x 4 y X = 4, K = t = (At K (At K = K 3 t 5 = NX nx = y ( N n X = 4, K = (At K 3 (At K =, K 4 3 = y (At K = K 4 = 5. Proprtis of Proposd Estimator For larg sampl approximation w assum that fbi y = Y ( 0 ; x = X( ; x = X ( ; α i = ; Ai fbi Ci Ci β i = A fb C i i E = E( = E( 0 ; ( 0 = ( M C δ i = αi E = ; βi i E ( 0 = M C 0 ; ( M C 0 = Mρ0C0 ; E ( 0 Mρ0C0 C E ( C M = n N E = ; = ; E ( = MρC C ; THEOREM 5.: []: Th stimator ( yf T in trms of 0, and up to first ordr of approximation could b xprssd as: [ 0 δ ( 0 β δ ( 0 β δδ ] ( yf T = Y (5. []: Bias of ( yf T up to first ordr approximation is: [ δ ( ρ0c0c βc δ ( ρ0c0c β C δδ ρc ] B( yf T = YM C (5. [3]: Man squard rror of yf T up to first ordr approximation is: [ C0 δ C δ C δρ 0C0C δ ρ0c0c δδ ρc ] = Y M M ( yf T C (5.3

28 STATISTICS IN TRANSITION-nw sris, March 0 7 Proof 5.: []: ( ( ( ( ( x C X fb A x fb X C A x C X fb A x fb X C A y y T F = 0 ( ( ( ( ( ( = Y y T F β β α α [ ] ( ( ( Y y T F δ δ β δ β δ = []: [ ] [ ] } ( ( { ( Y E Y y E T F δ δ β δ β δ = [ ] ( ( ( C C C C C C C C YM y B T F ρ δ δ β ρ δ β ρ δ = [3]: [ ] ] ( ( [ ( Y Y y T F δ δ β δ β δ = ] [ ( C C C C C C C C C M Y y M T F ρ δ δ ρ δ ρ δ δ δ = THEOREM 5.: [4]: Th stimator ( T F y in trms of 0, and up to first ordr of approximation could b xprssd as: [ ] ( ( ( Y y T F δ δ α δ β δ = (5.4 [5]: Bias of ( T F y up to first ordr approximation is: [ ] ( ( ( C C C C C C C C M Y y B T F ρ δ δ ρ α δ β ρ δ = (5.5 [6]: Man squard rror of ( T F y up to first ordr approximation is: [ ] ( C C C C C C C C C M Y y M T F ρ δ δ ρ δ ρ δ δ δ = (5.6 Proof 5.: [4]: ( ( ( ( ( x fb X C A x C X fb A x C X fb A x fb X C A y y T F = 0 ( ( ( ( ( ( = Y y T F α β β α [ ] ( ( ( Y y T F δ δ α δ β δ =

29 8 D. Shukla, Sh. Pathak, N. Singh Thakur: Estimation of [5]: [ ] [ ] ( ( ( E Y Y y E T F δ δ α δ β δ = [ ] ( ( ( C C C C C C C C YM y B T F ρ δ δ ρ α δ β ρ δ = [6]: [ ] ( ( Y y E y M T F T F = [ ] ( C C C C C C C C C M Y y M T F ρ δ δ ρ δ ρ δ δ δ = THEOREM 5.3: [7]: Th stimator 3 ( T F y in trms of 0, and up to first ordr of approximation could b xprssd as: [ ] ( ( ( Y y T F δ δ β δ α δ = (5.7 [8]: Bias of 3 ( T F y up to first ordr approximation is: [ ] ( ( ( C C C C C C C C YM y B T F ρ δ δ β ρ δ ρ α δ = (5.8 [9]: Man squard rror of 3 ( T F y up to first ordr approximation is: [ ] ( C C C C C C C C C M Y y M T F ρ δ δ δ ρ δ ρ δ δ = (5.9 Proof 5.3: [7]: 3 ( ( ( ( ( x fb X C A x C X fb A x C X fb A x fb X C A y y T F = 0 3 ( ( ( ( ( ( = Y y T F α β β α [ ] ( ( ( Y y T F δ δ β δ α δ = [8]: [ ] ( ( ( Y y T F δ δ β δ α δ = [ ] ( ( ( C C C C C C C C YM y B T F ρ δ δ β ρ δ ρ α δ =

30 STATISTICS IN TRANSITION-nw sris, March 0 9 [9]: E [( y Y ] = E[ Y { δ ( α δ ( β δ δ }] F T [ C δ C δ C ρ C C δ ρ C C δ δ δ ρ C ] F T 3 = Y M M ( y C 6. Minimum Man Squard Error & Optimal Choics for Proposd Estimator(s In this proposd stimator w hav multipl choics of th combination K i ; i = (, and optimal conditions obtaind by man squard rror of all proposd dsigns. For minimum man squard rror by ( yf T diffrntiating (5.3 with rspct to δ and δ rspctivly and quating to zro. C δ C C ρ δ ρ C C ρ C C δ C 0 δ ρ C C = 0 = 0 By solving ths simultanous quations, w hav (6. C0 ρ0ρ ρ0 δ ˆ = = δ C ( ρ C0 ρ0ρ ρ0 and δ ˆ = = δ C ( ρ (6. At ths valus of ˆ δ ˆ and δ th minimum man squar rror of th proposd stimator is [ V ( V ρ U ( U ρ UV ] F T = Y C0 M 0 0 Min MSE( y ρ (6.3 ρ0ρ ρ whr U = ( ρ 0 and V ρ = 0 ρ ( ρ ρ 0 By adopting th sam procdur w can obtain th minimum man squard rror corrsponding to ( yf T and ( yf T 3 by (5.6 and (5.9.

31 30 D. Shukla, Sh. Pathak, N. Singh Thakur: Estimation of Th information of optimization rgarding ( yf T and ( yf T 3 is ˆ δ = ˆ δ ; ˆ δ = ˆ δ ; ˆ δ = ˆ δ and ˆ δ = ˆ δ (6.4 Rwriting (6., as ˆ C δ = C ˆ δ 0 C = C 0 ρ ρ 0 ρ ( ρ 0 ρ ρ ρ ( ρ 0 0 = = ( say ( say (6.5 From (6.5 w can obtain th rlation in th form of charactrizing scalar as follows ( ( K 3 K 3 ( f ( f f f K 9 K (3 5 f 5 f 6 K (4 f 4 f 4 = 0 ( f f K (4 f 4 f 4 = 0 (6.6 Abov polynomial (6.6 provids thr choics of Kand K for th minimum man squard rrors of proposd stimators. In th similar way ˆ δ = ; ˆ δ ˆ ˆ = ; δ = andδ = will also provid th polynomials of dgr thr i.. in ach cas w hav thr diffrnt choics of constant K i ; i =, to improv th stimator. 7. Empirical study Th targt in this sction is to valuat th gain in fficincis (in trms of ms obtaind by th proposd stimators. To s th prformanc of th various stimators discussd hr, w ar considring two diffrnt population data usd arlir by othr rsarchrs. Th mpirical analysis is discussd blow. Population - [sourcs: Andrson (958] y : Had lngth of scond son x : Had lngth of first son x : Had bradth of first son

32 STATISTICS IN TRANSITION-nw sris, March 0 3 Th rquird information is givn in Tabl 7.. Tabl 7.. Population Paramtrs. Paramtr Valu Paramtr Valu Paramtr Valu Paramtr Valu Y n 7 C ρ X 85.7 N 5 C ρ ρ X 5. f 0.8 C Tabl 7.. Prcnt Rlativ Efficincy of various stimators with rspct to man pr unit stimator for Population. Estimator(s PRE ( with rspct to y ( yf T ( yf T ( yf T 3 y t t t t t t t t t t t t t t t * ( yf T * ( yf T * ( yf T

33 3 D. Shukla, Sh. Pathak, N. Singh Thakur: Estimation of Population - [sourcs: Stl and Torri (960, p.8] y : Log of laf burn in sc x : Potassium prcntag x : Chlorin prcntag Th information rgarding population - is givn in Tabl 7.3. Tabl 7.3. Population - Paramtrs. Paramtr Valu Paramtr Valu Paramtr Valu Paramtr Valu Y n 6 C ρ X N 30 C 0.95 ρ ρ X f 0.0 C Tabl 7.4. Prcnt Rlativ Efficincy of various stimators with rspct to man pr unit stimator for Population. % RE ( with rspct to y Estimator(s ( yf T ( yf T ( yf T 3 y t t t t t t t t t t t t t t t * ( yf T * ( yf T * ( yf T

34 STATISTICS IN TRANSITION-nw sris, March Discussion & Conclusion For population- th choics to optimization of man squard rror of ( yf T can b drivd from (6.5 which giv a polynomial of dgr thr (6.6. On solution w hav [ K ] = ; [ K ] = ; [ K ] 3 =. 65 ; [ K ] = ; [ K ] =. 985 and[ K ] 3 = For ( y F T th valus ar[ K ] = [ ] 4 K, [ K ] [ ] 5 = K ; [ ] [ ] K 6 = K 3 and [ K ] 4 =. 93. Similarly for ( yf T 3 valus ar[ ]. 906 K = whras K 7 = ; [ K ] = [ ] 7 K ; [ K ] = [ ] 8 K and [ ] [ ] 9 K 3 othr roots ar imaginary. For population- th choics of th constant scalar squard rror of ( yf T ar 39.. K i to rduc th man [ K ] 95 ; [ K ] 5859 ; [ K ]. 097 and [ ]. 939 = 4 = = 3 = K. For = 5 K K = ; ( y F T th valus ar[ K ] = [ ] 4 K, [ K ] = [ ] ; [ ] [ ] 6 [ ] 3 K ; [ K ]. 855 and [ ] = valus ar[ ] * 7 = * 6 = 7 K K = K and [ ] [ ] ( yf T, ( yf T and ( yf T to man pr unit stimator in th abov mntiond tabls. * 3 K ( yf T K. Similarly for 3. Th rmaining roots ar imaginary. dnots th optimal fficincy gain with rspct From ths rsults it is crtain that th proposd stimators submit a wid ground for th optimization by multipl choics of th charactrizing scalar K i. Sinc th gnration of th stimators by th proposd classs is asy, a numbr of stimators can b abl to achiv for mor study. Th proposd stimator proposd a wid choic for th charactrizing scalar, which is th bauty of th proposd analysis. By th compilation of th prcntag rlativ fficincis corrsponding to population- and shown in tabl-7. and tabl-7.4 it is clar that th proposd stimators ar mor fficint than th othr xisting stimators as ratio stimator, product stimator, dual to ratio stimator, man pr unit stimator, ratio-cumproduct typ stimator, tc., and many mor chain typ stimators which ar discussd abov, with considrabl gain in trms of man squar rror. Thus, th proposd stimators ar rcommndd for us in practic.

35 34 D. Shukla, Sh. Pathak, N. Singh Thakur: Estimation of REFERENCES ABU-DAYYEH, W.A., AHMED, R.A. and MUTTLAK, H.A. (003: Som stimators of finit population man using auxiliary information, Applid Mathmatics and Computation, 39, ANDERSON, T.W. (958: An introduction to multivariat statistical analysis, John Wily and Sons, Inc., Nw York. COCHRAN, W.G. (005: Sampling Tchniqus. John Wily and Sons, Nw York. COCHRAN, W.G. (940: Th stimation of th yilds of cral xprimnts by sampling for th ratio gain to total produc, Journal of Agricultural Socity, 30, COCHRAN, W.G. (94: Sampling thory whn th sampling units ar of unqual sizs, Journal of Amrican Statistical Association, 37, 9 3. DALABEHARA, M. and SAHOO, L.N. (994: A class of stimators in stratifid sampling with two auxiliary variabls, Jour. Ind. Soc. Ag. Stat., 50,, DALABEHARA, M. and SAHOO, L.N. (000: An unbiasd stimator in two - phas sampling using two auxiliary variabls, Jour. Ind. Soc. Ag. Stat., 53,, DESRAJ (965: On a mthod of using multi-auxiliary information in sampl survys, Journal of Amrican Statistical Association, 60, HANSEN, M.H., HURWITZ, W.N. and MADOW, W.G. (953: Sampl survy mthods and thory, John Wily and Sons, Nw York. KADILAR, C. and CINGI, H. (004: Estimator of a population man using two auxiliary variabls in simpl random sampling, Intrnational Mathmatical Journal, 5, KADILAR, C. and CINGI, H. (005: A nw stimator using two auxiliary variabls, Applid Mathmatics and Computation, 6, KHARE, B.B. and SRIVASTAVA, S.R. (98: A gnralizd rgrssion ratio stimator for th population man using two auxiliary variabls, Th Aligarh Journal of Statistics, (, MUKHOPADHYAY, P. (000: Thory and mthods of survy sampling, Prntic Hall of India Pvt. Ltd., Nw Dlhi. MURTHY, M.N. (964: Product mthod of stimation, Sankhya, 6, A,

36 STATISTICS IN TRANSITION-nw sris, March 0 35 MURTHY, M.N. (976: Sampling Thory and Mthods, Statistical Publishing Socity, Calcutta. NAIK, V.D. and GUPTA, P.C. (99: A gnral class of stimators for stimating population man using auxiliary information, Mtrika, 38, -7. PERRI, P.F. (007: Improvd Ratio-cum-product typ stimator, Statistics in Transition, 8,, RAY, S.K. and SAHAI, A. (980: Efficint familis of ratio and product typ stimators, Biomtrika, 67, 5 7. SAHOO, J. and SAHOO, L.N. (993: A class of stimators in two-phas sampling using two auxiliary variabls, Jour. Ind. Soc. Ag. Stat., 3, SAHOO, L.N., SAHOO, R.K. (00: Prdictiv stimation of finit population man in two phas sampling using two auxiliary variabls, Jour. Ind. Soc. Ag. Stat., 54, 4, SHUKLA, D. (00: F-T stimator undr two-phas sampling, Mtron, 59, -, SHUKLA, D., SINGH, V.K. and SINGH, G.N. (99: On th us of transformation in factor typ stimator, Mtron, 49, -4, SHUKLA, D., THAKUR, N.S., PATHAK SHARAD and RAJPUT, D.S. (009: Estimation of man undr imputation of missing data using factor-typ stimator in two-phas sampling, Statistics in Transition, 0, 3, SINGH, M.P. (965: On th stimation of ratio and product of th population paramtrs, Sankhya B, 7, SINGH, M.P. (965: Ratio cum product mthod of stimation, Mtrika,, SINGH, V.K. AND SHUKLA, D. (987: On paramtr family of factor-typ ratio stimator. Mtron, 45, -, SINGH, V.K. AND SHUKLA, D. (993: An fficint on paramtr family of factor-typ stimator in sampl survy. Mtron. 5, -, SINGH, V.K. AND SHUKLA, D. (987: On paramtr family of factor typ ratio stimator, Mtron. 45, -, SINGH, V.K. AND SINGH, G.N. (99: Chain typ stimator with two auxiliary variabls undr doubl sampling schm, Mtron, 49, SINGH, V.K., SINGH, G.N. AND SHUKLA, D. (994: A class of chain ratio stimator with two auxiliary variabls undr doubl sampling schm, Sankhya, Sr. B., 46,, 09-.

37 36 D. Shukla, Sh. Pathak, N. Singh Thakur: Estimation of SRIVASTAVA, S.K. (97: A gnralizd stimator for th man of a finit population using multi-auxiliary information, Journal of Amrican Statistical Association, 66, SRIVASTAVA, S.K. and JHAJJ, H.S. (983: A class of stimators of th population man using multi-auxiliary information, Calcutta Statistical Association Bulltin, 3, SRIVENKATARAMANA, T. (980: A dual to ratio stimator in sampl survy, Biomtrika, 67, STEEL, R.G.D and TORRIE J.H.(960: Principls and procdurs of statistics, Mc Graw Hill Book Co. SUKHATME, P.V., SUKHATME, B.V., SUKHATME, S. and ASHOK, C. (984: Sampling Thory of Survys with Applications, Iowa Stat Univrsity Prss, I. S. A. S. Publication, Nw Dlhi.

38 STATISTICS IN TRANSITION-nw sris, March 0 37 STATISTICS IN TRANSITION-nw sris, March 0 Vol. 3, No., pp MODIFIED ESTIMATORS OF POPULATION VARIANCE IN PRESENCE OF AUXILIARY INFORMATION Dr. Rajsh Tailor, Balkishan Sharma ABSTRACT This papr proposs stimator of population varianc using information on known paramtrs of auxiliary variabl. Th variancs of th proposd stimators ar obtaind. It has bn shown that using modifid sampling fraction th proposd stimators ar mor fficint than th usual unbiasd stimator of population varianc and usual ratio stimator for population varianc undr crtain givn conditions. Empirical study is also carrid out to dmonstrat th mrits of th proposd stimators of population varianc ovr othr stimators considrd in this papr. Ky words: Finit population varianc, Bias, Man squard rror Auxiliary information and Efficincy.. Introduction It is known fact that in many practical situations auxiliary information is availabl or may b mad availabl in chap cost in survys. If this information is usd intlligibly, it may giv bttr stimators in trms of fficincy in comparison to th stimators in which auxiliary information is usd. Th problm of constructing fficint stimators for th population varianc S has bn widly discussd by various authors such as [3]Das and Tripathi y (978, [3]Srivastava and Jhajj (980, [4]Upadhyay and Singh (983, [4]Garcia and Cbrian (996, [0]Singh S. and Joardr, A. H. (998, []Singh t al. (998, []Cbrian and Garcia (997 and []Singh, H. P. and Singh, R. (003. Latr on [9]Singh and Tailor (003 dfind a gnralizd class of stimators of varianc using population man, varianc, cofficint of variation of School of Studis in Statistics. Vikram Univrsity, Ujjain-45600, M.P., India. [email protected]. Assistant Profssor in Statistics. Dpartmnt of Community Mdicin. Sri Aurobindo Institut of Mdical Scincs, INDORE, (M. P., India. [email protected].

39 38 R. Tailor, B. Sharma: Modifid Estimators auxiliary variat and corrlation cofficint btwn study and auxiliary variat whras [5]Upadhyaya, L. N. and Singh, H. P. (006 and [7]Kadilar, C. and Cingi, H. (006 considrd th problm of stimating th varianc of th ratio stimator. Ths motivat authors to propos modifid stimators of population varianc basd on sampling fraction using auxiliary information. Lt U = ( U, U,..., U N b th finit population of siz N and y b a ral valud function, i.. random variabl taking th valus y i (i=,,..., N for th th i unit of th population U. N N Lt Y = y i and S y = ( yi Y N N i= dnot unknown population man and population man squar of (varianc th study charactr y. Suppos x is an auxiliary variat which is positivly corrlatd with study variat y taking valu is larg so that finit population trms ar ignord. i= xi on unit U i. Assuming that population siz N s y Th usual unbiasd stimator for population varianc n = ( yi Y n i= S y is givn as (. whr y = n n y i i= sampl man of y, Y = N N y i i= population man of y and S y = N N i= ( y i Y Whn th population varianc of auxiliary variat S x is known, [5]Isaki (983 proposd a ratio stimator for population varianc S y of study variat y as S x s ˆ = R s y (. sx

40 STATISTICS IN TRANSITION-nw sris, March 0 39 whr s x = n n i= ( x i X is an unbiasd stimator for population varianc S x = N N i= ( x i X Th varianc of s y and man squard rror of s ˆR up to th first ordr of approximation ar givn as ( N n 4 V ( s y = S y [ β ( y ], (.3 Nn ( N n 4 MSE( sˆ R = S y [ β ( y β ( x h], (.4 Nn µ 40 µ 04 whr β ( y =, β ( x =, µ µ 0 0 h =, µ µ 0 µ 0 S 4 y = N N i= ( y Y i 4 and N s t µ st = ( yi Y ( xi X. N i= Hr β ( y and β ( x ar th population cofficints of kurtosis of th study variat and auxiliary variat rspctivly.. Stratgy-I Using th sampling fraction f, modifid ratio typ stimator for population varianc of study variat y is givn as S = s y (. s f s y ( f t x x To obtain th bias and man squard rror of suggstd stimator t, w writ s = S and s = S y y ( 0 x x ( such that E ( = 0, i=0 and i E( 0 = ( β ( y, n N

41 40 R. Tailor, B. Sharma: Modifid Estimators E( = ( β ( x and n N E ( 0 = ( h. n N Now, th suggstd stimator t in trms of ' i s may b writtn as [ f ( 0 ( f ( 0 ( ] = S E { ( f ( f ( } = S t y, E ( t S y y 0 0 f { ( x h}, (. B( t = ( f S y β. (.3 Squaring and taking xpctation of both sids of quation (., w gt man squard rror of suggstd stimatort, up to th first dgr of approximation as { ( f ( f } E( t, (.4 4 S y = S y E 0 [ V ( s ( f V ( s ( f Cov( s, s ] MSE( t =, (.5 whr y x y x s y and rspctivly and s x ar th population variancs of th study and auxiliary variats 4 V ( s y = S y [ β ( y ], n N 4 V ( sx = S x [ β ( x ] and n N Cov ( s, s = S y S x h n N [ ] y x. 0

42 STATISTICS IN TRANSITION-nw sris, March Efficincy comparisons for t. From (8..3, (8..4 and (8..5, it is obsrvd that (i Suggstd stimator t would b mor fficint than usual unbiasd stimator for population varianc MSE ( t - V s <0 if ( y s y, i.. f Cov ( s y, sx < V ( s x (3. (ii Suggstd stimator t would b mor fficint than [5]Isaki (983 ratio stimator s ˆR, i.. MSE ( t - MSE sˆ <0 if ( R f Cov( s y, s < V ( sx x (3. 4. Stratgy-II Anothr modifid ratio typ stimator for population varianc of study variat y using th sampling fraction f, is givn as f 3 f S y t = s y s y (4. f f sx To obtain th bias and man squard rror of suggstd stimator t, w writ s y = S y ( 0 and sx = S x ( such that E ( i = 0, i=0 and E( 0 = ( β ( y, E( = ( β ( x and n N n N E ( 0 = ( h n N

43 4 R. Tailor, B. Sharma: Modifid Estimators Now, th suggstd stimator t may b writtn in trms of ' i s as = 0 0 ( ( 3 ( f f f f S t y = ( 3 ( 3 ( 3 ( 0 0 f f f f f f E S S t E y y (4. { } h x S f f t B y = ( ( 3 ( β (4.3 Squaring and taking xpctation of both sids of quation (4., w gt Man squard rror of suggstd stimator t, up to th first dgr of approximation as = ( f f f f E S S t E y y, (4.4 =, ( 3 ( 3 ( ( x y x y s s COV f f s V f f s V t MSE, (4.5 whr y s and x s ar th population variancs of th study and auxiliary variats rspctivly and xprssd in prvious sction. 5. Efficincy comparisons for t From (.3, (.4 and (4.5 it is obsrvd that (i Suggstd stimator t would b mor fficint than usual unbiasd stimator for population varianc y s, i.. ( t MSE - ( y s V <0 if (, ( 3 x x y s V s s Cov f f < (5.

44 STATISTICS IN TRANSITION-nw sris, March 0 43 (ii Suggstd stimator t would b mor fficint than Isaki (983 ratio stimator s ˆR, i.. MSE ( t - MSE sˆ <0 if ( R 3 f < f Cov ( s V ( s y x, s x (5. 6. Stratgy-III Th suggstd modifid ratio typ stimator for population varianc of study variat y is givn as f 4 f S y t 3 = sy sy (6. 3 f 3 f sx To obtain th bias and man squard rror of suggstd stimatort 3, w writ s y y ( 0 = S and s = S x x ( such that E ( = 0, i=0 and n i N E = ( β ( y, = ( ( x ( 0 E ( = h n N ( 0 E( β and n N Now, th suggstd stimator t 3 may b writtn in trms of f 4 f t3 = S y ( 0 ( 0 (, 3 f 3 f 4 f 4 f E( t3 S y = S y E 0 0 ( 3 f ( 3 f ' i s as 4 f, (6. ( 3 f f B t = 4 ( S y { ( x h} ( 3 f 3 β. (6.3

45 44 R. Tailor, B. Sharma: Modifid Estimators Squaring and taking xpctation of both sids of quation (6., w gt man squard rror of suggstd stimator t 3, up to th first dgr of approximation as 4 4 f 4 f E( t3 S y = S y E f 3 f (6.4 4 f 4 f MSE ( t3 = V ( s y V ( sx Cov( s y, sx (6.5 3 f 3 f whr s y and s x ar th population variancs of th study and auxiliary variats rspctivly and xprssd in prvious sction. 7. Efficincy comparisons for t 3 From (.3, (.4 and (6.5 it is obsrvd that (i Suggstd stimator t 3 would b mor fficint than usual unbiasd stimator for population varianc MSE ( t 3 - V s <0 if ( y s y, i.. 4 f 3 f < Cov ( s V ( s y x, s x (7. (ii Suggstd stimator t 3 would b mor fficint than [5]Isaki (983 ratio stimator s ˆR, i.. MSE ( t 3 - MSE sˆ <0 if ( R 4 f Cov( s y, sx < f V ( s x (7. Sction 3, 5 and 7 providd th conditions undr which proposd stimators t, t and t 3 hav lss man squard rrors in comparison to usual unbiasd stimator for population varianc and ratio stimator for population varianc.

46 STATISTICS IN TRANSITION-nw sris, March Empirical study To analyz th prformanc of th proposd stimators t, t and t 3 in comparison to othr stimators, w considr th data givn in [8]Murthy (967, p.-6. Th variats and data st is givn as y : Output and x : numbr of workrs. N=80, n=30, β ( =.667, β ( =3.65 and h= y x Tabl 8.. Prcnt Rlativ Efficincis of s ˆR, t, t and t 3 with rspct to s y. PRE s Prcnt Rlativ Efficincis Estimators s y s ˆR t t t It is obsrvd from th tabl 8. that thr is a significant gain in fficincy by using proposd varianc stimators t, t and t 3 in comparison to unbiasd stimator for population varianc s y and ratio stimator for population varianc s ˆR givn by [5]Isaki (983. Thrfor suggstd stimators t, t and t 3 ar rcommndd for thir us in practic. REFERENCES CEBRIAN, A.A. and GARCIA, R.M. (997. Varianc stimation using auxiliary information. An almost unbiasd multivariabl ratio stimator. Mtrika, 45, COCHRAN, W.G. (977. Sampling Tchniqus. Third U. S. Edition. Wily Eastrn Limitd, 35. DAS, A.K. and TRIPATHI T.P. (978. Us of auxiliary information in stimating th finit population varianc. Sankhya, C, 40,

47 46 R. Tailor, B. Sharma: Modifid Estimators GARCIA, M. RUEDA and CEBRIAN, A.A. (996. Rpatd substitution mthod. Th ratio stimator of th population varianc. Mtrika, 43, ISAKI, C.T. (983. Varianc stimation using auxiliary information, Journal of th Amrican Statistical Association 78, 7-3. KADILAR, C. and CINGI, H. (006. Ratio stimators for population varianc in simpl and stratifid sampling, Applid Mathmatics and Computation 73, , 006. KADILAR, C. and CINGI, H. (006. Improvmnt in varianc stimation using auxiliary information, Hacttp Journal of Mathmatics and Statistics 35 (, 5. MURTHY, M.N. (967. Sampling thory and mthods, statistical publishing socity, Calcutta. SINGH, H. P. and TAILOR, R. (003. Us of known corrlation cofficint in stimating th finit population man, Statistics in Transition, 6, SINGH, S. and JOARDER, A.H. (998. Estimation of finit population varianc using random non-rspons in survys sampling. Mtrika,47, SINGH, H.P. UPADHYAYA, L.N. NAMJOSHI, U.D. (988. Estimation of finit population varianc, Currnt Scinc 57, SINGH, H.P. and SINGH, R. (003. Estimation of varianc through rgrssion approach in two phas sampling. Alig. Jour. Stat., 3, SRIVASTAVA, S.K. AND JHAJJ H.S. (980. A class of stimators using auxiliary information for stimating finit population varianc. Sankhya, C, 4, UPADHYAYA, L.N. AND SINGH, H.P. (983. Us of auxiliary information in th stimation of population varianc. Mathmatical forum, 4,, UPADHYAYA, L.N. and SINGH, H.P. (006. Almost unbiasd ratio and product-typ stimators of finit population varianc in sampl survys, Statist. in Transi.,7 5,

48 STATISTICS IN TRANSITION-nw sris, March 0 47 STATISTICS IN TRANSITION-nw sris, March 0 Vol. 3, No., pp CROP ACREAGE AND CROP PRODUCTION ESTIMATES FOR SMALL DOMAINS - REVISITED G.C. Tikkiwal, Alka Khandlwal ABSTRACT For any country advanc and final stimats of yild of principl crops, at National and Stat lvls, ar of grat importanc for its macro lvl planning. But, for dcntralizd planning and for othr purposs lik crop insuranc, loan to farmrs, tc., th rliabl stimats of crop production for small domains ar also in grat dmand. This papr, thrfor, discusss and rviw critically th mthodology usd to provid crop acrag and crop production stimats for small domains, basd on indirct mthods of stimation, including th SICURE modl approach. Th indirct mthods of stimation so dvlopd us data obtaind ithr through traditional survys, lik Gnral Crop Estimation Survys (GCES data, or a combination of th survys and satllit data. Ky words: Timly Rporting Schm (TRS; Gnral Crop Estimation Survys (GCES; Simulation-cum- Rgrssion (SICURE modl.. Introduction Th advanc and final stimats of crop production of principl crops at national and sub-national lvl lik districts, countis, blocks for any country ar of importanc for its macro and micro lvl planning. In many countris, including India, th yild rat of principl crops ar bing stimatd through crop-cutting xprimnts. Th tchniqu of crop-cutting xprimnts is mostly dvlopd in India in arly svntis. Th stimation of crop yild is don undr th national programm known as Gnral Crop Estimation Survys (GCES using crop-cutting xprimnts. Th GCES ar bing conductd through survy mthodology dvlopd mostly in 940's [Mahalanobis (946, Sukhatm and Agarwal (946-47, ]. Dpartmnt of Mathmatics and Statistics, Jai Narain Vyas Univrsity, Jodhpur 34005, India. [email protected]. Dpartmnt of Mathmatics and Statistics, Jai Narain Vyas Univrsity, Jodhpur 34005, India. [email protected].

49 48 G. C. Tikkiwal, A. Khandlwal: Crop acrag and Th stimation of crop yild involvs two componnts viz. th stimation of crop acrag and th stimation of yild rats. As rgard crop acrag stimation, a schm known as Timly Rporting Schm (TRS has bn in vogu sinc arly svntis in most of th Stats of India. Th TRS has th objctiv of providing quick and rliabl stimats of crop acrag statistics and thrby production of th principl crops during ach agricultural sason on th basis of 0 prcnt sampl villags, using dirct stimators. Th prformanc of dirct stimators is satisfactory at national and stat lvl, as th sampling rror of th stimators is within 5 prcnt, but not at lowr lvls as shown by Tikkiwal and Tikkiwal (998, Tikkiwal and Ghiya (000, 004. Th authors dvlopd and usd synthtic and composit mthods of stimation to provid crop acrag stimation for small domains. Furthr, it has bn obsrvd that composit mthod of stimation is asy to apply and this approach ovrcoms th limitation of synthtic stimator to som xtnt [cf. commnts by Francisco (998, p.54]. Whr this approach dos not work, thn SICURE modl can b trid or othr modl basd stimation mthods may provid satisfactory rsults. Apart from traditional approach th rmot snsing tchnologis wr initiatd aftr launch of many advancd satllits, to provid crop acrag and crop production stimats for major and minor domains [Dadhwal t al. (985]. For xampl, th National Agricultural Statistics Srvic (NASS of th Unitd Stats of Amrica has bn using Landsat sris of satllits sinc 950 s, and Franc ntrd th fild of arth rsourcs satllits in 986 with th launch of SPOT-I [cf. Bllow t al. (996]. In India this work has bn ntrustd to Indian Spac Rsarch Organization. Th modl basd stimation mthods for small domains, using survy and satllit data has bn dvlopd ovr a priod of tim by authors Batts t al. (988, Singh t al. (99, Shaibl and Casady (994, Srivastava (007 and othrs. Ths mthods may provid fficint stimators providd a suitabl modl is slctd and thr should not b problm of mixd cropping. This papr provids a comprhnsiv rviw of th work don on crop production stimats of small domains. In this papr Sction dscribs th mthods of stimating crop acrag statistics. Th Sction 3 dscribs th cropcutting xprimnts and prsnts mthod of stimation of crop yild. Sction 4 discusss and rviw th mthodology usd to provid crop acrag and crop production stimats for small domains, basd on survy data, whras th modl basd stimation mthods for small domains using survy and satllit data ar discussd in Sction 5.. Crop acrag statistics In Tmporarily Sttld Stats (th stats, in which land rvnu is fixd for a dfinit priod of yars and is subjct to rvision at th nd of this priod of India crop acrag statistics ar collctd on complt numration basis, whras in

50 STATISTICS IN TRANSITION-nw sris, March 0 49 Prmanntly Sttld Stats (th stats, in which land rvnu is fixd for prptuity thy ar stimatd through slction of 0 prcnt villags. In ordr to provid quick and rliabl advancd stimats of th crop production, in tmporarily sttld stats also crop acrag statistics ar stimatd undr Timly Rporting Schm (TRS. Th TRS has bn in vogu sinc arly svntis in ths Stats of India. Undr th schm th Patwari (Villag Accountant is rquird to collct acrag statistics on a priority basis in a 0 prcnt sampl of villags. Ths villags ar slctd by stratifid linar systmatic sampling schm, taking Thsil as a stratum. Ths statistics ar furthr usd to provid stat lvl stimats using dirct stimators viz. unbiasd (basd on sampl man and ratio stimators. Th prformanc of both dirct stimators in th stat of Rajasthan, lik in othr stats, is satisfactory at stat lvl, as th sampling rror is within 5 prcnt. Howvr, th sampling rror of both dirct stimators incrass considrably, whn thy ar usd for stimating acrag statistics of various principl crops vn at district lvl, what to spak of lvls lowr than a district. Tikkiwal and Ghiya (000, 004 notic that th sampling rror of dirct ratio stimator for Kharif crops of Jodhpur district (of Rajasthan stat for th agricultural sason 99-9 varis approximatly btwn 6 to 68 prcnt. Thrfor, thr is a nd to us indirct stimators at district and lowr lvls for dcntralizd planning and othr purposs lik crop insuranc, bank loan to farmrs. As rgards stimation of yild rats, it is bing don through crop-cutting xprimnts. It may b notd hr that for administrativ purposs India is dividd into th numbr of stats, ach stat consists of a numbr of districts, ach district consists of a numbr of thsils and furthr ach thsil consists of a numbr of villags. Th crop acrag statistics ar also collctd by th Indian Spac Rsarch Organization undr its Crop Acrag and Crop Production (CAPE projct, through rmot snsing tchnology. But du to mixd cropping pattrn, prvaild in India, this tchniqu of th crop acrag statistics ar not so rliabl. Land Us and Land Covr statistics of India and th stat of Rajasthan ar shown hr using th satllit data obtaind from Rgional Rmot Snsing Cntr-Wst, Indian Spac Rsarch Organization, Dpartmnt of Spac (India.

51 50 G. C. Tikkiwal, A. Khandlwal: Crop acrag and LAND USE / LAND COVER STATISTICS OF INDIA (00- Sourc: AWIFS Satllit data (00- LAND USE / LAND COVER STATISTICS OF RAJASTHAN (00- Sourc: AWIFS Satllit data (00- In Indian systm thr ar mainly thr agricultural sason s viz. Kharif, Rabi and Zaid. (i Kharif crops th crops sown in Jun-July and harvstd in Octobr- Novmbr vry yar. (ii Rabi crops th crops sown in Novmbr-Dcmbr and harvstd March-April vry yar. (iii Zaid crops th crops grown btwn March and Jun ar known as Zaid.

52 STATISTICS IN TRANSITION-nw sris, March Estimation of crop yild Final stimats of crop production basd on complt numration of ara and yild bcom availabl much aftr th crops ar actually harvstd. Howvr, th Govrnmnt may rquir advanc stimats of production for taking various policy dcisions rlating to pricing, markting, xport/import, distribution, tc. Considring th gnuin rquirmnt of crop stimats much bfor th crops ar harvstd for various policy purposs, a tim schdul of rlasing th advanc stimats has bn volvd undr a national programm known as Gnral Crop Estimation Survys (GCES. Th GCES uss th tchniqu of crop-cutting xprimnts. 3.. Crop cutting xprimnts undr GCES Th most important factor of Crop production statistics is th stimation of yild rats. Prsntly th yild rats ar stimatd through crop-cutting xprimnts undr GCES. Th GCES covrs 68 crops (5 foods and 6 non foods in stats and 04 union trritoris. Such survys ar conductd twic a yar to covr diffrnt typs of crops. About fiv hundrd thousand crop-cutting xprimnts, for major crops throughout th country, ar conductd annually undr this programm. Th sampling dsign adoptd for th GCES is a multistag stratifid random sampling with thsils/inspctor land rvnu circls/community dvlopmnt blocks, tc. as strata, th villags slctd randomly form th primary stag sampling unit, th filds from ach slctd villag formd th scond stag sampling unit and th xprimntal plot within th fild form th ultimat stag of sampling. A sampl of villags is slctd from diffrnt strata in proportion to th ara undr crop. From ach slctd villag, two filds ar slctd randomly and from ach fild a plot of fixd shap and siz usually masuring (5mtr x 5mtr is slctd for rcording th grn yild by actual harvsting th crop. 3.. Estimation Procdur Estimation procdur for stimating of crop yild through Crop Estimation Survys: Th mthodology gnrally adoptd for stimating th avrag yild of crop is as blow: At th stratum (thsil lvl, th stimatd avrag yild of th crop is obtaind as a simpl arithmtic man of plot yilds. For this, lt Y ijk Th grn yild (nt in gms/plot of th k-th plot in th j-th villag in th i-th stratum.

53 5 G. C. Tikkiwal, A. Khandlwal: Crop acrag and n ij Numbr of xprimnts analyzd in th j-th villag of i-th stratum. mi Numbr of villags in which xprimnts ar analyzd in th i-th stratum. ni Numbr of xprimnts analyzd in th i-th stratum. S Numbr of strata in a district. ai Th ara (nt of th crop in th i-th stratum. f Th convrsion factor for convrting th grn yild pr plot into th yild of dry marktabl produc pr hctar. Stratum lvl avrag of th grn yild for th i-th stratum is and furthr, District lvl stimatd avrag yild of th dry marktabl produc pr hctar is givn by Y s = i= s ai. Yi. f a i= i Thn, is to b multiplid by th District lvl crop acrag stimats of that particular crop, to hav an stimat of th yild. 4. Estimation for small domains using survy data For dcntralizd planning and othr purposs lik crop insuranc, loan to farmrs, tc., th Govrnmnts nd rliabl agricultural statistics for small domains lik district, CD block, countis, tc. But th stimats providd by National Agncis such as NSSO, TRS and EARAS ar gnrally rliabl at th stat lvl and not at district lvl. In such situation Small Ara Estimation mthods hold out a promising solution. 4.. Synthtic and composit mthods Tikkiwal, B.D. and Tikkiwal, G.C. (998 in thir invitd papr prsnts an xcllnt rviw of th landmarks in th dvlopmnt of crop yild and acrag statistics in India and othr dvloping countris. As rgards providing stimats of avrag crop yild at small ara (Assistant Agricultural Officr (AAO circl lvl th authors us dirct mthods only, bcaus th sampl siz was

54 STATISTICS IN TRANSITION-nw sris, March 0 53 sufficintly larg. In th absnc of such information/sufficint data th SICURE modl can b hlpful. Th authors furthr dmonstrat th us of synthtic and composit stimators to provid rliabl acrag statistics at small ara lvls. Th small aras in this study ar Inspctor Land Rvnu Circls (ILRC s, th subgroups of Thsils. Th study suggsts th us of composit stimators, if th synthtic assumption closly mts. Whn this assumption dos not mt, thy suggst th us of othr typs of stimators such as thos obtaind through th SICURE modl (993. Th following discussant Francisco Juvir Gallgo s (998, p. 54 commnts on this papr show applicability of th rsults. Th approach might ovrcom som limitations of synthtic stimators and looks asir to apply than othr small ara stimation procdurs that hav bn usd in agricultural statistics [For xampl, Batts t al. (988]. Som additional clarifications would b of intrst on th computation of varianc from a singl sampl. If th rsults prsntd ar confirmd in othr countris, th mthod would b of intrst, and not only for dvloping countris, as statd in th papr. Actually, India is a dvlopd country if w spak about statistics. Tikkiwal, G.C. and Ghiya, A. (000 dfin and discuss a gnralizd class of synthtic stimators with application to crop acrag stimation for small domains (ILRC s, using auxiliary information, undr diffrnt sampling schms. Th gnralizd class of synthtic stimators, among othrs, includs th simpl, ratio and product synthtic stimators. Th proposd class of synthtic stimators givs consistnt stimators if th synthtic assumption holds. Furthr, th authors compar th rlativ prformanc of a numbr of synthtic stimators with dirct stimators, mpirically, through a simulation study using liv data. Th study rvals that for th domains whr synthtic stimators do not dviat considrably from thir corrsponding assumption, prformanc of th synthtic stimator is satisfactory. Whn th synthtic stimators dviat considrably from thir corrsponding assumption, thn th authors suggst to look for othr typs of stimators such as thos obtaind through th SICURE modl [Tikkiwal (993]. Sisodia and Singh (00 dvlop thr synthtic stimators of total crop production Y i of i-th block (small ara lvl using crop production and othr rlativ information at district lvl, as givn blow: Estimator ( whr, P Y i = W j X j Y (4.. j= Y = A Y ; Y is obtaind through multipl linar rgrssion modl. A = Ara undr th crop in a givn yar X j = Valu of j-th prdictor at th block lvl in a givn yar W j = Wight assign to ach prdictor.

55 54 G. C. Tikkiwal, A. Khandlwal: Crop acrag and Estimator ( & Estimator (3 ar of th form Y ~ b Y i = i i whr, bi ar constants such that a a ~ Yi = bi Y i = Y i= i= For b i = b (constant scond stimator of Y i is, i.. Estimator ( ~ ( Y Yi = Y i a Y i= i Y = actual crop production rportd at district lvl through crop-cutting xprimnts in a givn yar. a Y Yi i= For bi = third stimator of Y i is, i.. ayi Estimator (3 a Y Yi ~ ( i Yi = Y = i a (4..3 a = Numbr of blocks in th district. (4.. Furthr, th authors carrid out an mpirical study for ric crop in Faizabad district of Uttar Pradsh during th yars 98-8 and to compar th rlativ fficincy of ths stimators undr multipl linar rgrssion modl. Th ~ ( i ~ ( i rlativ fficincy of Y and Y ovr Y i coms out to b sam for all th blocks, i % and 05.88% rspctivly during th yar Similarly, during th yar it coms out to b 0.80% and 05.88% rspctivly. ~ ( Thus Y i is found to b most fficint whn comparing with ~ ( Y i and Y i in cas whn wights ar givn to b mor than. In cas whn wights ar lss ~ ( Y i and ~ ( Y i ar found to b mor fficint thany i. But than both stimators ~ ( Y i nd not b th most fficint stimator. Th rsults prsntd in th Tabl 4 and Tabl 5 (p. 33 & 35 dos not corrlat with th findings, whn th

56 STATISTICS IN TRANSITION-nw sris, March 0 55 stimatd valus ar compard with th actual stimats basd on crop-cutting xprimnts. All th thr stimators considrd by th authors ar nothing but synthtic, rgrssion typ, stimators and, thrfor, thir fficincy dpnds on th validity of th assumption of th corrsponding synthtics stimator undr us. Also, th thr stimators ar dsign-biasd; thrfor, ignoring th bias rmains a srious limitation. But ths stimators can b furthr improvd upon by th tchniqu of composit stimation. [cf. Tikkiwal and Ghiya (004]. Tikkiwal and Ghiya (004 dfin and discuss a gnralizd class of composit stimators for small domains, using auxiliary information, undr diffrnt sampling schms. Th proposd stimator of population many i, basd on auxiliary variabl 'x' undr SRSWOR dsign is dfind as: β β xi x y, = ( c i wi yi wi y ; (0 w i (4..4 X i X i whr, β and β ar suitably chosn constants. Th stimator y c, i is a wightd sum of th gnralizd dirct stimator [Srivastava (967] and th gnralizd synthtic stimator [Tikkiwal and Ghiya (000]. Th proposd stimator has dsirabl consistncy proprty (in traditional sns, whn th following assumption is satisfid. Y i β β ( X Y ( X i (4..5 It is to b notd that th synthtic stimator may b havily biasd unlss th abov assumption is satisfid [cf. Tikkiwal and Ghiya (000, Eq. (4.]. Th proposd gnralizd class of composit stimators includs a numbr of dirct, synthtic and composit stimators as spcial cass. Hr follows a list of such stimators with corrsponding choic of valus of th diffrnt constants.

57 56 G. C. Tikkiwal, A. Khandlwal: Crop acrag and Tabl 4.. Various Dirct, Synthtic and Composit Estimators as Spcial Cass of th Gnralizd Composit Estimators S No Estimator w ( i β β w i Simpl Dirct ( y i Simpl Synthtic ( y y Simpl Ratio i X i x i 4 Ratio Synthtic y X i x x Simpl Product i yi X i y Product Synthtic x X i 7 Composit : Combining simpl w i ( w 0 0 i dirct with simpl synthtic wi yi ( wi y 8 Composit: combining simpl w i ( w 0 - i dirct with ratio synthtic y wi yi ( wi X i x 9 Composit : combining simpl w i ( w - - i ratio with ratio synthtic yi y wi X i ( wi X i x x i Furthr, th authors comparing th various mpirical rsults of Absolut Rlativ Bias (ARB and Simulatd rlativ standard rror (Srs, draw th conclusion that if th synthtic stimators do not dviat considrably from thir corrsponding assumptions (dscrib in Eq. 4..5, thn prformanc of th composit stimators (givn at S.No.9 in th Tabl 4., basd on a sampl of 0% villags, is satisfactory at th lvl of ILRCs. Thrfor, ths stimators will crtainly prform bttr up to th lvl of district. Whn th givn condition is not satisfid w should look for othr mthods of stimation. On of such mthod is to us SICURE modl (993 or th mthods prsntd in Ghosh & Rao (994. Sharma, Srivastava and Sud (004 considr two diffrnt synthtic stimators basd on auxiliary variabls for providing crop yild stimat at Gram Panchayat

58 STATISTICS IN TRANSITION-nw sris, March 0 57 (small ara lvl. Th proposd stimators for i-th Gram Panchayat (GP ar dfind as follows: T i = xi AY, i =,,..., a a (4..6 A x i= i i and, a A i xi ' i= T = x Y i i iopt (4..7 A β β iopt = A i σ A xi a Ai σ xi ni V Y A i= ni a = numbr of GP in a block. A = Ara undr a particular crop for th i-th GP. i a A i i= A = = Total ara undr th crop in th block. N i = Numbr of farmrs in th i-th GP. n i = Numbr of farmrs slctd in th i-th GP for obtaining information about th xpctd yild of th crop grown in th fild. x = xpctd yild as obtaind from j-th farmr in th i-th GP; j =,,...,n i. ij Y = block lvl stimat of crop yild as obtaind through th mthod of cropcutting xprimnt. x i = n i ni j= x ij, avrag of xpctd yild of i-th GP. In th mpirical study th proposd stimators ar basd on crop yild stimats obtaind through crop-cutting xprimnts undr Gnral Crop Estimation Survys and stimat of crop production obtaind through data collctd from a frsh slctd random sampl of 0 farmrs from ach of all th GP s in a district. Analysis of data obtaind from a survy carrid out on what crop in th Basti district of th stat of Uttar Pradsh in India in th yar 000 rvald that both th stimators prform satisfactorily in trms of th critrion of

59 58 G. C. Tikkiwal, A. Khandlwal: Crop acrag and prcntag root man squard rror as it varis from % to 0% in most of th cass. Th biass of both th stimators ar also ngligibl. Hr, it may b notd that th stimators proposd by Sharma t al. (004 dpnd on th stimat of crop production obtaind through crop-cutting xprimnts and on th basis of frsh sampls slctd indpndntly from ach Gram Panchayat (GP of th block. In th cas study, for xampl, a block roughly consists of 90 GP s which rsults in a slction of an additional sampl of 900 farmrs. This mthod, thrfor, dos not fall within th domain of small ara stimation mthods. Also basis of th proposd stimator is th assumption that ovr stimation and undr stimation, with rspct to stimats obtaind through mthod of crop-cutting xprimnts, bhav in similar way in all th domains of a block of intrst; which is not ralistic. Apart from this thr ar rrors in th formula of Bias and Man Squar Errors [Eq. (6., (6.3 of th papr]. 5. Estimation for small domains using satllit and survy data National Agricultural Statistics Srvic (NAAS of th U.S. Dpartmnt of Agricultur has bn a usr of rmot snsing data sinc 950 s whn it bgan using mid-altitud arial photography to construct sampling frams for th 48 stats of th continntal Unitd Stats. A nw ra in rmot snsing bgan in 97 with th launch of th Landsat I arth-rsourc monitoring satllit. Four Landsats hav bn launchd sinc 97 with Landsat IV and V which ar still in opration. A rgrssion stimator was dvlopd which rlatd th groundgathrd ara fram data to th computr classification of Landst MSS (multispctral scannr imags. Th basic rgrssion approach usd to produc stat stimats dos not produc rliabl county (small ara stimats. Thr domain indirct rgrssion stimators hav bn usd or considrd for producing small ara county stimats using ancillary satllit data by NAAS. From 97 to 98 th Huddlston-Ray stimator was usd, from 983 to 990 Batts-Fullr family of stimators was usd and sinc 99, th Batts-Fullr modl has bn usd to produc country stimats with Landsat TM (Thmatic Mappr data. Th dtails of ths modls hav bn discussd in dtail by Bllow t al. (996. In India, as mntiond abov, at prsnt crop ara statistics ar basd on complt numration of all filds and crop yild statistics basd on GCES. With th advnt of rmot snsing tchnology satllit data has bn widly usd by many countris including India for obtaining various crop statistics. Svral studis hav bn conductd during th past dcad by th India s Dpartmnt of Spac undr th Crop Acrag and Production Estimation (CAPE projct for crop acrag and production stimation for various major crops using satllit spctral data. Rcntly som studis hav bn takn at th Indian Agricultural Statistics Rsarch Institut, Nw Dlhi, India to dvlop mor fficint stimator of crop yild using satllit data along with survy data of crop yild basd on crop-cutting xprimnts. [cf. Singh t al. (99, Gol t al. (994, Shaibl and

60 STATISTICS IN TRANSITION-nw sris, March 0 59 Casady (994, Singh t al. (999, Singh and Gol (000, Singh (004, Srivastava (007]. Singh and Gol (000 usd synthtic stimators to provid th yild stimats at Thsil and Block lvls, using crop yild data for Rabi crops obtaind from GCES and th satllit spctral data of IRS-D LISS-III. Th study shows that th standard rror of synthtic stimator is lss than th corrsponding dirct stimator. Th study also dvlopd yild stimats at District lvl, using th dirct stimator undr post-stratification. Th standard rror of th dirct stimator at district lvl is vry small (around 5%. This confirms th rsults of arlir study by Singh t al. (999. Singh (003 usd th farmr s y stimat of crop yild corrsponding to th crop plots slctd for crop-cutting xprimnt as an auxiliary variabl along with th vgtation indics for improving th crop yild forcasting modls. Th yild data prtains to what crop yild data for district Rohtak for th yar basd on crop-cutting xprimnts. Spctral data in th form of vgtation indics RVI and NDVI has bn obtaind from IRS B-LISS II datd Fbruary 7, 996 for th rgion. Th farmr s y stimat is obtaind from th slctd farmrs for th filds in which crop-cutting xprimnts wr conductd. Singh (004 rviwing th arlir work also dvlopd rgrssion stimats using RVI (x, NDVI (x and farmrs y stimat of crop yild of th corrsponding plot (x 3 as auxiliary variabls for forcasting cop yild at district lvl. In all th abov studis th prformanc of th synthtic stimators ar masurd in trms of standard rrors. Howvr, ignoring th bias rmains a srious limitation. In country lik India almost 70% population is dpndnt on agricultur. Th farm sizs in India ar vry small with divrsifid crops in ach sason. Th practic of mixd cropping is quit dominant. Thrfor, it may not b possibl to prpar accurat ara fram using rmot snsing tchnology du to limitations of satllit snsor in dtcting and diffrntiating small filds and crops grown, both for major as wll as for minor domains. Rao, J. N. K. (004 provids an appraisal of indirct stimats, both traditional and modl basd. H provids a brif account of small ara stimation in th contxt of agricultur survys. H prsnts modl basd small ara stimation undr a basic ara lvl modl and a basic unit lvl modl. H rviws work of Fullr (98, Batts t al. (988, Stasny t al. (99 and Singh and Gol (000. Fullr (98 applis th mixd ara lvl modl θ = z β v, i=,,...,m (5. i T i i i to stimat man soyban hctars pr sgmnt in 978 at th county lvl.

61 60 G. C. Tikkiwal, A. Khandlwal: Crop acrag and This modl is combination of a basic ara lvl modl θ i = θi i, i=,,...,m and a linar rgrssion modl T θ i = z i β vi, i =,,...m whr, sampling rror i ' s ar assumd to b indpndnt across ara with man 0 and known varianc ψ, and i modl rror v ' i s ar assumd to b indpndnt and idntically distributd with man 0 and varianc σ, z ( z,..., z T v i = ara spcific auxiliary variats. i Using th data * θ i, z i, i =,..., m w can obtain stimats, θ i, of th ralizd valus of θi from th mixd modl. It may b notd that mpirical bst linar unbiasd prdiction (EBLUP mthod is applicabl for mixd linar modls and its stimats do not rquir normality assumption on th random rrors v i and i. EBLUP stimat of θi is a composit stimat of th form θ * = θ T i wi i wi zi β ; Pi σ v w i = σ v ψ i (5. which is a wightd combination of dirct stimat θ i and a rgrssion synthtic stimat z β. T i β is th wightd last squar stimat of β with wights v σ is an stimat of th varianc componnt σ v. σ v ψ i. Fullr obtaind modl basd stimats of th population mans, Y i for th sampld county (m=0 as wll as th non sampld countis. His modl is givn by y z = β β z z v (5.3 i 3i 0 i β 3i i with known rror varianc σ v and σ. z i = man numbr of pixls of soybans pr ara sgmnt ascrtaind by satllit imaginary. i

62 STATISTICS IN TRANSITION-nw sris, March 0 6 z 3 i = man soyban hctars from th 974 U.S. Agricultural Cnsus, as county (ara lvl covariats. Not that z and z 3 ar known for all th 6 countis. i i Th modl (5.3 is a spcial cas of (5. with θ = and i yi z3i ψ i = ψ = σ. Fullr's stimat of Y i for sampld countis is obtaind from (5.. as * * * = g θ = θ z ( i i i yif 3 T T = z3 i zi β w yi z3i zi β, i s σ v w = whr, σ v σ For th non sampld countis, * yif 3i T = z z β, i s * H concluds that th modl basd stimats, y if, outprform in trm of total MSE. Thy ar also bttr than th dirct stimats y i in trms of total MSE for th sampld countis. Batts t al. (988 also considr th problm of crop acrag stimation using farm intrviw data in conjunction with LANDSAT satllit data. Th T authors us th nstd rror linar rgrssion modl y ij = xij β vi ij ; j =,,..., N i ; i =,...,m to stimat ara undr corn and ara undr soybans for i-th small ara (countis in north-cntral Iowa. y is variabl undr study rlatd to unit-spcific auxiliary data ij x, ij ij ij (, x x T = and normally distributd rrors vi and ij. Authors prsnt th EBLUP stimats of small ara mans for both crops. Estimatd standard rrors of th EBLUP stimats and th survy rgrssion T y i X i xi β ar also givn. Th ratio of th stimatd standard rror of th EBLUP stimat to that of th survy rgrssion stimat dcrass as th siz of sampl dcrass. stimats ( Rao (004 furthr uss Hirarchical Bays approach to tst th fitnss of th modl givn by Batts t al. with auxiliary data ij x. Undr th critrion of postrior probabilitis us, it is notd that for valus of such probabilitis clos to 0.5 it indicatd good fit but for probabilitis clos to 0 and, it suggsts poor fit of th modl. i

63 6 G. C. Tikkiwal, A. Khandlwal: Crop acrag and Th major problm with th modl basd approach is of slction a suitabl modl. Thrfor, slction and validation play a vital rol in modl basd stimation. If th assumd modls do not provid a good fit to th sampl data, th modl basd approach can lad to rronous stimats. Acknowldgmnt Th rsarch was supportd by th grant rcivd from Dpartmnt of Scinc and Tchnology, Nw Dlhi undr Womn Scintist Schm. Th authors ar thankful to th Rfr for his constructiv suggstions which hlpd to improv th papr. REFERENCES BATTESE, G.E., HARTER, R.M. and FULLER, W.A. (988: An rrorcomponnts modl for prdiction of crop aras using survy and satllit data. J. Amr. Statist. Assoc., 83, BELLOW, M., GRAHAM, M. and IWIG, W. C. (996: Country stimation of crop acrag using satllit data. Indirct Estimation in U.S. Fdral Programs, Springr, CSO (990: Working group on small ara dvlopmnt programm statistics. Rport, Dpartmnt of Statistics, Ministry of Planning, Govrnmnt of India, Nw Dlhi. DADHWAL, V.K. and PARIHAR, J.S. (985: Estimation of what acrag of Karnal district (Haryana using landsat MSS digital data. Tchnical not, IRS-UP/SAC/CPF/TN/09, Spac Application Cntr, Ahmdabad. FRANCISCO, J.G. (998: Commnts on th invitd papr ntitld Small ara stimation in India Crop yild and acrag statistics by Tikkiwal, B.D. and Tikkiwal, G.C. Procdings of th Intrnational Confrnc Agricultural Statistics 000, FULLER, W.A. (98: Rgrssion stimation for small aras. Rural Amrica in Passag: Statistics for Policy, National Acadmy Prss, Washington, D.C., GHOSH, M. and RAO, J.N.K. (994: Small ara stimation: An appraisal. Statist. Sci., 9, MAHALANOBIS, P.C. (946: Sampl survys of crop yilds in India. Sankhya,

64 STATISTICS IN TRANSITION-nw sris, March 0 63 RAO, J.N.K. (004: Small ara stimation with applications to agricultur. J. Ind. Soc. Agril. Statist., 57, SCHAIBLE, W.L. and CASADY, R.J. (994: Th dvlopmnt, application, and valuation of small ara stimators. Statistics in Transition, (6, SHARMA, S.D., SRIVASTAVA, A.K. and SUD, U.C. (004: Small ara crop stimation mthodology for crop yild stimats at Gram Panchayat lvl. J. Ind. Soc. Agril. Statist., 57, SINGH, D. (968: Doubl sampling and its application in agricultur. J. Ind. Soc. Agril. Statist. (Pans Mmorial volum. SINGH, R. (003: Us of satllit data and farmrs y stimat for crop yild modling. J. Ind. Soc. Agril. Statist., 56 (, SINGH, R. (004: Application of rmot snsing tchnology for crop yild stimation. J. Ind. Soc. Agril. Statist, 57, SINGH, R. and GOEL, R.C. (000: Us of rmot snsing satllit data in crop survys. Tchnical Rport, Indian Agricultural Statistics Rsarch Institut, Nw Dlhi. SINGH, R., GOEL, R.C., PANDEY, L.M. and SAHA, S.K. (999: Us of rmot snsing tchnology in crop yild stimation survys- II, Projct Rport, IASRI, Nw Dlhi. SINGH, R., GOYAL, R.C., SAHA, S.K. and CHHIKARA, R.S. (99: Us of satllit spctral data in crop yild stimation survys. Int. J. Rm. Sns., 3 (4, SISODIA, B.V.S. and SINGH, A. (00: On small ara stimation An mpirical Study. J. Ind. Soc. Agril. Statist., 54 (3, SRIVASTAVA, A.K. (007: Small ara stimation A prspctiv and som applications. J. Ind. Soc. Agril. Statist., 6 (3, STASNY, E.A., GOEL, P.K. and RAMSEY, D.J. (99: County stimats of what production. Survy Mthodology, 7, -55. SUKHATME, P.V. and AGARWAL, O.P. (946-47, : Crop-cutting survy on what by th random sampling mthod. Rport, Indian Council of Agricultural Rsarch, Nw Dlhi. TIKKIWAL, B.D. (99: Modling through survy data for small domains. Kynot Addrss at th Symposium on Modling hld at Kurukshtra Univrsity, March 7 9, 99. TIKKIWAL, B.D. (993: Modling through survy data for small domains. Proc. Scintific Confrnc on Small Ara Statistics and Survy Dsign hld in Sptmbr 99 at Warsaw, Poland.

65 64 G. C. Tikkiwal, A. Khandlwal: Crop acrag and TIKKIWAL, B.D. and TIKKIWAL, G.C. (998: Small ara stimation in India Crop yild and acrag statistics. Invitd papr in th Procdings of th Intrnational Confrnc Agricultural Statistics 000 (along with th commnts of Dr. J.G. Francisco, th discussant of th papr, Th Confrnc was hld in March 998 at Washington, D.C., USA. TIKKIWAL, G.C. and GHIYA, A. (000: A gnralizd class of synthtic stimators with application to crop acrag stimation for small domains. Biomtrical Journal, 4 (7, TIKKIWAL, G.C. and GHIYA, A. (004: A gnralizd class of composit stimators with application to crop acrag stimation for small domains. Statistics in Transition, (6,

66 STATISTICS IN TRANSITION-nw sris, March 0 65 STATISTICS IN TRANSITION-nw sris, March 0 Vol. 3, No., pp ESTIMATION OF POPULATION MEAN IN POST- STRATIFIED SAMPLING USING KNOWN VALUE OF SOME POPULATION PARAMETER(S Aloy C. Onyka ABSTRACT Following Khoshnvisan t.al. (007 and Koyuncu and Kadilar (009, this papr dvlops a gnral family of combind stimators of th population man in post-stratifid sampling (PSS schm, using known valus of som population paramtrs of an auxiliary variabl. Proprtis of th proposd family of stimators, including conditions for optimal fficincy, ar obtaind up to first ordr approximations. Th rsults ar illustratd mpirically. Ky words: Auxiliary information, gnral family of stimators, post-stratifid sampling, man squard rrors 000 AMS Classification: 6D05. Introduction Th us of auxiliary information in constructing stimators of population paramtrs of th variabl of intrst is highly ncouragd in survys, spcially whn an auxiliary variabl is highly corrlatd with th study variabl. Apart from using th known population man X of an auxiliary variabl x, many authors hav vnturd into th us of othr known population paramtrs of x. Notabl studis along this lin, undr th simpl random sampling without rplacmnt (SRSWOR schm, includ Sarls (964, who usd th cofficint of variation (CV of x in stimating th population man Y of th study variabl y, and Sisodia and Dwivdi (98, who usd th CV of x in ratio stimation of Y. Singh t.al. (973 usd known cofficint of kurtosis in stimating th population varianc of y. Sn (978 and Sarls and Intarapanich (990 also usd known cofficint of kurtosis in stimating Y. Singh and Tailor (003 usd known corrlation cofficint in ratio stimation of Y. Singh (003 usd known Dpartmnt of Statistics. Fdral Univrsity of Tchnology. PMB 56, Owrri, Nigria. [email protected].

67 66 Onyka, A.C.: Estimation of population standard dviation of th auxiliary variabl x in stimating Y. Khoshnvisan t.al. (007 proposd a gnral family of stimators of Y undr th SRSWOR schm, which uss known paramtrs of th auxiliary variabl x such as standard dviation, cofficint of variation, skwnss, kurtosis and corrlation cofficint. Motivatd by Khoshnvisan t.al. (007, th prsnt study intnds to dvlop a gnral family of stimators of Y undr th post-stratifid sampling schm. Undr th stratifid random sampling schm, Cochran (977 discussd th usual stratifid sampling stimator, y st, and also sparat and combind ratio-typ stimators of Y. Kadilar and Cingi (003, motivatd by th works don undr th SRSWOR schm by Sisodia and Dwivdi (98, Singh and Kakran (993, and Upadhyaya and Singh (999, proposd som stimators of Y in stratifid random sampling using known valus of population man X h, cofficint of variation C xh, and cofficint of kurtosis β h (x of th auxiliary variabl x in stratum h. Kadilar and Cingi (003 rstrictd thir work to ratio stimation of Y in stratifid random sampling. Koyuncu and Kadilar (009 proposd a mor gnral family of combind stimators of Y in stratifid random sampling along th lin of Khoshnvisan t.al. (007. Chaudhary t.al. (009 considrd, in a mor rcnt papr, a gnral family of combind stimators of Y in stratifid random sampling undr non-rspons. Motivatd by Khoshnvisan t.al. (007 and Koyuncu and Kadilar (009, w considr in th prsnt study, a gnral class of combind-typ stimators of Y in post-stratifid sampling schm, using information on known valus of som population paramtrs of an auxiliary variabl.. Th Proposd Estimators Lt yhi (xhi dnot th i th obsrvation in stratum h for th study (auxiliary variat in post-stratifid sampling schm. Lt a random sampl of siz n b drawn from a population of N units using SRSWOR mthod, and lt th sampld units b allocatd to thir rspctiv strata, whr n h (a random variabl is th numbr of units that fall into stratum h such that L h= n h = n. W assum that n is larg nough such that P(n h = 0 = 0, h. Following Khoshnvisan t.al. (007 and Koyuncu and Kadilar (009, w propos a gnral family of combind stimators of th population man Y in post-stratifid sampling schm as

68 STATISTICS IN TRANSITION-nw sris, March 0 67 y pss g ax b y = ps (. (axps b ( (ax b α α whr, L y = ω y is th usual post-stratifid stimator of Y ps h= L h= L h h x = ω x is th usual post-stratifid stimator of X ps h= h h X = ωhx h is th known population man of th auxiliary variat x. a( 0, b ar ithr constants or functions of known population paramtrs of th auxiliary variat, such as Standard dviation ( σ x, Cofficint of variation ( C x, Skwnss ( β (x, Kurtosis ( β (x, and Corrlation cofficint ρ, and ( yx ω h = N h /N is stratum wight, L is th numbr of strata in th population, N h is th numbr of units in stratum h, N is th numbr of units in th population, X h is th population man of th auxiliary variat in stratum h, and yh (xh is th sampl man of th study (auxiliary variat in stratum h. Undr th conditional argumnt, that is, for th achivd sampl configuration, n = (n,n,,n, th post-stratifid stimator, y ps is unbiasd for Y with varianc, L L L ω L = ω n S yh hs h yh (yps h = ωhs yh h= Nh nh h= nh N h= V (. whr V rfrs to conditional varianc and in stratum h. S yh is th population varianc of y For rpatd sampls of fixd siz n, w obtain th unconditional varianc of y ps by taking th xpctation of quation (.. This givs th unconditional varianc of y ps as: L L V (yps = E(V (yps = ωh E Syh ωhs yh (.3 h= nh N h=

69 68 Onyka, A.C.: Estimation of population Following Stphan (945, w obtain, to trms of ordr n, ωh E n = h nωh n ωh (.4 Consquntly, th unconditional varianc of y ps obtaind up to first ordr approximation is L f V (yps = ωhs yh (.5 n of ps ps h= Similarly, th unconditional varianc of x ps and th unconditional covarianc y and x ar obtaind rspctivly as L f V (xps = ωhsxh (.6 n and Cov (y ps, x ps h= L f = ωhs yxh (.7 n h= whr f = n/ N is th population sampling fraction, S xh is th population varianc of x in stratum h, and S yxh is th population covarianc of y and x in stratum h. Lt and 0 yps Y = (.8 Y x = ps X X Undr th unconditional argumnt, w obtain (.9 E (0 = E( = 0 E( V(y L ps f 0 = = ω hsyh Y Y n h= (.0 (.

70 STATISTICS IN TRANSITION-nw sris, March 0 69 and E( E( V(x L ps f = = ω hsxh X X n h= Cov(y, x L ps ps f 0 = = ωhs yxh YX YX n h= (. (.3 W can rwrit quation (. in trms of 0 and as y g pss = Y( 0( αλ (.4 ax g whr λ =. Assuming αλ <, so that th sris ax b ( αλ convrgs, and xpanding quation (.4 up to first ordr approximations in xpctd valu, w obtain th xprssions: (y pss Y = Y(0 αλg αλg0 α λ g(g (.5 and ( ypss Y = Y (0 α λ g αλg0 (.6 To obtain th unconditional bias and man squard rror of th proposd stimators y w tak th unconditional xpctations of quations (.5 and pss (.6, and us quations (.0 (.3 to mak th ncssary substitutions. This givs th unconditional bias and man squard rror of y pss, rspctivly as B(y L αλg f = ωh( αλ(g RS X n h= pss xh Syxh (.7 and MSE(y L f pss = ωh(s yh α λ g R Sxh αλgrsyxh n h= (.8 whr R = Y / X.

71 70 Onyka, A.C.: Estimation of population 3. Spcial Cass Th proposd stimator, y pss is a gnral class of stimators capabl of gnrating an infinit numbr of combind stimators of Y by making appropriat choics of th valus of α, g, a and b in quation (.. Th following ar som spcial cass of th proposd stimators, y pss, of Y in poststratifid sampling schm. Estimator. Usual stratifid stimator, y pss ( = y ps = L h= ω y. Usual Combind ratio-typ stimator, yps ypss ( = ypsrc = X x 3. Sisodia-Dwivdi (98 stimator, X Cx ypss(3 = ypssd = yps x C 4. Singh-Kakran (993 stimator X β(x (, ypss(4 = ypssk = yps x β (x 5. Upadhyaya-Singh (999 stimator (, Xβ(x Cx ypss(5 = ypsus = yps x β (x C 6. Upadhyaya-Singh (999 stimator (, XCx β(x ypss(6 = ypsus = yps x C β (x ps h h ps ps ps ps x x x Valus of α g a b 0 0 C x β (x β (x C x C x β (x

72 STATISTICS IN TRANSITION-nw sris, March 0 7 Estimator 7. Singh-Tailor (003 stimator (, X ρyx ypss(7 = ypsst = yps x ρ 8. Th usual combind product-typ ypsx stimator, ypss (8 = ypspc = X 9. Pandy-Duby (988 stimator, xps Cx ypss(9 = ypspd = yps X C 0. Upadhyaya-Singh (999 stimator (3, xpsβ(x Cx ypss(0 = ypsus3 = yps Xβ (x C. Upadhyaya-Singh (999 stimator (4, xpscx β(x ypss( = ypsus4 = yps XC β (x. G.N. Singh (003 stimator (, xps σ ypss( = ypsgns = yps X σ 3. G.N. Singh (003 stimator (, xpsβ(x σ ypss(3 = ypsgns = yps Xβ (x σ 4. G.N. Singh (003 stimator (3, xpsβ(x σ ypss(4 = ypsgns3 = yps Xβ (x σ 5. Singh-Tailor (003 stimator (, xps ρyx ypss(5 = ypsst = yps X ρ 6. Singh-Kakran (993 stimator (, xps β(x ypss(6 = ypssk = yps X β (x ps x x yx yx x x ps x x x x x Valus of α g a b ρ yx 0 C x β (x C x C x β (x σ x β (x σ x β (x σ x ρ yx β (x

73 7 Onyka, A.C.: Estimation of population Notic that th usual post-stratifid stimator y ps is a spcial cas of th proposd family of stimators y pss if and only if w choos g = 0, no mattr th valus of α, a and b. Again, w obsrv that th nxt six (6 spcial cass, (i, i =,,7 ar ratio-typ stimators, whil th rmaining nin (9 y pss spcial cass (i, i = 8,, 6 ar xampls of product-typ stimators of Y y pss in post-stratifid sampling schm. 4. Efficincy Comparisons Using quation (.8, w obtain th unconditional varianc/man squard rrors of th stimators, (i, i =,,, 6 as follows: V(y y pss L f pss( = V(yps = ωhs yh n h= L f pss ( = MSE(ypsRC = ωh(s yh R Sxh RSyxh n h= L f pss (3 = MSE(ypsSD = ωh(s yh θsxh θsyxh n h= L f pss (4 = MSE(ypsSK = ωh(s yh θsxh θsyxh n h= L f pss (5 = MSE(ypsUS = ωh(s yh θ3sxh θ3syxh n h= L f pss (6 = MSE(ypsUS = ωh(s yh θ4sxh θ4syxh n h= L f pss (7 = MSE(ypsST = ωh(s yh θ5sxh θ5syxh n h= L f pss (8 = MSE(ypsPC = ωh(s yh R Sxh RSyxh n h= L f pss (9 = MSE(ypsPD = ωh(s yh θsxh θsyxh n h= L f pss (0 = MSE(ypsUS3 = ωh(s yh θ3sxh θ3syxh n h= MSE(y MSE(y MSE(y MSE(y MSE(y MSE(y MSE(y MSE(y MSE(y (4. (4. (4.3 (4.4 (4.5 (4.6 (4.7 (4.8 (4.9 (4.0

74 STATISTICS IN TRANSITION-nw sris, March 0 73 MSE(y MSE(y MSE(y MSE(y MSE(y MSE(y whr L f pss ( = MSE(ypsUS4 = ωh(s yh θ4sxh θ4syxh n h= L f pss ( = MSE(ypsGNS = ωh(s yh θ6sxh θ6syxh n h= L f pss (3 = MSE(ypsGNS = ωh(s yh θ7sxh θ7syxh n h= L f pss (4 = MSE(ypsGNS3 = ωh(s yh θ8sxh θ8syxh n h= L f pss (5 = MSE(ypsST = ωh(s yh θ5sxh θ5syxh n h= L f pss (6 = MSE(ypsSK = ωh(s yh θsxh θsyxh n h= Y R =, X Y θ =, X C x Y θ =, X β (x YCx θ 4 =, XCx β(x and Y Y Yβ(x θ 5 =, θ 6 =, θ 7 =, θ X ρ X σ Xβ (x σ yx x x 8 Yβ (4. (4. (4.3 (4.4 (4.5 (4.6 (x θ 3 =, Xβ(x Cx Yβ(x = Xβ (x σ Applying th last squars mthod, th (optimum choic of α that minimizs quation (.8, is obtaind as β0 α opt = (4.7 λgr and th rsulting optimum unconditional man squard rror of y pss is obtaind as L 0 h= f MSE opt(ypss = ( ρ ωhs yh (4.8 n whr x

75 74 Onyka, A.C.: Estimation of population β 0 = L h= L h= ω S h h xh ω S yxh, ρ 0 = L h= L h= ω S ω S h yh h yxh L h= h xh ω S (4.9 Notic that quation (4.8 is th sam as th unconditional varianc of th usual combind post-stratifid rgrssion stimator, y = y β (x X. psreg This implis that th fficincy of th proposd gnral family of stimators may not b improvd byond th fficincy of th customary combind rgrssiontyp stimator in post-stratifid sampling. Howvr, using quations (4. and (4.8, w obsrv that: f V(yps MSEopt(ypss = ρ0 ωhs yh > 0 n L h= ps 0 ps (4.0 This shows that undr optimum conditions, th proposd family of stimators is mor fficint than th usual post-stratifid stimator, y ps in trms of having a smallr man squard rror. Again, lt L A 0 = ωhs yh and = h= (4. and (4.8, w obsrv that L ωhsxh h= A. Thn, using quations f MSE(ypss ( MSEopt(ypss = ( ρ0a0 RA > 0 n (4. This shows that th optimum stimator in th proposd family of stimators is mor fficint than th usual combind ratio-typ stimator y psrc. Similarly, it could b shown that non of th spcial cass of th proposd family of stimators is mor fficint than th optimum stimator in th proposd gnral family of stimators. 5. Empirical Illustration W hav applid th proposd gnral family of stimators on th data on th acadmic prformanc of 96 studnts of Statistics dpartmnt, Fdral Univrsity of Tchnology, Owrri, 008/009 acadmic sssion. (Sourc: Dpartmnt of Statistics, Fdral Univrsity of Tchnology, Owrri, Nigria. Hr, w usd th cumulativ grad point avrag (CGPA as th study variat, and prformanc in a gnral (prtst Statistics xamination as th auxiliary variat. Stratification

76 STATISTICS IN TRANSITION-nw sris, March 0 75 was carrid out by gndr, and w assumd, hypothtically, that th numbr of mal and fmal studnts to b includd in th sampl might not b dtrmind until aftr sampl slction. Consquntly, w first took a random sampl of siz n = 0, which showd th distribution of mal and fmal studnts, aftr sampl slction, as 8 mals and fmals. Th data statistics, consisting mainly of population paramtrs, ar shown in Tabl, whil Tabl shows th prcntag rlativ fficincis (PRE of th proposd stimators ovr th customary poststratifid stimator y ps of th population man, Y in post-stratifid sampling schm. Tabl. Data Statistics POPULATION MALES = STRATUM FEMALES = STRATUM N = 96 N = 7 N = 4 n = 0 n = 8 n = X = 68.3 X = 68. X = Y =.44 Y =. 44 Y =. 46 S x = 7.03 S x = 7. 8 S x = S x = S x = S x = S y = 0.57 S y = S y = S y = 0.33 S y = S y = 0. 5 S yx = 3.6 S yx = S yx =. 75 ρ yx = 0.8 ρ yx = ρ yx = ρ yx = 0.67 ρ yx = ρ yx = C x = 0.0 C x = 0. C x = C y = 0.3 C y = 0. 4 C y = 0. 0 β (x =.0 β (x =. 3 β (x = β (y = 0. β (y = 0. 4 β (y = 0. 4 β (x = 3.83 β (x = β (x =. 34 β (y =.7 β (y =. 40 β (y = 0. 3 γ = 0.04 γ = γ = 0. 6 ω = ω = 0. 5 ω = = R = , θ = , θ = , θ 3 = , θ 4 = 0.096, θ 5 = , θ 6 = , 7 = , θ 8 = ,

77 76 Onyka, A.C.: Estimation of population Tabl. PRE of som post-stratifid combind stimators of Y ovr y ps Estimator Varianc / MSE PRE ovr y st y pss ( y pss ( y pss ( y pss ( y pss ( y pss ( y pss ( y pss ( y pss ( y pss ( y pss ( y pss ( y pss ( y pss ( y pss ( y pss ( y pss (opt From Tabl, w obsrv that not vry stimator in th proposd gnral family of stimators prformd bttr than th usual post-stratifid combind stimator y. Th tabl also confirms that th optimum stimator y pss (opt is ps th most fficint stimator in th proposd family of combind stimators of Y in post-stratifid sampling schm. Again, w obsrv that for th givn data st, th combind ratio-typ stimators, y ps (i, i =,3,, 7 prformd bttr than th customary post-stratifid stimator y ps in trms of having smallr man squard rrors, whil th combind product-typ stimators, y ps (i, i = 8,9,,6 did not prform bttr than y ps. This is xpctd sinc for th givn data st, thr is a strong positiv corrlation (0.8 btwn th study and auxiliary variabls. Th product-typ stimators would prform bttr than y ps and th ratio-typ stimators whn thr is a strong ngativ corrlation btwn th study and auxiliary variabls.

78 STATISTICS IN TRANSITION-nw sris, March Concluding Rmark W hav proposd a gnral family of combind stimators of Y, in poststratifid sampling (PSS schm, which is found, undr som optimum conditions, to b as fficint as th post-stratifid rgrssion stimator y psreg, but mor fficint, in trms of having a smallr man squard rror, than th usual post-stratifid combind stimator, y ps Proprtis of th proposd gnral family of stimators ar obtaind up to first ordr approximations and illustratd mpirically. REFERENCES CHAUDHARY, M.K., SINGH, R., SHUKLA, R.K., KUMAR, M. and SMARANDACHE, F. (009: A family of stimators for stimating population man in stratifid sampling undr non-rspons. Pak. J. Stat. Opr. Rs. V(, COCHRAN, W.G. (977: Sampling Tchniqus, John Wily and Sons, Nw York. KADILAR, C. and CINGI, H. (003: Ratio Estimators in Stratifid Random Sampling. Biomtrical Journal 45(, 8-5. KHOSHNEVISAN, M., SINGH, R., CHAUHAN, P., SAWAN, N., and SMARANDACHE, F. (007. A gnral family of stimators for stimating population man using known valu of som population paramtr(s, Far East Journal of Thortical Statistics,, 8 9. KOYUNCU, N. and KADILAR, C. (009. Ratio and product stimators in stratifid random sampling, Journal of Statistical Planning and Infrnc 39 (8, PANDY, B.N. and DUBEY, VYAS (988: Modifid product stimator using cofficint of variation of auxiliary variat, Assam Statistical Rv., (, SEARLS, D.T. (964: Th utilization of known cofficint of variation in th stimation procdur. Journal of Amrican Statistical Association, 59, 5-6. SEARLS, D.T. and INTARAPANICH, P. (990: A not on an stimator for th varianc that utilizs th kurtosis. Th Amrican Statistician, 44(4, SEN, A.R. (978: Estimation of th population man whn th cofficint of variation is known. Commun. Statist., Thory-Mth. A(7,

79 78 Onyka, A.C.: Estimation of population SINGH, G.N. (003: On th improvmnt of product mthod of stimation in sampl survys. Jour. Ind. Soc. Agric. Statistics, 56(3, SINGH, H.P. AND KAKRAN, M.S. (993: A Modifid Ratio Estimator Using Known Cofficints of Kurtosis of an Auxiliary Charactr (unpublishd. SINGH, H.P. AND TAILOR, R. (003: Us of known corrlation cofficint in stimating th finit population man. Statistics in Transition, 6(4, SINGH, J., PANDEY, B.N. and HIRANO, K. (973: On th utilization of a known cofficint of kurtosis in th stimation procdur of varianc. Ann. Inst. Stat. Math., 5, SISODIA, B.V.S. and DWIVEDI, V.K. (98: A Modifid Ratio Estimator Using Cofficint of Variation of Auxiliary Variabl. Journal of Indian Socity Agricultural Statistics 33, 3-8. STEPHAN, F. (945: Th xpctd valu and varianc of th rciprocal and othr ngativ powrs of a positiv Brnoulli variat. Ann. Math. Stat., 6, UPADHYAYA, L.N. and SINGH, H.P. (999: Us of Transformd Auxiliary Variabl in Estimating th Finit Population Man. Biomtrical Journal 4(5,

80 STATISTICS IN TRANSITION-nw sris, March 0 79 STATISTICS IN TRANSITION-nw sris, March 0 Vol. 3, No., pp NONRESPONSE BIAS IN THE SURVEY OF YOUTH UNDERSTANDIG OF SCIENCE AND TECHNOLOGY IN BOGOTÁ Edgar Mauricio Buno Castllanos ABSTRACT Th Colombian Obsrvatory of Scinc and Tchnology -OCyT- dvlopd, in 009, a survy about undrstanding of Scinc and Tchnology in studnts of high school in Bogotá, Colombia. Th sampling dsign was stratifid according to th natur of school (public or privat. Two sourcs of unit nonrspons wr dtctd. Th first on corrsponds to schools that did not allowd to collct information. Th scond sourc corrsponds to studnts who did not assist during th days whn survy was applid. Estimats wr obtaind through two diffrnt approachs. Rsults obtaind in both cass do not show visibl diffrncs whn stimating ratios; vn though, som grat diffrncs wr obsrvd whn stimating totals. Rsults obtaind using th scond approach ar blivd to b mor rliabl bcaus of th mthodology usd to handl itm nonrspons. Ky words: Sampling dsign; nonrspons bias; calibration.. Introduction In 009, th Colombian Obsrvatory of Scinc and Tchnology -OCyTdvlopd th Survy of Youth Undrstanding of Scinc and Tchnology in Bogotá, which inquirs about topics rlatd to undrstanding about scintist, nginrs and bnfits and risks of scinc and tchnology. Rsults and analysis of th survy ar prsntd by Daza t. al (0. As xpctd, on th data collcting procss, thr wr studnts who wr not possibl to contact (unit nonrspons and othrs that did not fulfill som of th qustions in th qustionnair (itm nonrspons. As a consqunc, ariss th nd to us mthodologis that allows to obtain stimations taking into account th prsnc of nonrspons. Colombian Obsrvatory of Scinc and Tchnology OCyT-. Bogotá Colombia. [email protected].

81 80 E. M. B. Castllanos: Nonrspons bias in Initially, itm nonrspons was considrd as a nw catgory and th unit nonrspons was handld by conforming Rspons Homognity Groups (Särndal, Swnsson and Wrtman, 99. Aftr that, it was proposd to obtain stimations through othr mthodology: to imput missing valus corrsponding to itm nonrspons and to us th calibration stimator for unit nonrspons. Th scond sction of this documnt dscribs th mthodology usd for dsign and dvlopmnt of th survy. Th third sction dscribs th causs of nonrspons in th survy and th two mthodologis proposd to handl it. In ordr to compar ths mthodologis, a Mont Carlo simulation was carrid out, its rsults ar dscribd in th fourth sction. This simulation allowd to s th bhavior of stimators undr diffrnt cass. In th last sction conclusions and suggstions ar prsntd basd on th xprinc achivd through th survy.. Mthodology Th survy targt population was conformd to studnts of th last two yars of high school of all th schools in Bogotá, Colombia. Th sampling fram usd to idntify th schools was th ducational stablishmnt rgistr from th Scrtaría d Educación d Bogotá (burau of ducation, which includs, bsids idntification and contact variabls, th natur of school (public or privat and information about th numbr of studnts rgistrd in yar 008 in vry grad. Th rgistr includs all th ducational stablishmnts in th city, thrfor, it was ncssary to liminat th institutions that dos not offr th grads dfind for th study and thos that offr thm but hav an approach on adult ducation. Finally, it was obtaind a sampling fram with 073 schools, 75 of ths ar privat and rportd studnts in 008, th rmaining 358 ar public and rportd 830 studnts in th sam yar. Onc conformd th final fram, th sampl was drawn. Th dsign was a Stratifid on-stag clustr sampling. Th natur of school was usd as stratification variabl. In ach stratum a sampl of schools was drawn using a probability proportional to siz -pps- dsign. Th siz variabl usd to assign probabilitis to schools was th numbr of studnts rportd for 008 according to th fram, incrmntd in on unity. Th qustionnair was applid to vry studnt in th last two yars in slctd schools. A sampl of 3 privat and 6 public schools was drawn (ordrd sampl. On public and two privat schools wr rslctd in th sampl, obtaining a stsampl of 9 privat and 5 public schools, which hav, rspctivly, 63 and 7498 studnts in 008. Throughout this documnt and unlss othrwis is spcifid, sampl will mak rfrnc to th ordrd sampl.

82 STATISTICS IN TRANSITION-nw sris, March 0 8 Whn th data collction stag ndd, papr qustionnairs wr transcribd, conforming a data st that was validatd and thn stimations wr carrid out. In a first momnt, it was plannd to obtain stimations using th stimator proposd by Hansn and Hurwitz (943, also known as with-rplacmnt sampling stimator pwr stimator-. This stimator could not b usd bcaus it was not possibl to obtain information from all individuals xpctd in th sampl. For this rason it was ncssary to idntify othr altrnativs to obtain stimations in th prsnc of nonrspons. Th nxt sction dscribs th altrnativs usd for th survy. 3. Daling with nonrspons As usual whn dvloping a survy, in th undrstanding survy both typs of nonrspons ariss: itm nonrspons and unit nonrspons. Two unit nonrspons sourcs wr idntifid. Th first on, du to dirctivs that dny data collction: th survy was implmntd in th 6 public schools, but only in 3 out of 3 privat schools drawn in th sampl; this cas will b rfrrd as clustr nonrspons. Th scond sourc corrsponds to studnts who blong to schools in which accss was allowd but did not assist during th days whn survy was applid, this cas will b rfrrd as lmnt nonrspons. Givn that all th qustions in th survy ar catgorical, in a first momnt stimations wr obtaind by considring itm nonrspons as a nw catgory for vry variabl. Unit nonrspons was handld by modifying xpctd sampl sizs by thos obsrvd. This approach will b rfrrd as Approach. Latr, it was dcidd to obtain nw stimations by th us of mthods allowing to control th nonrspons ffcts: th narst nighbor mthodology was usd to imput valus blonging to itm nonrspons and th calibration stimator was usd to handling unit nonrspons. This approach will b rfrrd as Approach and is dscribd in Sction 3.. a. Approach In this approach th nonrspons was handld according to: Itm nonrspons: Missing valus du to itm nonrspons was considrd as a nw catgory. By doing this, a rctangular data st is obtaind, in which missing valus ar rplacd by a cod rprsnting its absnc. On advantag of th mthodology is that allows to obtain a compltly rctangular data st allowing to mak cross tabulation of variabls in survy; on th othr hand, som disadvantags ar th arising of maninglss cross-classifid clls and that nothing is don in ordr to control th bias du to nonrspons. Unit nonrspons: Elmnt nonrspons was handld by assuming that, in vry school, studnts who participatd in th survy conform a simpl random sampl of studnts. Th bias gnratd by this assumption is xpctd to b small givn

83 8 E. M. B. Castllanos: Nonrspons bias in that th nonrspons rats within th schools that participat in th survy wr low. Clustr nonrspons was handld by assuming a rspons homognity group modl with groups givn by th natur of school. This mans that is assumd that th rspons probability,, in ach group of schools (public or privat is fixd and stimatd by. In this cas, pwr stimator taks th form whr is th stimation of th total of variabl in th th school, is th numbr of studnts in th th school. This numbr was rcordd for vry school in th rspons st, is th numbr of studnts who answrd th qustionnair in th th school, is th rspons st of studnts blonging to th th school, is th rspons st of schools in th stratum, is th numbr of slctd schools in stratum, is th numbr of schools in th rspons st in stratum, is th valu of for th th, is th slction probability of th school. At first glanc, th stimator in ( dos not control th bias or th varianc incrmnts that may b gnratd as a consqunc of th nonrspons. Evn so, this stimator satisfis th dsirabl proprty of rproducing totals for th siz variabl usd to obtain th slction probabilitis of individuals: For th cas of lmnt sampling from a population, which counts with valus of for vry lmnt in th sampl of siz, lt th total of siz variabl and th valu of associatd to th th individual. Slction probability for th individual is dfind as. Whn applying th pwr stimator to valus of in th sampl, w obtain ( This rsult, obtaind for lmnt sampling, works also for th modification proposd for handling nonrspons, quation (, This proprty indicats that, if, th stimator givn in ( will obtain prfct stimations for for vry sampl, no mattrs th nonrspons, this proprty rsmbls th calibration stimator. It is clar that is impossibl that th

84 STATISTICS IN TRANSITION-nw sris, March 0 83 proportionality b satisfid in practic, vn so, th proprty suggst that whil thr xists a high corrlation btwn and, both, varianc and bias du to nonrspons will b small. For th undrstanding survy it is rquird that totals in schools ( to b proportional to th numbr of studnts rportd for 008 (. b. Approach Th nonrspons was handld according to: Itm nonrspons: Missing valus du to itm nonrspons wr imputd using th narst nighbor mthodology: For vry variabl in th qustionnair,, a st of variabls, which is xpctd to b rlatd to, is idntifid and thn sortd according to xplanatory powr xpctd with, this is, th first variabl in will b th on that xplain th most of, th scond will b th on following this rul, and so on. It is important to clarify that vry variabl in th study was qualitativ and that th choic of th variabls in and its ordr wr du to subjctiv critria. Individuals in th data st wr dividd in two groups according to th valus for : th rspons st and th nonrspons st, whr is th st of individuals having information for at last on of th variabls in th qustionnair. Th valu (in is imputd as follows: Th matrix is cratd from as:, whr is th numbr of individuals in. For vry individual,, in w calculat. Individual that maximizs is idntifid and its valu is assignd to. Whn thr ar tis, is obtaind as th mod of th valus associatd to thos individuals that maximizs. If thr is not a uniqu mod, a random valu of is chosn from th st of mods. It is clar that th distanc mtric is such that matching in dominats matching in th rmaining variabls to ; if dos not match, dominats matching in th rmaining to ; and so on. This situation was dcidd in ordr of rducing th burdn of calculations that would imply th assignation of diffrnt wights to vry variabl in for vry variabl in th qustionnair. Unit nonrspons: Elmnt nonrspons was handld in th sam fashion that in Approach : it was assumd that, in vry school, studnts who participatd in th survy conform a simpl random sampl from th total of studnts.

85 84 E. M. B. Castllanos: Nonrspons bias in Särndal and Lundström (005 proposd th calibration stimator for th Horvitz and Thompson stimator (95 at th lvl of individuals. For clustr nonrspons a variation of this stimator was usd. Du to th absnc of auxiliary information at th lvl of studnts, calibration was carrid out at th lvl of schools using on quantitativ and two catgorical variabls for classification. Quantitativ variabl,, is th total of studnts in th th school during 008. Th first classification variabl,, is th sam variabl usd for stratification, th natur of school (public or privat,, whr and Th scond classification variabl,, is an indicator of th siz of school, dfind as, whr, and Th auxiliary vctor associatd to th th school,, is conformd as and th input vctor rquird is th total of studnts in vry group in 008: is not includd in ordr to avoid singularitis in th matrix to b invrtd to obtain th calibratd slction probabilitis. Onc dfind th auxiliary vctor and th input vctor, th calibratd slction probabilitis,, ar calculatd as with = λ ' t and λ vi ' x i r X h rh m h pi mh = h r t r x i h t x i t p ' x i i and thn, th total of is stimatd as

86 STATISTICS IN TRANSITION-nw sris, March 0 85, ; with ( A comparison btwn th stimators and is prsntd in th nxt sction. 4. A Mont Carlo simulation study In ordr to compar th bias and varianc of and, dfind in quations ( and (, rspctivly, a Mont Carlo simulation study was carrid out. This procss took into account only clustr nonrspons; lmnt nonrspons and itm nonrspons wr ignord. A population of individuals in 073 schools was cratd. Th numbr of schools was fixd to match th numbr of schools in th sampling fram, whil th numbr of individuals was fixd to match th stimatd numbr of studnts according to Approach. Thr auxiliary variabls at th lvl of schools (, and, on xognous variabl ( and thr study variabls at th lvl of studnts (, and wr gnratd as follows: : Numbr of studnts in th th school according to th sampling fram, : Th natur of th school (public or privat,. This variabl is usd also for conforming strata. : Th siz of th school,. : A dichotomous xognous variabl rlatd to th natur of school. By xognous variabl I man a variabl that is compltly unknown in th survy: it is not an auxiliary variabl known bforhand, and also is not masurd in th qustionnair as a study variabl: : A dichotomous variabl that taks valu with diffrnt probabilitis according to th natur of school: and and

87 86 E. M. B. Castllanos: Nonrspons bias in : A dichotomous variabl that taks valu dpnding on strata (, and th valu of z:,, =0, ==0.5 and : A dichotomous variabl that taks valu dpnding only on th valu of z: and It is clarifid that th auxiliary variabls, and ar prsnt at th lvl of schools, whil th study variabls, and ar prsnt at th lvl of studnts and thy ar rlatd to th auxiliary variabls through its totals within schools. Th ida bhind th stup for th study variabls and th rspons distribution (stp 4 of th simulation procss will b dscribd blow. Figur. Simulatd individuals by school: vs. Th numbr of individuals in th th school,, was dfind in ordr that th corrlation cofficint btwn th siz in th fram,, and was (approximatly qual to :. whr and is an obsrvation of a random variabl, with chosn proprly and is th slop of th rgrssion lin of on,

88 STATISTICS IN TRANSITION-nw sris, March 0 87 Two corrlation lvls btwn and wr gnratd: high ( and low (. Th lft panl of Figur shows th scattr plot btwn th numbr of studnts for school according to th sampling fram and th numbr of studnts obsrvd for th cas. Th right panl shows th cas. It is clarifid that th minimum valu for th simulatd populations is qual to. With ach of ths populations th following procss was carrid out:. A stratifid (with rplacmnt pps of 3 privat and 6 public schools was drawn. Th slction probability for th th school was dfind as. All studnts in slctd schools wr slctd.. Th totals by stratum of,, and th population siz,, from th full sampl using th pwr stimator wr stimatd:. 3. Th totals by stratum of,, and th population siz,, using th calibration stimator including and as classification variabls and as quantitativ wr stimatd:. 4. A school rspons distribution was gnratd by a fixd rspons probability dpnding on th strata and th school total of. was dfind in ordr that th rspons probability in Stratum and Stratum, was and, rspctivly. 5. Onc dfind th rspons st, totals for th four alrady mntiond variabls wr stimatd using th stimator (:. 6. Totals of th four variabls wr stimatd using th calibration stimator:. 7. A stratifid simpl random sampl -srs- of th full population of schools was drawn. This procdur was carrid out in ordr to compar a dsign that includs auxiliary information (pps against on that dos not includ it (srs. Th numbr of schools, (, was chosn with th goal that th numbr of individuals xpctd undr th srs sampl was (approximatly qual to th numbr of individuals xpctd undr th pps sampl. 8. Totals of,, and th population siz,, wr stimatd by using th Horvitz-Thompson stimator (also known as -stimator (95:, with th numbr of schools in stratum. 9. In addition, with vry stimator, th ratio was stimatd. Also and wr stimatd. Th rsults obtaind ar similar to thos obtaind for.

89 88 E. M. B. Castllanos: Nonrspons bias in Th procdur dscribd in numrals to 9 is rpatd tims. Evry tim th stimations obtaind through th fiv stimators ar rcordd. Th (simulatd xpctation of ach stimator is obtaind as and th (simulatd varianc is obtaind as. Tabl shows th paramtrs to stimat: totals of variabls, and, total of individuals in th population and th ratio. Tabl. Population totals and ratios Total Privat schools Official schools N t y t y t y R 0,6 0,80 0,50 Tabls and 3 shows (simulatd rlativ bias and (simulatd cofficint of variation for cass and, rspctivly. Th (simulatd rlativ bias,, of th th stimator for total is calculatd as and th (simulatd cofficint of variation, total is calculatd as, of th th stimator for A fw words on th rspons distribution, th variabls, and, and th auxiliary vctor : According to Särndal and Lundström (005 thr is a tripl associatd to vry individual in th population. It is clar that, by

90 STATISTICS IN TRANSITION-nw sris, March 0 89 construction, dpnds partially on th known and partially on th unknown. Givn that dpnds only on not on, in this cas th nonrspons is compltly xplaind by th auxiliary vctor, so this cas can b considrd as Missing at Random -MAR-. dpnds on both and, so th nonrspons is partially xplaind by. Finally, dpnds only on th unknown variabl, so th auxiliary vctor is unabl to xplain th nonrspons distribution, at last dirctly. Tabl shows th rsults for th cas in which th corrlation btwn th numbr of individuals by school in th fram and th numbr of individuals obsrvd by school is. About th bias, Tabl suggsts th following rsults: It is known that and ar unbiasd in total stimation and is asymptotically unbiasd. Th simulation allows to s ths facts. Th bias of and is also small. In th stratum of high nonrspons (stratum th bias for th calibration stimator undr nonrspons ( although small, is notably gratr than th bias for th pwr stimator undr nonrspons (. Manwhil, in th stratum, thr is a rvrs situation: bias of is smallr than th bias of. Th bias of th fiv stimators for th ratio ar small. Tabl. Simulatd rlativ bias and simulatd cofficint of variation (as a prcntag of fiv stimators for th cas. Rlativ bias Cofficint of variation Strata Paramtr t ( t ( t (3 t (4 t (5 t ( t ( t (3 t (4 t (5 Stratum Stratum N 0,0 0,00-0,03-0, -0,4 3,43 3,58 5,53 6,9,74 t y 0,0-0,0-0,05-0, -0,3 3,6 3,78 5,86 6,4,8 t y 0,04 0,0 0,00-0,4-0,4 3,53 3,68 5,67 6,3,8 t y3 0,0 0,00-0,07-0,7-0,3 3,67 3,8 5,90 6,48,7 R 0,00-0,0-0,0 0,00 0,00,0,05,64,6 0,67 N -0,05-0,0-0,06 0,0-0,3 5,8 5,7 5,37 5,50 4,67 t y -0,04-0,0-0,05 0,0-0, 5,57 5,66 5,7 5,84 4,68 t y -0,05-0,3-0,05 0,04-0,5 5,80 5,90 6,00 6,8 4,8 t y3-0,05-0,0-0,06 0,0-0,5 5,46 5,55 5,6 5,76 4,7 R 0,0 0,00 0,0 0,0 0,0,7,74,76,8,8

91 90 E. M. B. Castllanos: Nonrspons bias in Som commnts on th cofficints of variation in Tabl : Th varianc of th stimators for totals is highly rducd whn including auxiliary information: CV of ar clarly gratr than thos of th othr four stimators. Th CV of th calibration stimator ar slightly gratr than thos for th pwr stimator: th CV of is slightly gratr than th CV of, for th cas of full rspons; and, th CV of is slightly gratr than th CV of, for th cas of nonrspons. Th CV of th stimators that works in th prsnc of nonrspons in th stratum ar clarly highr than thos of th stimators that works undr full rspons; on th othr hand, in stratum this diffrnc is small. This is a consqunc of th rspons probabilitis in ach stratum. Whn stimating th ratio, th rsults diffrs from thos for totals: in this cas th smallst CV corrsponds to th stratgy (srs, -stimator, a stratgy that dos not includs auxiliary information in th dsign or th stimation stag. This is du to th fact that whn stimating totals, th siz variabl usd in to is mor or lss rlatd to th totals within schools, so rducing th varianc; whras, whn stimating a ratio, th siz variabl dos not xplain th variation in th variabl of intrst, and can vn caus a loss of fficincy with rgard to a stratgy that dos not includ auxiliary information. Tabl 3. Simulatd rlativ bias and simulatd cofficint of variation (as a prcntag of fiv stimators for th cas. Rlativ bias Cofficint of variation Strata Paramtr t ( t ( t (3 t (4 t (5 t ( t ( t (3 t (4 t (5 Stratum Stratum N -0, 0,49-7,53-0,9 0,8 3,73 4,53 44,04 47,79,5 t y -0, 0,48-7,5-0,9 0,8 3,78 4,58 44, 47,87,57 t y -0, 0,48-7,55-0,90 0,8 3,70 4,50 44,0 47,76,54 t y3-0,3 0,48-7,63 -,0 0,8 3,7 4,5 44,07 47,78,46 R -0,0-0,0 0,0 0,04 0,00,05,08,7,6 0,65 N 0,34 0,4,34,43 0,30 3,3 3,8 3, 33,97 3,3 t y 0,35 0,4,35,44 0,30 3, 3,5 3,99 33,83 3, t y 0,33 0,,33,44 0,7 3, 3,5 3,0 34,00 3,46 t y3 0,34 0,5,35,45 0,30 3,7 3,3 3,5 34,04 3,40 R 0,06 0,06 0,07 0,07 0,03,85,88,90,97,6

92 STATISTICS IN TRANSITION-nw sris, March 0 9 Tabl 3 show th rsults for th cas whn corrlation btwn th numbr of individuals by school in th fram and th numbr of individuals obsrvd is. In rfrnc to th bias, it is obsrvd that, in this cas thr is a strong bias in th two stimators that works undr nonrspons ( and in th stratum of high nonrspons (stratum. This is du to th fact that nithr th dsign nor th auxiliary variabls wr (nough corrlatd to th study variabls, so thy wr unabl to control th bias gnratd by th nonrspons. Evn so, th bias for is still small. Som commnts on th variancs in Tabl 3: Th incrmnt in th varianc of all th stimators for totals whn comparing with thos in Tabl is clar. Th varianc of th two stimators that works with auxiliary information and counts with a full sampl, and, is similar. This varianc is, indd, similar with that obtaind for th stimator. This rsult suggst that in this cas, th gain obtaind by th siz variabl (at th dsign stag and by th auxiliary vctor (at th stimation stag is ngligibl as a consqunc of th low corrlation btwn ths and th study variabls. Th ffct of nonrspons in th varianc is visibly gratr in th first stratum: compar and with and, rspctivly. This rsult is a consqunc of th low rspons probability in stratum and th low corrlation btwn th auxiliary variabls and th rspons distribution. Th varianc of th stimators whn stimating a ratio dos not show an incrmnt whn comparing with th rsults in Tabl ; onc mor, is th stimator with th smallr varianc. It is intrsting that although, and wr gnratd undr diffrnt conditions, th rsults ar not affctd by this fact. Th xplanation is that although is not includd dirctly in th survy, it is xplaind indirctly by th siz of th schools. In my opinion, th most intrsting rsult that is obtaind from th simulation study alrady dscribd is that, although th nonrspons hav visibl ffcts in bias and varianc of th stimators whn stimating totals (ffcts that bcoms vn biggr whn auxiliary information is not highly corrlatd with th survy variabls, this waknss dos not sm to b inhritd whn stimating a ratio: stimations ar still rliabl, no mattr th prsnc or absnc of powrful auxiliary information or th pattrns imposd on th nonrspons distribution.

93 9 E. M. B. Castllanos: Nonrspons bias in This is important for th undrstanding survy givn that ratios (proportions ar th most important paramtrs to b stimatd in it. Two aspcts wr takn into account in ordr to mak a choic on on of th approachs: handling of unit nonrspons (in trms of th bias and th varianc in th simulation study and th handling of itm nonrspons. Finally, it was dcidd to choos th Approach. Th rasons to mak this choic ar: With rgard to th bias, both stimators hav a similar bhavior: whn stimating totals th bias is small if thr is a high corrlation btwn th xpctd and obsrvd numbr of studnts; on th othr hand, th bias is qually grat for both stimators whn th corrlation is low. Whn stimating a ratio (proportion th bias is ngligibl for both stimators. With rgard to th varianc, again both stimators hav a similar bhavior: a small CV whn thr is a high corrlation btwn th xpctd and obsrvd numbr of studnts; a gratr CV whn this corrlation is low and an vn gratr CV whn thr is a low nonrspons. With rgard to th handling of itm nonrspons, it is strongly blivd that th mthodology usd in Approach ovrcoms to that usd in Approach, whr littl is don, whil in Approach th rlation btwn study variabls is usd to imput th missing valus. Handling of itm nonrspons in Approach crats a nw catgory for vry variabl, this catgory dos not corrspond to th original qustionnair, it is a consqunc of an unlucky although common- vnt: partially incomplt information on th rsponss of an individual. This nw catgory is not a problm in Approach, in which final tabls kps th structur xpctd at th momnt of th qustionnair dsign. This fact facilitats th rsults intrprtation. 5. Conclusions Although it is clar that nonrspons is an undsirabl, but almost invitabl vnt in any survy, in th undrstanding survy dvlopd by th OCyT thr was th fortun of idntifying a variabl associatd with its occurrnc: th natur of school. Givn that this variabl was considrd sinc th dsign stag as a stratification variabl, th ffct that nonrspons could hav on bias and varianc was rducd. Estimations for totals yilds clar diffrncs btwn both approachs, morovr, Approach yilds lowr stimats than Approach. Evn so, ths

94 STATISTICS IN TRANSITION-nw sris, March 0 93 diffrncs ar rducd whn stimating proportions. This rsult is consistnt with th simulations carrid out, whr proportions wr lss snsitiv to th stimator. Furthrmor, stimations for ratios happnd to b insnsitiv to dsign, stimator or rspons distribution. Although thr was not auxiliary information availabl at th lvl of individuals, availabl variabls at th lvl of school (natur of school, numbr of studnt in th last yar allowd to build stimators that rducd th ffct of nonrspons on th final stimations. Th pwr stimator for a probability proportional to siz -pps- dsign rsmbls th calibration stimator in th sns that it rproducs xactly th total of th siz variabl. A consqunc of this proprty is that, whn th slction probabilitis ar highly corrlatd to th study variabls, a rduction in bias and varianc gnratd by nonrspons is obtaind. Th rsults from th simulation study shows that both stimators hav similar bhaviors and that achivs satisfactorily th goal of controlling bias and varianc gnratd by nonrspons whn thr is a high corrlation btwn th xpctd and th obsrvd numbr of studnts in schools. Simulations shown in sction 4 allow to s th bhavior of both proposd stimators in a st of cass. Ths cass wr proposd in th contxt of th undrstanding survy and thy wr usful to mak dcisions on th stimators. Evn so, it is important to rcall that rsults must not b gnralizd, sinc thy dpnds on th simulatd population, considrd dsigns, auxiliary variabls includd, rspons distribution, and so on. REFERENCES DAZA, S. ED, (0. Entr datos y rlatos: prcpcions d jóvns scolarizados sobr la Cincia y la Tcnología. Obsrvatorio Colombiano d Cincia y Tcnología, Bogotá. HANSEN, M.H., and HURWITZ W.N. (943. On th thory of sampling from finit populations. Annals of Mathmatical Statistics 4, HORVITZ, D.G., and THOMPSON, D.J. (95. A gnralization of sampling without rplacmnt from a finit univrs. Journal of th Amrican Statistical Association 47,

95 94 E. M. B. Castllanos: Nonrspons bias in R Dvlopmnt Cor Tam, (0. A Languag and nvironmnt for Statistical Computing, http_// SÄRNDAL, C.E. and SWENSSON, B. and WRETMAN, J., (99. Modl Assistd Survy Sampling. Springr. SÄRNDAL, C.E. and LUNDSTRÖM, S., (005. Estimation in Survys with Nonrspons. Wily.

96 STATISTICS IN TRANSITION-nw sris, March 0 95 STATISTICS IN TRANSITION-nw sris, March 0 Vol. 3, No., pp CUMULATIVE SUM CONTROL CHARTS FOR TRUNCATED NORMAL DISTRIBUTION UNDER MEASUREMENT ERROR R. Sankl, J.R. Singh, I.K. Mangal 3 ABSTRACT In th prsnt papr Cumulativ Sum Control Chart (CSCC for th truncatd normal distribution undr masurmnt rror (r is discussd. Th snsitivity of th paramtrs of th V-Mask and th Avrag Run Lngth (ARL is studid through numrical valuation for diffrnt valus of r. Ky words: Truncatd Normal Distribution, Masurmnt Error, ARL and CSCC.. Introduction Th purpos of this papr is to show how truncatd data affct th fild prformanc of controlling manufacturing procss. Failur to account for truncation can lad to biasd infrncs. Cumulativ Sum (CUSUM Control Charts ar widly usd instad of standard Shwhart charts whn dtction of small changs in a procss paramtr is important. Patl and Gajjar (994 provid rfrncs on rsarch prformd on CUSUM charts. Errors of masurmnts ar th diffrncs btwn obsrvd valus rcordd undr idntical conditions and som fixd tru valus. Huntr (986 showd that finally all masurmnt should b tracabl to nation standard th most important ara for studying th ffct of masurmnt rror and misclassification in th sampling inspction plan and control charts. Most of th standard statistical tsts ar drivd on th assumption that th sampl is combind from a complt population. But this assumption appars to b an unralistic on. Truncations in th parnts distributions at on or both th School of Studis in Statistics, Vikram Univrsity, Ujjain (M.P., India. [email protected]. School of Studis in Statistics, Vikram Univrsity, Ujjain (M.P., India. [email protected]. 3 Madhav Scinc Collg, Ujjain (M.P., India.

97 96 R. Sankl, J.R. Singh, I.K. Mangal: Cumulativ sum tails may hav considrabl ffct on th CUCUM control charts. Woodroof (985 gav a comprhnsiv discussion of th xact stimation thory as wll as consistncy and asymptotic normality of th product limit stimator. Woodroof also survyd th history and application of this thory within astronomy but did not put it into th contxt of survival analysis. This was don by Wang t al. (986 and by Kiding and Gill (987 who wnt on to show how th xact and asymptotic proprtis of th stimators may b obtaind as corollaris from statistical thory of counting procsss and Markov procsss, and Nlson (990 strsss th distinction btwn truncation and cnsoring. Chang (990 and Schnidr (986 contain som basic rsults concrning th proprtis of th truncatd normal distribution. Johnson and Lon (96 considrd mathmatical procdur for construction of CUSUM Control Chart for Poisson variabl using th rlationship btwn Wald s Squntial Probability Ratio Tst (SPRT and CUSUM on th assumption that th probability of th scond kind of rror is small. Thy usd this rlationship to construct CUSUM charts for th man and standard dviation of a normal distribution. Yh t al. (004 gav a unifid CUSUM charts for monitoring procss man and variability. Cox (009 studid control charts for monitoring obsrvations from a truncatd normal distribution. Nns and Tagaras (00 valuatd th proprtis of a CUSUM chart dsignd for monitoring th procss man in short production runs. Grigg and Spiglhaltr (008 dvlopd an mpirical approximation to th null stady-stat distribution of CUSUM statistics. Ryu t al. (00 usd ARL-basd prformanc masur and proposd a mthod to optimally dsign a CUSUM chart basd on xpctd wightd run lngth. In this papr w hav constructd CUSUM chart for man undr truncatd normal distribution and masurmnt rror. For diffrnt truncation points and diffrnt sizs of masurmnt rror tabls hav bn prpard for th avrag run lngth, lad distanc and th angl of mask.. Dtrmination of mask paramtrs undr masurmnt rror Assuming that th tru masurmnt x and th random rror of masurmnt ar additiv, w can writ th obsrvd masurmnt X as (. whr x and ar indpndnt. Th constants θ (unknown and (known ar th man and th standard dviation of th tru quality masurmnt x and has th normal distribution, N (0,. Th corrlation cofficint btwn th tru and th obsrvd masurmnt can b writtn as (.

98 STATISTICS IN TRANSITION-nw sris, March 0 97 whr (say is th standard dviation of X, and th siz of th masurmnt rror (.3 Aftr som mathmatical manipulation Singh (984 showd that (.4 Lt x b th tru valu of th variabl which is distributd as (.5 whr (.6 and a and b ar th points of truncation with If ar m indpndnt random variabls whos probability dnsity function (p.d.f. is givn by (.5. Th liklihood ratio of th hypothsis against th altrnativ hypothsis is givn by (.7 whr Th continuation rgion of SPRT discriminating btwn th two hypothss, against is givn by (.8

99 98 R. Sankl, J.R. Singh, I.K. Mangal: Cumulativ sum whr For vry small valu of th right hand inquality of (.8 rducs to (.9 But for th obsrvd valus For constructing a CUSUM Chart for th man undr obsrvd masurmnts, w plot th sum against th numbr of obsrvations m. 3. Th ffct on th dimntions and th ARL of CUSUM chart for man of a truncatd normal distribution undr masurmnt rror A narrow V-mask will dtct chang mor quickly but it will giv mor frqunt fals alarms. On th othr hand, w could rduc th frquncy of fals alarms by widning th angl of mask, but th avrag run lngth for ral changs would b incrasd. Undr th masurmnt rror th paramtr of th mask, namly th angl of th mask and th lad distanc d ar givn by whr (3. (3.

100 STATISTICS IN TRANSITION-nw sris, March 0 99 and (3.3 For ARL w considr th situation whr th tru man has shiftd from to. For vry small valu of th ARL that is xpctd numbr of obsrvation bfor th chang from to is dtctd (s Mood and Graybill 963 is approximatly whr For obsrvd valus ( Tabulation of rsults and conclusions In Tabl-, Tabl- and Tabl-3 th angl of th mask, lad distanc and ARL for th man chart ar givn, assuming and th siz of th masurmnt rrors r=, 4, 6 and. Th truncation points hav bn takn as. Th valus of considrd ar 0., 0.4, 0.6, 0.8,.0,.5,.0,.5 and 3.0. Th valus of ar takn to b 0.05, 0.05, 0.0 and It is vidnt from th Tabl- that for fixd rang of truncation with incrasing magnitud of rror trm and, an angl of mask incrass. But for on sidd truncation angl of mask dcass for incras in rror trm and incrass with incras in. From tabls for lad distanc and ARL it is sn that as th siz of masurmnt rror incrass th lad distanc and ARL incrass for fixd rang of truncation in cas of symmtrical truncation. But for on sidd truncation it is obsrvd that thr is lss incras in lad distanc as compard to symmtrical truncation and rvrs is th cas for ARL i.. th dcras in ARL is sn with incras rror trm.

101 00 R. Sankl, J.R. Singh, I.K. Mangal: Cumulativ sum Tabl. Angl of th Mask for Man for diffrnt Truncation Points (a, b (a, b δ /r 4 6 (-.5,.5 (-.5,.5 (-, (0,.5 (0,

102 STATISTICS IN TRANSITION-nw sris, March 0 0 Tabl. Lad Distanc for Man for diffrnt Truncation Points(a, b and Masurmnt Error( r r δ /α 0 (a=-.5,b=.5 (a=-.5,b=

103 0 R. Sankl, J.R. Singh, I.K. Mangal: Cumulativ sum Tabl. Lad Distanc for Man for diffrnt Truncation Points(a, b and Masurmnt Error( r (cont. r δ /α 0 (a=-,b= (a=0,b=.5 (a=0,b=

104 STATISTICS IN TRANSITION-nw sris, March 0 03 Tabl 3. ARL for Man for diffrnt Truncation Points (a,b and Masurmnt Error( r r δ /α 0 (a=-.5,b=.5 (a=-.5,b=

105 04 R. Sankl, J.R. Singh, I.K. Mangal: Cumulativ sum Tabl 3. ARL for Man for diffrnt Truncation Points (a,b and Masurmnt Error( r (cont. r δ /α 0 (a=-,b= (a=0,b=.5 (a=0,b=

106 STATISTICS IN TRANSITION-nw sris, March 0 05 Also it is sn that th angl of mask incrass as th rang of th truncation is incrasd, and is biggr in cas of on sidd truncation. Th ARL and lad distanc dcass with incras in rang of truncation. With incras in th angl of mask incrass, whil th ARL and th lad distanc dcrass. Th ARL and lad distanc incrass as is dcasd and as is dcasd. For on sidd truncation w s that lad distanc is lss and angl of mask is gratr compard to symmtrical truncation. This shows that in cas of symmtrical truncation, as angl of mask is smallr, it will dtct chang mor quickly, but it will giv mor frqunt fals alarms, as sn by comparing tabl for ARL for rror fr cas for both symmtrical truncation and on sidd truncation. This papr considrd th normal distribution cas. For othr symmtrical distribution this modl will not b suitabl. W hav to dvlop anothr modl for othr symmtrical distribution. From th abov discussion it is clar that truncatd normal distribution undr masurmnt rror appars frquntly in quality control problms. In ordr to mt crtain spcification th supplir uss som tchniqu to nsur that th quality charactristic must satisfy rror fr obsrvations, rror pron data crat a srious problm for dtrmining th valu of th mask paramtr and th ARL. This papr may b practically implicatd within nginring, financ, mdicin, nvironmntal statistics, and many othr filds. REFERENCES A.B. YEH, D.K. LINAND and C. VENKATARAMANI. (004.Unifid CUSM Charts for Monitoring Procss Man and Variability, Quality Tchnology and Quantitativ Managmnt, Vol., No., pp CHANG, M.N. (990. Wak Convrgnc of a Slf Consistnt Estimator of th Survival Function with Doubly Cnsord Data, Annals of Statistics, 8: G.NENES and G. TAGARAS. (00. Evaluation of CUSUM charts for Finit- Horizon Procsss, Communication in Statistics-Simulation and Computation, Vol.39, Issu 3, pp HUNTER, J.S. (986. Th Exponntially Wightd Moving Avrag,Journal of Quality Tchnology, 8:03-0. J. H. RYU, H. WAN and S.KIM. (00. Optimal Dsign of a CUSUM Chart for a Man Shift Of Unknown Siz, Journal of Quality Tchnology, Vol.4, No.3, pp.-6.

107 06 R. Sankl, J.R. Singh, I.K. Mangal: Cumulativ sum JOHNSON, N.L. and LEONE, F.C. (96. Cumulativ Sum Control Charts: Mathmatical Principls Applid to thir Construction and Us Part II, Industrial Quality Control XIV(, pp.-8. KEIDING, N. and GILL, R.D. (987. Rsarch Rport No. 87/3, Statistical Rsarch Unit, Univrsity Copnhagn, Dnmark. M.A.A. COX. (009. Control charts for monitoring obsrvations from a truncatd normal distribution, Journal of Risk Financ, Vol. 0 Iss: 3, pp MOOD, A.M. & GRAYBILL, F.A. (963. Introduction to th Thory of Statistics; Mc Graw Hill Book Co.Inc. scond Edition. NELSON, W. (990. Hazard Plotting of Lft Truncatd Lif data, Journal of Quality Tchnology, : O,A.GRIGG and D.J. SPIEGELHALTER. (008. An Empirical Approximation to th Null Unboundd Stady-Stat Distribution of th Cumulativ Sum Statistic, Tchnomtrics, 50(4:50-5. PATEL, M.N. and GAJJAR, A.V. (994. Cumulativ Sum Control Charts for Intrvnd Gomtric Distribution, Intrnational Journal of Managmnt and Systms,0(:8-88. SCHEIDER, H. (986. Truncatd and Cnsord Sampls from Normal Distribution, Marcl Dkkr, Nw York. WOODROOFE, M. (985. Estimating a Distribution Function with Truncatd Data, Annals of Statistics, 3:

108 STATISTICS IN TRANSITION-nw sris, March 0 07 STATISTICS IN TRANSITION-nw sris, March 0 Vol. 3, No., pp DATA INTEGRATION AND SMALL DOMAIN ESTIMATION IN POLAND EXPERIENCES AND PROBLEMS Elżbita Gołata ABSTRACT Th aim of th study could b idntifid twofold. On th on hand, it was a prsntation of Polish xprincs as concrns th most important mthodological issus of contmporary statistics. Ths ar th problms of data intgration (DI and statistical stimation for small domains (SDE.On th othr hand, attmpts to dtrmin rlationship btwn ths two groups of mthods wr undrtakn. Givn convrgnc of th objctivs of both SDE and DI, that is: striving to incras fficincy of th us of xisting sourcs of information, simulation study was conductd. It was aimd at vrifying th hypothsis of synrgis rfrring to combind application of both groups of mthods: SDE and DI. Kywords: Small domain stimation, data intgration.. Aim of th study Th study was aimd at prsntation of Polish xprincs in Small Domain Estimation (SDE and Data Intgration (DI. This goal will b achivd in an indirct way. First, som basic rmarks concrning both mthods will b discussd pointing out similaritis and dissimilaritis, spcially in such dimnsions as: purpos, mthods and tchniqus, data sourcs, valuation and othr problms and thrats that appar with practical application. In gnral, both mthods ar usd to improv th quality of th statistical stimats, to incras thir substantiv rang and prcision using all availabl sourcs of information. It can b assumd that combind application of both mthods will rsult in synrgy ffcts on th quality of statistical stimats. Small Domain Estimation ar tchniqus aimd to provid stimats for subpopulations (domains for which sampl siz is not larg nough to yild dirct stimats of adquat prcision. Thrfor, it is oftn ncssary to us Poznan Univrsity of Economics, Dpartmnt of Statistics, al. Nipodlgłości 0, Poznań, Poland, -mail: [email protected].

109 08 E. Gołata: Data intgration indirct stimats that borrow strngth by using valus of variabls of intrst from rlatd aras (domains or tim, and somtims of both: tim and domains. Ths valus ar brought into th stimation procss through a modl. Availability of good auxiliary data and suitabl linking modls ar crucial to indirct stimats (Rao 005. Rviw of small ara stimation mthods is includd, among othrs, in such works as Gosh and Rao (994, Rao (999, 003, Pfffrmann (999 and Skinnr C. (99. Data Intgration could b undrstood as a st of diffrnt tchniqus aimd to combin information from distinct sourcs of data which rfr to th sam targt population. Moriarity and Schurn (00, p.407 indicatd that practical nds formd th basis for th dvlopmnt of statistical mthods for data intgration (Schurn 989. Among th basic studis in this subjct, th following should b mntiond Kadan (00, Rogrs (984 Winklr (990, 994, 995, 999, 00, Hrzog T. N., Schurn F. J., Winklr W.E. (007, D Orazio M., Di Zio M., Scanu M. (006 and Rasslr (00. Bcaus of th growing nd for complx, multidimnsional information for diffrnt substs or domains, in tims of crisis and financial constraints, data intgration is bcoming a major issu. Th problm is to us information availabl from diffrnt sourcs fficintly so as to produc statistics on a givn subjct whil rducing costs and rspons burdn and maintaining quality (Scanu 00. Both groups of tchniqus rfr to additional data sourcs that ar spcifically xploitd. Ths can b two data sts that ar obtaind from indpndnt sampl survys. Anothr, oftn ncountrd situation rfrs to th us of administrativ data rsourcs as rgistrs. In this cas data from rgistrs ar linkd to survy data. Via data intgration procss w can xtnd - nrich th information availabl from a sampl survy with data from administrativ rgistrs. In this way w nabl 'borrowing strngth from othr data sourcs at individual lvl, which, assuming a strong corrlation, allows for stimating from th sampl for domains at lowr aggrgation lvl than th on rsulting from th original sampl siz. This sms to b th most important connction btwn SDE and DI and th main advantag of th joint implmntation of both tchniqus. For this rason, an attmpt was mad to dtrmin rlationship btwn ths two groups of mthods. Givn convrgnc of th objctivs of both SDE and DI, that is: striving to incras fficincy of th us of xisting sourcs of information, simulation study was conductd. It was aimd at vrifying th hypothsis of synrgis in data quality and availability rsulting from combind application of both groups of mthods: SDE and DI. Th structur of th papr rflcts studis which hav bn takn to achiv th abov targt. First basic charactristics of both groups of mthods will b prsntd in th contxt of Polish xprincs which ar shortly dscribd in Sction of th papr. Spcial attntion was givn to th us of altrnativ data sourcs in Polish official statistics, spcially administrativ rgistrs in th contxt of population cnsus 0. This cnsus was th first survy dsignd to intgrat administrativ rgistrs and data from a 0% sampl. Nxt, two simulation studis which attmpt

110 STATISTICS IN TRANSITION-nw sris, March 0 09 to apply th indirct stimation mthodology for databass rsulting from th intgration of diffrnt sourcs will b discussd. In sction 3 stimation is conductd for linkd data from sampl survy and administrativ rcords. This cas is illustratd with th xprincs from MEETS Projct. Scond cas study prsntd in Sction 4 rfrs to linkd data from two survys. Procdurs usd in simulation studis ar discussd in mor dtail with rfrncs to th litratur. An mpirical assssmnt of th simulation studis will form th basis for final conclusions discussd in Sction 5.. Data Intgration and Small Domain Estimation in Poland For a long tim th nd to us altrnativ sourcs of information in Polish public statistics was not conscious. Excption may constitut such filds which traditionally mad us of administrativ rsourcs as justic statistics. But on th othr hand vn in such basic aras as vital statistics, th administrativ rcords wr not fully accptd. For xampl, th Cntral Population Rgistr PESEL, ovr th yars was not usd for constructing population projctions (Paradysz 00. Significant diffrncs wr obsrvd in th population structur by ag and plac of rsidnc according to official statistics stimats basd on cnsus structur and th rgistr (fig.. Th divrgnc masurd by th rlativ W L diffrnc t / Pt in th numbr of population stimats by official statistics (Lt and Population Rgistr (Pt for th city of Poznan at th nd of 000 (cf. formula (, amount to vn mor than 30%. ( Lt Pt 00 WL t / P t = ( Pt Thr highst rlativ diffrncs dsrv particular attntion. Th first is almost 8 prcntag of th surplus of population stimats in comparison with th rgistrd for thos at zro yars of ag (childrn bfor first yar. As this diffrnc rlats to th sam dgr for both sxs, it can b assumd that it stms from th dlay in births rgistr. Anothr charactristic is th xcss in population stimats for ag 8-5 yars. Th rason for this is probably du to rcognition by th cnsus of young popl (studnts or working in Poznan as prmannt rsidnts, although thy do not hav such status. But population rgistr rfrs to lgal status notifid by prmannt rsidnc. For popl ovr 5 yars, a systmatic dcras in th rlativ diffrncs can b noticd. This may indicat a rturn of prsons to thir plac of prmannt rsidnc, or lgalization of thir rsidnc bcaus of work or marriag. Th MEETS projct was conductd undr Grant Agrmnt No signd on btwn th Europan Commission and th Cntral Statistical Offic of Poland btwn and Th Projct was aimd at Modrnisation of Europan Entrpris and Trad Statistics, spcially to xamin th possibilitis of using administrativ rgistr to stimat ntrpris indicators.

111 0 E. Gołata: Data intgration Also, a significant ngativ diffrnc could b noticd btwn population stimats and rgistr for population agd about 85 yars and mor. This is probably rlatd to th undr-covrag of th ldrly in th National Cnsus of Population and Housing in 00. Confirmation of this hypothsis can b found in population tabls for subsqunt yars aftr th cnsus, in which ngativ numbrs of popl agd ovr 90 should b obsrvd, if dath by ag would b considrd for various lvls of spatial aggrgation. It follows that th dying prson wr not includd in th cnsus (Multivariat analysis of rrors, 008, p.3-4. Figur : Rlativ diffrncs btwn population stimats by official statistics (L t and Population Rgistr (P t, city of Poznan, Sourc: Tomasz Józfowski, Bata Rynarzwska-Pitrzak, 00. Changs in th intnsity of us of administrativ rcords took plac within th last fiv yars, during prparations for th National Cnsus of Population and Housing which was conductd from April to Jun 0. This cnsus was basd on th population rgistr but usd data from about 30 othr rgistrs. In addition, a survy on a 0% sampl allowd collction of dtaild information on dmographic and social structurs as wll as conomic activity. Among Polish main xprincs in SAE and DI on should mntion:. EURAREA Enhancing Small Ara Estimation Tchniqus to mt Europan nds, IST , Poznan Univrsity of Economics, ESSnt on Small Ara Estimation SAE , Statistical Offic in Poznan, ESSnt on Data Intgration DI , Statistical Offic in Poznan, 00 0

112 STATISTICS IN TRANSITION-nw sris, March 0 4. Modrnisation of Europan Entrpris and Trad Statistics MEETS , Cntral Statistical Offic, Exprimntal rsarch conductd by Group for mathmatical and statistical mthods in : Polish Agricultur Cnsus PSR 00 and National Cnsus of Population and Housing NSP 0 Data Intgration of Cntral Population Rgistr PESEL and Labour Forc Survy, July 009 Nonparamtric matching: datasts from a micro-cnsus and Labour Forc Survy, 0 Propnsity scors matching: Labour Forc Survy and Polish Gnral Social Survy PGSS to nlarg th information scop of th social data bas, May 0 Both groups of mthods: Data Intgration as wll as Small Domain Estimation rfr to additional data sourcs. In SDE auxiliary data is ndd to borrow strngth. To mt this rquirmnt, th additional, xtrnal data sourc should b a rliabl on. Typically, du to spcifid by law, ruls rgulating organization of th rgistrs, administrativ rcords data should satisfy this rquirmnt. It is also important, that in many cass, rgistrs provid population data and population total (though th population in task might b diffrntly dfind. On th othr hand, thr ar som small ara stimators that rquir domain totals. Thus, in th stimation procdur individual data is not always ncssary. To rsum, w bgin with applying small domain stimation mthodology with ara lvl modls. Firstly, w us intgratd data from sampl and rgistr, and scondly th cas of two intgrating sampls is considrd. In ach of th two cass a simulation study was conductd and small domain stimators: GREG, SYNTHETIC and EBLUP wr applid to intgratd data. In th nxt sction prsntation of xprincs in intgration sampl data with rgistrs rfr to rsults obtaind within th MEETS projct. In th following sction, study on intgration of two sampls was basd on a psudo-population data from Polish micro-cnsus 995. Th procss of stimating statistics for small domains applid in both sctions rlid on findings of th EURAREA projct. Th main task of th projct was to populariz indirct stimation mthods and to assss thir proprtis with rspct to complx sampling dsigns usd in statistical practic. In addition to conducting a dtaild analysis of th rsarch problm, th projct participants cratd spcialist softwar dsignd to implmnt stimation Of cours ach rgistr nds spcial valuation. For xampl, analysis conductd by Młodak and Kubacki (00 showd that matching data on individual farms for th nds of Agricultural Cnsus 00 showd larg discrpancis btwn various rgistrs and borrowing strngth was sriously disturbd. Th Europan projct ntitld EURAREA IST Enhancing Small Ara Estimation Tchniqus to mt Europan nds was part of th Fifth framwork programm of th Europan Community for rsarch, tchnological dvlopmnt and dmonstration activitis. Th projct was coordinatd by ONS Offic for National Statistics, UK with th participation of six countris: Th Unitd Kingdom, Finland, Swdn, Italy, Spain and Poland.

113 E. Gołata: Data intgration tchniqus dvlopd in th projct. Th softwar, with associatd thortical and tchnical documntation, was publishd on th Eurara projct wbsit (Eurara_Projct_Rfrnc_Volum, 004. Estimation within both sctions was conductd using th EBLUPGREG program. Dtail dscription of th stimation tchniqus usd in th study is givn in R. Chambrs and A. Sai ( Empirical valuation of SDE for linkd data - intgrating sampl data with rgistr - MEETS On of th goals of th MEETS projct was to highlight possibilitis of using administrativ rsourcs to stimat ntrpris 3 indicators in twofold way (Us of Administrativ Data for Businss Statistics (0: - to incras th stimation prcision - to incras th information scop by providing stimats taking into account kind of businss activity (PKD classification at rgional lvl. Data Intgration Th following administrativ systms constituting potntial sourcs for shorttrm and annual statistics of small, mdium and big ntrpriss wr idntifid, dscribd and usd as auxiliary data sourc in th stimation procss: Tax systm information systm conductd by th Ministry of Financ fd with data from tax dclarations and statmnts as wll as idntification rqust forms in th fild of: databas on taxpayrs of th prsonal incom tax PIT databas on taxpayrs of th corporat incom tax CIT databas on taxpayrs of th valu addd tax VAT National Taxabl Prsons Rcords KEP. Systm of social insuranc information systm conductd by th Social Insuranc Institution, th so-calld Comprhnsiv IT Systm of th Social Insuranc Institution (KSI ZUS fd with data from insuranc documnts concrning contribution payrs and th insurd Cntral Rgistr of th Insurd (CRU and Cntral Rgistr of Contribution Payrs (CRPS: rgistr of natural prsons (GUSFIZ rgistr of lgal prsons (GUSPRA. Th primary sourc of data on companis in Poland is th DG survy carrid out by Cntral Statistical Offic. This survy covrs all larg companis (of mor Th Eurara_Projct_Rfrnc_Volum (004 can b downloadd from Vijann A., Djrf K., Sőstra K., Lhtonn R., Nissinn K., 004, EBLUPGREG.sas, program for small ara stimation borrowing Strngth Ovr Tim and Spac using Unit lvl modl, Statistics Finland, Univrsity of Jyväskylä. 3 Th projct covrd ntrpriss mploying mor than 9 prsons.

114 STATISTICS IN TRANSITION-nw sris, March 0 3 than 50 mploys and 0% sampl of mdium-sizd ntrpriss (th numbr of mploys from 0 to 49 popl. In th rsarch th following data rfrring to DG survy wr usd: Th DG- databas dirctory - list of all small, mdium and larg conomic units usd as a fram DG- survy for 008. Th data availabl constitutd of ovr 80 fils of diffrnt siz and structur. For purposs of th study Dcmbr 008 was tratd as a rfrnc priod, as for this priod most information from administrativ databass was availabl. To match th rcords from diffrnt datasts, two primary kys wr usd: NIP and REGON idntification numbrs. Th purpos of intgration was to crat a databas, in which an conomic ntity would b dscribd by th largst possibl numbr of variabls. Th DG- dirctory from Dcmbr 008 was usd as a starting point. This data st was combind with information from th administrativ databass and DG- rporting. Th main obstacl to matching rcords wr missing idntification numbrs. Tabl. Rsults of intgrating datasts from statistical rporting and administrativ databass Voivodships Numbr of matchd rcords all sctions 4 sctions * DG- DG- DG- DG- dirctory dirctory Prcntag of unmatchd rcords Numbr of rcords with NIP duplicats Dolnoslaski ,7 37 Kujawskopomorski , 3 Lublski ,4 Lubuski ,4 7 Lodzki , 56 Malopolski ,6 45 Mazowicki ,5 67 Opolski ,7 7 Podkarpacki ,3 6 Podlaski ,9 7 Pomorski , 6 Slaski ,5 47 Switokrzyski ,8 4 It should b strssd that th REGON numbr is usd as th main idntification numbr for statistical sourcs, whil institutions such as th Ministry of Financ or th Social Insuranc Institution rly mostly on th NIP numbr.

115 4 E. Gołata: Data intgration Tabl. Rsults of intgrating datasts from statistical rporting and administrativ databass (cont. Voivodships Numbr of matchd rcords all sctions 4 sctions * DG- DG- DG- DG- dirctory dirctory Prcntag of unmatchd rcords Numbr of rcords with NIP duplicats Warminskomazurski ,7 7 Wilkopolski , 57 Zachodniopomorski ,7 3 Rmark: * Th study was rstrictd to th following four biggst PKD sctions: procssing industry, manufacturing, trad, transport. Sourc: Us of Administrativ Data for Businss Statistics, GUS, US Poznan 0. In th procss of databas intgration a spcial MEETS ral data st was cratd. It containd rcords about conomic ntitis rprsnting th four PKD sctions of conomic activity (manufacturing, construction, trad, transport, which participatd in th DG- survy in Dcmbr 008 and which wr succssfully combind with information from th th KEP, CIT, PIT and ZUS databass (tab.. Th databas was tratd as th population in th simulation study. Thr wr various rasons for multipl matching of NIP numbrs. In th cas of som ntrpriss, th ZUS rgistr containd or mor NIP numbrs for on REGON numbr. Th majority of rcords that couldn t b matchd wr thos rlating to small ntitis. For xampl, out,83 rcords of th DG- dirctory for th Wilkopolska voivodship that couldn t b matchd with rgistr rcords,,73 wr small ntitis. This indicats that th DG- dirctory is largly out of dat with rspct to ntrpriss mploying from 0 to 49 prsons. In th cas of mdium and big ntrpriss, which ar all subjct to th DG- rporting, th data This situation occurrd whn th activity of a givn ntrpris was carrid out by mor prsons, ach idntifid by a sparat NIP numbr. In th cas of th parnt businss unit and its local units, th first 9 digits of 4-digit REGON numbrs wr idntical. As DG- dirctory contains only 9-digit numbrs, idntifying th parnt businss unit, data intgration rsultd in combining information about th parnt businss unit as wll as othr rlatd local units prsnt in th databass. In Polish official statistics th catgory of mdium ntrpriss compriss conomic ntitis mploying from 0 to 49 prsons and thos mploying mor than 49 prsons ar rfrrd to as big. Accssion to th EU causd th ncssity of adjustmnt of national rgulations concrning th division of ntrprnurs to th Union s lgal articls, i.. Rcommndation of th Commission of 6 May 003 concrning th dfinition of micro-, small and mdium ntrpriss (Rcommndation 003/36/EC. Basing on lgal dfinitions th st of ntitis is dividd into th following groups: (i micro-ntrpriss mploying not mor than 9 prsons, (ii small ntrpriss mploying from 0 to 49 prsons, (iii mdium ntrpriss mploying from 50 to 49 prsons, (iv big ntrpriss mploying mor than 49 prsons.

116 STATISTICS IN TRANSITION-nw sris, March 0 5 ar rgularly updatd. In contrast, only 0% of small ntrpriss ar subjct to DG- rporting. Consquntly, it is impossibl to updat th DG- dirctory for this sction of ntrpriss Annual Rvnu PIT / CIT, 008 Annual Rvnu PIT l/ CIT Annual Rvn A. Scal fittd to units with th highst rvnu (limitd to PLN Annual Rv B. Scal not fittd to units with th highst rvnu (limitd to PLN Figur : Rlationship btwn th valus of accumulatd rvnu - from DG-, PIT or CIT rgistr, all units togthr 008. Sourc: G. Dhnl (0, pp Following th intgration of databass it was possibl to assss th quality of information providd by th statistical rporting. On notworthy fact was a considrabl numbr of conomic ntitis with th null valu for rvnu in th DG- survy and positiv valus of rvnu in th PIT and CIT databass (fig..a and.b. Most discrpancis btwn valus in th databass and thos in th DG- survy could b accountd for by a crtain trminological incompatibility btwn th dfinition of rvnu in ach of th data sourcs. In th DG- survy th variabl rvnu compriss only sals of goods and srvics producd by th ntrpris. Consquntly, if an ntrpris dosn t produc anything but acts only as a sals agnt, it arns no rvnu according to this dfinition. Scattrplot prsnting DG and PIT data (fig..a sm to cntr around th idntity lin. Howvr closr analysis rvals that th lin is formd largly by rlativly numrous units charactrizd by xtrm valus of rvnu. If ths units wr omittd by limiting rvnu to th lvl of PLN 0,000, th rsulting pictur is significantly diffrnt (fig..b. In addition to units, for which rvnu rportd in th DG- survy coincids with th valu rportd in tax rturn forms (y =y, on can s two othr pattrns. First, thr is a larg group of units rporting positiv rvnu in th DG- survy whil displaying missing or zro valus in th tax rgistr (rprsntd by dots lying on th X-axis. This Statistical offics hav only rgistration information at th start of conomic activity whn REGON numbr is assignd. Information about th activity closur has only bn systmatically availabl sinc th introduction of nw rgulations in 3 March 009.

117 6 E. Gołata: Data intgration phnomnon can partly b accountd for by th trminological discrpancy btwn th dfinition of rvnu in th DG- survy and th PIT/CIT tax rgistr. Anothr, qually larg group, is mad up of units whos rvnu rportd in tax rturn forms considrably xcdd valus rportd in th DG- survy (rprsntd by dots lying abov th idntity lin (y =y. It s worth noting that thr wr virtually no cass of units rporting lowr rvnu in tax rturn forms than in th DG- survy. In ordr to stimat slctd variabls of conomic ntitis thir spcific charactristics should b takn into account. On of th major challngs ar nonhomognous distributions. This rfrs both to variabls stimatd on th basis of sampl survys and thos coming from administrativ databass, which ar usd as auxiliary variabls in th stimation procss (fig. 3.A and 3.B. Th distribution of rvnu shows that a rlativly larg prcntag of conomic ntitis display zro valus. For xampl 9% of ntitis that participatd in th DG- survy rportd no rvnu. On th othr hand, many ntitis in PIT and CIT rgistr didn t hav information about rvnu. Businsss with missing or zro valus accountd for 4% of all units containd in th MEETS ral data st Nubmr of ntrpriss 4500 Numbr of Entrpriss Annual Rvnu Annual Rvnu A. DG data B. PIT or CIT Rgistr data Figur 3: Distribution of ntrpriss by annual rvnu, 008. Sourc: G. Dhnl (0, pp.57. Th ffct of outlirs on stimation can b significant, sinc in such situations stimators don t rtain thir proprtis such as rsistanc to bias or fficincy. Outlirs, non-typical data or null valus, howvr, ar an intgral part of ach population and cannot b dismissd in th analysis. For this rason, in addition to using th classic approach, work is bing don to dvlop mor robust mthods. Such mthods could b mntiond as GREG stimation, th modl of Chambrs Som basic statistical dscription might b additionally givn by th following charactristics: Annual rvnu DG-, 008: man 457, mdian 594, std , CV 86%; Annual rvnu PIT or CIT, 008: man 7947, mdian 54, std , CV 89%. Robust stimation mthodology, as mor complicatd and challnging to us, will b dalt with in mor dtaild in furthr studis.

118 STATISTICS IN TRANSITION-nw sris, March 0 7 or Winsor stimation (R. Chambrs, 996, R. Chambrs, H. Falvy, D. Hdlin, P. Kokic, 00 and Dhnl, 00. All variabls from th DG- survy and administrativ databass wr takn into account in modlling and corrlation analysis. Dspit of crtain discrpancis btwn variabl valus in th two sourcs corrlation was rgardd as strong. Simulation study was conductd on 000 sampls drawn from th MEETS ral data st according to th sampling dsign as th on usd by GUS. For ach sampl standard SDE stimators: GREG, SYNTHETIC and EBLUP wr applid to stimat rvnu and othr conomic indicators in th brakdown of PKD sctions at country and at rgional lvl. Estimation of rvnu by PKD sction Th rsults of stimating rvnu at th lvl of slctd PKD sctions ar prsntd in Tabls 4. Tabl contains xpctd valus obtaind in th simulation study aftr 000 rplications. Th last column contains man rvnu within ach sction in th MEETS ral data st. It is usd as th bnchmark to assss th convrgnc of stimats. Th actual assssmnt of stimation prcision and bias is possibl using information prsntd in tabls 3 and 4. Tabl : Th xpctd valu of stimators for rvnu, 008 Estimator PKD Sction DIRECT GREG SYNTHETIC EBLUP Population MEAN Manufacturing Construction Trad Transport Sourc: Golata (0. Tabl 3: REE of stimators for rvnu, 008 REE (% PKD Sction DIRECT GREG SYNTHETIC EBLUP Manufacturing Construction Trad Transport Sourc: Golata (0. Th stimators rfrrd to as standard in trms of EURAREA projct ar: dirct (Horvitz- Thompson, GREG (Gnralisd REGrssion, rgrssion synthtic and EBLUP (Empirical Bst Linar Unbiasd Prdictor stimators. All programming and stimation work was carrid out in th Cntr for Small Ara Estimation at th Statistical Offic in Poznan.

119 8 E. Gołata: Data intgration Th Man Squard Error (MSE of an stimator is a masur of th diffrnc btwn valus implid by an stimator and th tru valus of th quantity bing stimatd. MSE is qual to th sum of th varianc and th squard bias of th stimator. Th Rlativ Error of th Estimat (REE was calculatd on th basis of th MSE as a prcntag of th tru population valu of th task variabl (rvnu. Th absolut bias of th stimator (tab. 4 was dfind as th diffrnc btwn th xpctd and ral valu. Tabl 4: Absolut bias of stimators for rvnu, 008 Absolut bias of stimators PKD Sction DIRECT GREG SYNTHETIC EBLUP Manufacturing Construction Trad Transport Sourc: Golata (0. To assss th composit stimation on can us REE. This masur is basd on stimats of MSE, which can b compard with its ral valu, thus accounting for stimation prcision and bias. Th GREG and EBLUP stimators yildd similar stimats for ach of th PKD sctions. A significant improvmnt in stimation prcision was obsrvd. For manufacturing, whr th bst rsults wr obtaind, REE is at 0.3 % of th ral valu. Th bias of th GREG stimator is considrably lowr than that of th EBLUP stimator, which oftn yilds bttr gnral rsults owing to its lowr varianc. In th cas of th transport sction, howvr, non of th stimators usd producd bttr rsults than thos obtaind by mans of dirct stimation. Estimation of rvnu by PKD sction and rgions (64 domains in all Owing to limitd spac, th rsults wr confind to th xpctd valu of rvnu for two PKD sctions. Additionally, Figurs 4 (manufacturing and 5 (construction dpict diffrncs in th xpctd valu of stimators and th ral valus. Th rsulting discrpancis ar obvious, givn th natur of availabl data and th mthod usd, but thy ar largly compatibl with th ral valus. In simulation survy th approximat valu of MSE stimat was computd using th following formula prsntd by Choudhry, Rao, 993 p. 76.

120 STATISTICS IN TRANSITION-nw sris, March 0 9 Dolnośląski Dolnośląski Zachodniopomorski 9000 Kujawsko-pomorski Zachodniopomorski 4000 Kujawsko-pomorski Wilkopolski Lublski Wilkopolski 0000 Lublski Warmińsko-mazurski Lubuski Warmińsko-mazurski Lubuski Świętokrzyski 0 Łódzki Świętokrzyski 0 Łódzki Śląski Małopolski Śląski Małopolski Pomorski Mazowicki Pomorski Mazowicki Podlaski Opolski Podlaski Opolski Podkarpacki ŚREDNIA W POPULACJI EST.DIRECT EST. GREG EST. SYNTHETIC EST. EBLUP Figur 4: Expctd valu of stimators for rvnu, manufacturing by voivodship, 008 Sourc: Golata (0. Podkarpacki ŚREDNIA W POPULACJI EST.DIRECT EST. GREG EST. SYNTHETIC EST. EBLUP Figur 5: Expctd valu of stimators for rvnu, construction by voivodship, 008 Sourc: Golata (0. Tabl 5. REE of stimators for rvnu in th construction sction by voivodship, 008 Voivodship REE (% DIRECT GREG SYNTHETIC EBLUP Dolnośląski 3,09 9,79 7,0 9,5 Kujawsko-pomorski 40,0 5,49 3,7 4,08 Lublski 4,3 8,34 0,47 3,85 Lubuski 70,40,34,93,3 Łódzki 4,68 8,56 8,84 4,56 Małopolski 53, 4,7,5,68 Mazowicki 54,8 0,0 3,77 9,0 Opolski 56,66,50 30,7 7,60 Podkarpacki 39,0 8,79 39,5 3,0 Podlaski 58,30 73,6,77 9,4 Pomorski 9,56 9,8 4,54 8,47 Śląski 9,5 7,9 4,65,7 Świętokrzyski 36,00 34, 9,7 5,34 Warmińskomazurski 43,70,70 5,9 4,78 Wilkopolski 06,50 7,77 4,94 4,76 Zachodniopomorski 54,4 9,8,37 3, Sourc: Golata (0.

121 0 E. Gołata: Data intgration Masurs of prcision in tab. 5 show an vidnt improvmnt in fficincy du to th us of indirct stimation and auxiliary data from administrativ databass. Synthtic assssmnt of stimats for all domains by sction Whn th Rlativ Estimation Error (REE, tab. 6 is chosn as a masur of prcision, accounting for both prcision and bias with rspct to th ral valus in th MEETS ral datast, on can obsrv an intrsting tndncy. Th us of indirct stimation basd on auxiliary information from administrativ databass contributs significantly to th improvmnt in stimation prcision in th cas of such variabls as rvnu, numbr of mploys and wags. This improvmnt can b as much as 50% of th REE obtaind by applying dirct stimation. Tabl 6. Man REE for all domains by sction, 008 VARIABLE Estimator DIRECT GREG SYNTHETIC EBLUP Man REE for all domains (% Rvnu Numbr of mploys Wags wightd man REE for all domains (% Rvnu Numbr of mploys Wags Sourc: Golata (0 Synthtic assssmnt of stimats for all domains by sction and voivodship Whn stimation is conductd at a lowr lvl of aggrgation, on can gnrally xpct a dcras in stimation prcision. That was also th cas this tim. Valus of REE, usd as a masur of prcision with rspct to such variabls as rvnu, numbr of mploys and wags, indicat a significant improvmnt in comparison with dirct stimation (tab. 7. Th lowr valus of REE (a dcras from 35.5% to 3.6% (Wags or from 4.7% to 6.6% (Numbr of mploys obtaind as a rsult of using administrativ rgistr data is promising. Tabl 7. Man REE for all domains by sction and voivodship, 008 VARIABLE Estimator DIRECT GREG SYNTHETIC EBLUP Man REE for all domains (% Rvnu Numbr of mploys Wags

122 STATISTICS IN TRANSITION-nw sris, March 0 Tabl 7. Man REE for all domains by sction and voivodship, 008 (cont. VARIABLE Estimator DIRECT GREG SYNTHETIC EBLUP wightd man REE for all domains (% Rvnu Numbr of mploys Wags Sourc: Golata (0 Finally, th us of wights accounting for th significanc of larg and mdium ntrpriss has an vidnt ffct on th combind assssmnt of stimation prcision. 4. Empirical valuation of SDE for linkd data - intgrating two sampl data simulation study Th scond simulation study rfrrd to situation whn data from two sampls wr intgratd. It was basd on a ralistic population. A psudo-population using ral data form Polish micro-cnsus 995 was constructd. Th psudo-population was calld POLDATA and consists of individuals 5 yars or oldr groupd into 6 strata. But du to tim-consuming calculations, for th purpos of this xprimnt, th psudo-population was rstrictd only to thr strata, which rfr to th following thr voivodships: Dolnoslaski, Kujawskopomorski and Wilkopolski thus finally consistd of individuals. This psudo-population was th basis on which th sampling procdur was applid. Th study was aimd at stimation of labour markt status for NTS3 as domains. Prcisly th charactristics to b stimatd was th mploymnt rat dfind as th prcntag of mployd population 5 yars and oldr. Thrfor datast A could b compard to Labour Forc Survy (LFS, which du to small sampl siz dos not yild stimats for local labour markt (NTS3. Datast B is much largr in trms of th numbr of rcords, but unfortunatly dos not includ all variabls important in th labour markt analysis. Lack of ths variabls prvnts construction of th modl, which according to prvious xprinc, could b usd to stimat th ncssary charactristics. This scarcity can b rmovd by adding variabls obsrvd in datast A to datast B. Th dcision as to which fil should b th donor or th rcipint dpnds on th charactr of th study. In on approach, th fil with mor rcords is tratd as a rcipint, to prvnt a loss of information (Rasslr, 00. Othr Authors hav pointd out that duplication of information from a smallr st to largr raiss Th numbr of voivodships in Poland. Th Labour Forc Survy was not usd in th xprimnt, but sampl A was constructd to rsmbl th LFS and th sampl was drawn in a similar way. Sampl of typ A, though small, containing data for many variabls, rprsnts rlativly comprhnsiv charactristics of th population in task. It rsmbls Polish LFS, in which sampls covr about 0,05% of th population agd 5 yars and mor.

123 E. Gołata: Data intgration risk of duplication, and thus distorts th distribution (Scanu, 00. Both situations could b considrd. Th smallr datast bing th rcipint fil and th largr as donor, sms vn mor ralistic in SDE, spcially whn making us of administrativ rcords. Th study was conductd according to th following schma:. Two typs of random sampls wr drawn from th POLDATA in 00 rplicats: a. Sampl typ A wr drawn using two stag stratifid sampling dsign with proportional allocation. Th strata wr dfind as voivodships (NTS - according to th trritorial division of th country. Th primary stag units wr dfind as communs gminas (NTS5 and on scond stag individuals wr chosn. On th scond stag th simpl random sampling without rplacmnt (SRS was applid. Th ovrall sampl siz qualld to about %. b. Sampl typ B wr drawn with stratifid proportional sampling. Similarly as for sampl typ A, voivodships wr dfind as strata and thn 5% SRS was implmntd.. Th following variabls wr considrd: AREA VARIABLES: i. NUTS Voivodship 3 catgoris ii. NUTS 3 units AGE 3 catgoris: 0 = lss than 30 = = 45 and ovr GENDER catgoris: 0 = mal = fmal CIVIL STATUS 3 catgoris: 0 = divorcd or = marrid = singl widowd PLACE OF RESIDENCE 3 catgoris 0 = rural aras and towns of lss than thousands = town 50 thousands = town 50 thousands and ovr EDUCATION LEVEL 4 catgoris: 0 = univrsity = lmntary = vocational 3 = scondary LABOUR MARKET STATUS 4 catgoris: 0 = unmployd = mployd = conomically inactiv a. Sampls of typ A containd all th variabls listd abov b. Sampls of typ B missd information about ducation lvl Th sampling procdur was not xactly th sam as in cas of LFS, but also follows th two-stag houshold sampling. Sampling schm for th LFS dfins cnsus units calld cnsus clustrs in towns or numration districts in rural aras, as th primary sampling units subjct to th first stag slction. Scond stag sampling units ar dwllings.

124 STATISTICS IN TRANSITION-nw sris, March Bginning with this stp, th following stimation procdurs wr conductd: a. Th two random sampls A and B wr matchd. On of th simplst but also most frquntly usd nonparamtric procdur for statistical matching basd on k narst nighbours was applid (knn. And th stimation procdur usd wights according to Rubin (986 b. Th two random sampls A and B wr matchd using th knn and th stimation procdur applid spcial wights calibratd according to domains dfind for stimation 4. To th linkd data th EBLUPGREG program was applid and in ach run th following stimats of conomic activity for local labour markt (domains dfins as NTS3 wr obtaind: a. DIRECT b. GREG i. upon Sampl B with no ducation - rfrrd to as no ducation approach NE ii. upon Sampl B with ducation matchd and Rubin s wights approach - rfrrd to as imputd ducation approach IE iii. upon Sampl B with ducation matchd and calibration wights approach - rfrrd to as imputd ducation and calibration approach CIE c. SYNTHETIC i. upon Sampl B with no ducation - NE ii. upon Sampl B with ducation matchd and Rubin s wights approach - IE iii. upon Sampl B with ducation matchd and calibration wights approach - CIE d. EBLUP i. upon Sampl B with no ducation - NE ii. upon Sampl B with ducation matchd and Rubin s wights approach - IE iii. upon Sampl B with ducation matchd and calibration wights approach - CIE 5. Th stimats obtaind in ach run wr usd to provid th mpirical valuation of th stimation prcision with rfrnc to ral population valu: a. Empirical varianc b. Empirical bias c. Empirical REE Th intgration algorithm Sinc both databass wr sampls, thy most probably did not contain data about th sam prson, nor thy had a uniqu linkag ky. Consquntly, such As k =, th imputation mthod was rducd to distanc hot dck.

125 4 E. Gołata: Data intgration data sourcs could not b intgratd using th dtrministic approach. In ordr to achiv th dsird objctiv, statistical matching was implmntd. Th intgrating algorithm usually may b brokn down into 6 basic stps (D Orazio, Di Zio, Scanu (006:. Variabl harmonisation. Slction of matching variabls and thir standardization or dichotomization 3. Stratification 4. Calculation of distanc 5. Slction of rcords in th rcipint and donor datasts with th last distanc 6. Calculation of th stimatd valu of variabls Th harmonization of variabls involvs adjusting of dfinitions and classifications usd in both survys : datast A and datast B. Th fact that in th simulation conductd both sampls wr drawn from th sam psudo-population, allowd us to skip th harmonization stp. But th importanc of ths procdurs should b strssd. Th scond stag was slcting th matching variabls to stimat th masur of similarity btwn rcords. In our cas th following variabls wr slctd: gndr, ag, marital status and plac of rsidnc. As this st of variabls includs catgorical as wll as quantitativ variabls thir standardization and dichotomization was ncssary. So th qualitativ variabls wr transformd into binary ons. Th quantitativ variabl: ag was catgorizd and dichotomizd as wll. Th third stp was to stratify. Th strata was cratd on th basis of two variabls: NUTS3 and labour markt status. Thr was lvn NUTS3 subrgions in th population but du to small numbr of units two of thm wr mrgd. Altogthr thr wr 7 strata cratd: 9 subrgions (NUTS3 rgions 3 and 4, and also 4 and 4 wr mrgd x 3 attributs of th mploymnt status (mployd, unmployd, conomically inactiv. An important rason for stratifying th datast was to optimiz th computing tim. Th masur of rcord similarity usd in th intgration was th Euclidan Squard Distanc givn by th formula: d N Ki A, B = aaik abik i= k = whr: ( ( a binary variabls cratd in th procss of dichotomization of qualitativ Aik variabls (i-th catgory of k-th variabl. In spit of dividing th data st into strata, duration of th intgration procss amountd to about 6 hours (Intl Cor i5 procssor, 4 GB RAM.

126 STATISTICS IN TRANSITION-nw sris, March 0 5 For a givn rcord in rcipint fil, th algorithm sarchs for a rcord in donor fil for which th distanc masur is th smallst. Th choic of Euclidan Squard Distanc was motivatd by th us of th intgration algorithm dvlopd by Bachr (00. Th algorithm was modifid and adjustd for purposs of th simulation. Th study was prformd undr conditional indpndnc assumption (CIA. Th intgration algorithm yildd a datast containing 8 75 rcords (th numbr of rcords in Sampl B - th largr on and 7 variabls dscribing th dmographic and conomic charactristics of Polish population as listd abov. Rubin approach Survy data for stimation or intgration procss gnrally ar drawn from population according to complx sampling schma. Whn this is th cas, it is ncssary to adjust sampling wights in stimation procss. Thr ar thr diffrnt approachs: fil concatnation proposd by Rubin (986, cas wights calibration (Rnssn, 998 and Empirical Liklihood according to Wu (004. Rubin (986 suggstd to combin th two fils A and B into AB and calculat nw wight w AB for ach ith unit in th nw fil (with som corrctions. If th ith unit in th sampl A is not rprsntd in sampl B, than its invrs probability quals to zro (undr sampling schma B. In such cas wight of this unit in th concatnatd fil AB is simply its wight from sampl A - w Ai. This mans not only that th population in task is th union of A B, but also that th stimatd distributions ar conditional of Y givn (w AB ; Z and Z givn (w AB ; Y. In our study th fil A was not concatnatd to fil B. Th intgration procss to join A and B was to imput in B originally unobsrvd variabls Z that charactriz th lvl of ducation by using th valus of X, which wr obsrvd in both fils. Thus, as suggstd by Rubin, th wight of ach obsrvation in th st B rmaind unchangd. Calibration approach Whn sampls ar drawn according to diffrnt complx survy dsigns it is important to considr th wights to prsrv th distribution of th variabl in task. Espcially whn th survy is originally plannd for th whol population and finally th stimation is conductd for unplannd domains. Th impact of sampling dsigns for th fficincy in small ara stimation is a qustion difficult to answr du to many optimisation problms. According to Rao J.N.K., (003 most important dsign issus for small domain stimation ar such as: numbr of strata, construction of strata, optimal allocation of a sampl, slction probabilitis. This list can b nlargd by dfinition of optimisation critria, availability of strongly corrlatd auxiliary information, choic of All programming and calculations was mad by W. Roszka in th Dpartmnt of Statistics at th Poznan Univrsity of Economics.

127 6 E. Gołata: Data intgration stimators and so on. In practic it is not possibl to anticipat and plan for all small aras. As a rsult indirct stimators will always b ndd, givn th growing dmand for rliabl small ara statistics. Howvr, it is important to considr dsign issus that hav an impact on small ara stimation, particularly in th contxt of planning and dsigning larg-scal survys (Sarndal t al 99. According to Särndal (007 calibration is a mthod of stimating th paramtrs for th finit population, which applis nw calibration wights. Th calibration wights nd to b clos to th original ons and satisfy th so-calld calibration quation. Applying calibration wights to stimat paramtrs of th targt variabl is spcially ndd in cas of no occurrnc, no rspons or othr non-sampling rrors to provid unbiasd stimats. Ths wights may also tak into account rlation btwn th targt variabl and an additional on to adjust th stimats to th rlation obsrvd at global lvl. Thrfor th GREG stimator is widly usd in SDE. Additionally w proposd to vrify th impact of calibration wights taking into account all th matching variabls to adjust th stimats for domains. Suppos that th objctiv of th study is to stimat th total valu of a variabl, dfind by th formula (Szymkowiak 0: N Y = y, (3 i= i whr y i dnots th valu of variabl y for i - th unit, i =,, N. Lt us assum that th whol population U = {,, N} consists of N lmnts. From this population w draw, according to a crtain sampling schm, a sampl s U, which consists of n lmnts. Lt π i dnot first ordr inclusion probability π i = P( i s and d i = th dsign wight. Th Horvitzπ i Thompson stimator of th total is givn by: n Yˆ HT = di yi = d i yi. (4 s i= Small sampl siz might caus unsufficint rprsntation of particular domains in th sampl, and thrfor nabl dirct stimats. If information for th variabl y is not known for som domains thn th Horvitz-Thompson stimator would b charactrisd of high varianc. Calibration approach as a mthod of nonrspons tratmnt is dscribd in dtail in Särndal C E., Lundström S. (005 Estimation in Survys with Nonrspons, John Wily & Sons, Ltd. In practic it might occur, that th domain is vn not rprsntd in th sampl. In our simulation study such situation was not considrd.

128 STATISTICS IN TRANSITION-nw sris, March 0 7 Propr choic of th distanc function is ssntial for constructing calibration wights and th rsults obtaind. In our study th distanc function was xprssd by th formula which allows to find th calibration wights in an xplicit form: m ( wi di D( w, d =, (5 d i= i Effctiv us of calibration wights wi dpnds on th vctor of auxiliary information. Lt x,, xk dnot auxiliary variabls which will b usd in th procss of finding calibration wights. In our simulation study w usd calibration wights obtaind for ach domain using additional information from th psudopopulation. As auxiliary data th following variabls wr usd: gndr, KLM, ducation, ag, marital status and labour markt status. Lt: N X = x, dnot total valu for th auxiliary variabl x j, j ij i= whr x ij is th valu of j-th auxiliary variabl for th i-th unit T j =,, k, (6 N N N X = xi, xi,, xik (7 i= i= i= is known vctor of population totals for of auxiliary variabls. Th vctor of calibration wights w = ( w,, w T m is obtaind as th following minimization problm: w = argmin D v ( v, d, (8 subjct to th calibration constraints ~ X = X, (9 whr m m m T ~ X = wi xi, wi xi,, wi xik. (0 i= i= i= m T If th matrix i = dixi xi is nonsingular thn th solution of minimization problm (8, subjct to th calibration constraint (9 is a vctor of calibration wights w = ( w,, T, whos lmnts ar dscribd by th formula: w m m T T ( X Xˆ dixi xi xi wi = di di ( i= whr m m m T Xˆ = d ixi, d ixi,, d ixik ( i= i= i=

129 8 E. Gołata: Data intgration and x ( T i = x i,, xik (3 is th vctor consisting of valus of all auxiliary variabls for th i-th rspondnt i =,,m. Assssmnt of data intgration In th litratur thr ar diffrnt approachs to assss matching quality. Rasslr (00 proposd to assss th two fils as wll matchd if thy mt th critria for th distribution complianc and prsrvation of rlations btwn variabls in th initial and matchd fils. Th four critria spcifid by Rasslr ar: (i th tru, unknown distribution of matchd variabls Z is rproducd in th nwly cratd, synthtic fil; (ii th ral, unknown cumulativ distribution of th variabls ( X, Y, Z is maintaind in th nwly cratd, synthtic datast; (iii corrlation and highr momnts of th cumulativ distribution of ( X, Y, Z and a marginal distribution of ( X Y and ( X Z ar prsrvd; (iv at last marginal distributions of Z and ( X Z in th fusd fil ar prsrvd. In practic it might b difficult, or somtims vn impossibl to vrify all thos critria (D Orazio,00. Also th statistical infrnc mthods ar not always suitabl, spcially in cas of administrativ data. Tabl 8. Statistical charactristics of th numbr of matchs Statistical charactristics of th numbr of matchs (togthr with no-matchd rcords Ovr all sampls Man Std Mdian Mod Min Max MIN 3,80 5, Q 4,48 6, Q 4,95 6, Q3 5,35 7, MAX 6,39 9, Statistical charactristics of th numbr of matchs (no-matchd rcords omittd Ovr all sampls Man Std Mdian Mod Min Max MIN 5,64 5, Q 6,60 6, Q 6,99 7,8 5 5 Q3 7,53 8, 5 7 MAX 8,54 0, Sourc: own calculations.

130 STATISTICS IN TRANSITION-nw sris, March 0 9 In th simulation procss th man numbr of matchs ovr all sampls qualld to 3,8 for all rcords and 5,64 if th no-matchd rcords wr omittd (tab. 8. And th highst numbr of matchs amountd to 8,54 (no-matchd rcords omittd. In th study th following quality assssmnt masurs wr usd: - total variation distanc (D Orazio, Di Zio, Scanu, 006: - Bhattacharyya cofficint (Bhattacharyya, 943: whr: proportion of i-th catgory of a variabl in th fusd fil, - proportion of i-th catgory of a variabl in th donor fil. Both of ths cofficints ar in th rang of. In cas of total variation distanc, th lowr cofficint, th gratr distribution compatibility is achivd. Th valu indicating th accptabl similarity of distributions is commonly assumd as. Convrsly, th lowr th valu of th Bhattacharyya cofficint, th lowr th compatibility of distributions achivd. As th cofficint proposd by Bhattacharyya gnrally taks high valu, two othr masurs of structur similarity wr applid: (4 (5 and, (6 whr: th minimum proportion of i-th catgory in th fusd and donor fil, th maximum proportion of i-th catgory in th fusd and donor fil. Ths cofficints tak valus from th intrval and is gnrally gratr than. Th gratr th valu of any of ths cofficints, th gratr th compatibility of th distributions. Valus that indicat th accptabl similarity of distributions ar usually assumd to b and (Roszka 0. Tabl 9. Total variation distanc as matching quality masur Matching variabl Plac of Marital Sourc of Gndr rsidnc Status maintnanc MIN 0,0830 0,0000 0,0070 0,0040 Q 0,58 0,0030 0,09 0,050 Q 0,790 0,0050 0,060 0,098 Q3 0,0 0,000 0,0 0,045 MAX 0,90 0,070 0,0405 0,0370 Sourc: own calculations.

131 30 E. Gołata: Data intgration Tabl 0. Bhattacharyya cofficint as matching quality masur Matching variabl Plac of rsidnc Gndr Marital Status Sourc of maintnanc MIN 0,9355 0,9996 0,9976 0,9978 Q 0,9607 0,9999 0,9988 0,999 Q 0,969 0,9993 0,9995 Q3 0,9769 0,9996 MAX 0,996 Sourc: own calculations. Vry good matching quality cofficints wr achivd for th variabls gndr, marital status and sourc of maintnanc. Much wors quality masurs wr obtaind for th variabl plac of rsidnc (tab. 9 and 0. This rsults from th fact that class of plac of rsidnc variabl was charactrizd by a wakr compatibility prior to intgration. Th similarity cofficints prsntd in tab. 9 and 0 charactris th matching quality in a synthtic way. That is, ovr all rplications and additionally, thy do not tak into account diffrncs of distributions across domains. Compatibility of th distributions obsrvd for th whol sampl, of cours, do not translat automatically to all domains for which stimation of conomic activity was conductd in th nxt stag. Th discrpancy in th complianc applis to both individual sampls and domains. Typically, in th conformity assssmnt distribution of matching variabls is takn into account. In cas of a simulation study, thr was also th possibility to valuat distribution of th matchd variabl. Comparability of th distributions for th variabl in task ducation showd that th distributions wr prsrvd. Tabl provids th comparison of ducation distribution by domains in population with dirct stimats upon on xmplary sampl aftr matching variabl ducation. Th Bhattacharyya cofficint is gnrally clos to on, on avrag gratr than Only for domain 4, it taks valu lowr than 0.95 (in rd colour. For this spcific domain also th othr two similarity cofficints tak xcptionally low valus. But thir mor dtaild analysis indicats that th ducation distribution is wll maintaind only for thr domains (numbr:, 6 and 4. Th rsults prsntd rfr to th situation whn originally sampling wights wr applid. In cas of wights calibratd for domains, th distributions wr idntical.

132 STATISTICS IN TRANSITION-nw sris, March 0 3 Tabl. Education distribution by rgions in population and dirct stimats upon xmplary sampl with matchd variabl Proportion of population of th following ducation lvl NTS3 Exmplary sampl * Population BC(p f;p d W p W p Elmntary Vocational Scondary Univrsity Elmntary Vocational Scondary Univrsity 0,47 0,7 0,0 0,06 0,45 0,8 0, 0,06 0,9997 0,976 0,954 0,55 0,6 0,4 0,05 0,43 0,9 0, 0,06 0,987 0,867 0, ,54 0,9 0,8 0,08 0,47 0,30 0,8 0,04 0,9900 0,894 0, ,5 0,6 0,4 0,8 0,9 0,9 0,34 0,9 0,9967 0,93 0, ,49 0,9 0,6 0,05 0,4 0,3 0,0 0,06 0,9970 0,99 0, ,50 0,8 0,6 0,06 0,49 0,6 0,9 0,06 0,9994 0,97 0, ,5 0,6 0, 0,03 0,48 0,9 0,9 0,05 0,9980 0,95 0, ,46 0,33 0,6 0,06 0,4 0,33 0,9 0,06 0,9988 0,96 0, ,46 0,34 0,3 0,07 0,43 0,30 0,0 0,06 0,9944 0,94 0, ,5 0,5 0,7 0,05 0,5 0,5 0,9 0,05 0,9998 0,984 0, ,54 0,0 0,0 0,07 0,4 0,4 0,34 0,8 0,9467 0,705 0,545 All domains 0,49 0,7 0,8 0,06 0,44 0,8 0, 0,07 0,9990 0,956 0,96 * Th first sampl was compard Sourc: Own calculations Comparability of th distributions for th variabl in task ducation showd that th distributions wr prsrvd. Tabl provids th comparison of ducation distribution by domains in population with dirct stimats upon on xmplary sampl aftr matching variabl ducation. Th Bhattacharyya cofficint is gnrally clos to on, on avrag gratr than Only for domain 4, it taks valu lowr than 0.95 (in rd colour. For this spcific domain also th othr two similarity cofficints tak xcptionally low valus. But thir mor dtaild analysis indicats that th ducation distribution is wll maintaind only for thr domains (numbr:, 6 and 4. Th rsults prsntd rfr to th situation whn originally sampling wights wr applid. In cas of wights calibratd for domains, th distributions wr idntical. Domain Spcific Evaluation of Estimation Prcision Assssing th quality of th stimats from domain spcific prspctiv, on can tak into account both: singl sampl and avrag valus for ach domain upon 00 rplications. Th rsults obtaind for stimators usd in th study for diffrnt rsarch approachs: with imputd ducation and calibratd wights, ar rathr xtnsiv. Thrfor, du to th limitd scop, this articl dscribs only slctd rsults. Th xmplary stimats obtaind for domain in ach of 00 rplicats ar shown in fig 6.

133 3 E. Gołata: Data intgration Figur 6: Estimats of th prcntag of conomically activ, diffrnt stimators and rsarch approachs, Domain Sourc: Own calculations.

134 STATISTICS IN TRANSITION-nw sris, March 0 33 And fig. 7 rprsnts xpctd valus of th on slctd stimator (EBLUP for diffrnt approachs by domains. First, it could b noticd that calibratd wights applid to dirct stimator gav th tru valu in ach rplicat. As concrns th GREG stimator, th on with imputd ducation and calibratd wights rsultd in stimatd clos to th tru valu in all rplicats. Th variation of th stimats was also small. Combining GREG with synthtics stimator rsultd in a considrabl incras in EBLUP stimats variation, vn in comparison with dirct stimator. Figur 7: Expctd valu of th EBLUP stimator for diffrnt approachs by domains, Sourc: Own calculations. It is worth to noticd that thanks to th simulation approach, th rsults discussd could b analysd with rfrnc to th tru valu, which usually is unknown. Anothr rfrnc valus might constitut th stimats obtaind modl including ducation or not (fig. 7. No mattr which rfrnc valu would b chosn, th stimats taking into account th imputd ducation ar on avrag clarly ovrstimatd in two domains (4 and 4. Ths rsults confirm nd for carful valuation of intgration procss and convrgnc of th distribution of all variabls, spcially thos xploit as auxiliary. Synthtic Evaluation of stimation prcision ovr all domains Assssing th stimation prcision ovr all domains avrag valus of man and rlativ stimation rrors (MSE and REE obtaind for diffrnt rsarch approachs wr analysd.

135 34 E. Gołata: Data intgration Figur 8: REE(GREG for diffrnt rsarch approachs by domains Sourc: Own calculations. Figur 9. REE(SYNTH for diffrnt rsarch approachs by domains Sourc: Own calculations.

136 STATISTICS IN TRANSITION-nw sris, March 0 35 Figur 0: REE(EBLUP for diffrnt rsarch approachs by domains Sourc: Own calculations. As it coms from prsntation of rlativ stimation rror for GREG and EBLUP stimators across all domains: stimats including imputd ducation improv prcision obtaind (rd and yllow bars on fig. 8 and 0. Of cours, this statmnt should not b gnralisd, as in cas of SYNTH stimator, th prsntd rsults indicat just an opposd opinion (for ach domain, fig. 9. As th main issu in th study was to valuat th stimats for linkd data, th rsults obtaind for sampls with ral ducation, wr considrd for rfrnc purposs (prsntd in gry in tabls and. Howvr rsults obtaind for sampls with imputd ducation includd in th modl (with original or calibratd wights might also b compard to th ons with no ducation, as this rflcts mor ralistic situation. Tabl. MSE for diffrnt stimators and rsarch approachs Rsarch approach Typ of stimator DIR GREG SYNTH EBLUP DIR GREG SYNTH EBLUP Avrag of MSE ovr all domains Wightd avrag of MSE ovr all domains Education 0,036 0,05 0,008 0,008 0,07 0,0099 0,008 0,0094 No Education 0,036 0,00 0,0094 0,03 0,07 0,003 0,0093 0,0099 Imputd Education Imputd Education, Calibration Wights Sourc: Own calculations. 0,036 0,05 0,07 0,0 0,07 0,0098 0,06 0,0096 0,054 0,03 0,07 0,0 0,05 0,006 0,06 0,0096

137 36 E. Gołata: Data intgration Tabl. REE for diffrnt stimators and rsarch approachs Rsarch approach Typ of stimator DIR GREG SYNTH EBLUP DIR GREG SYNTH EBLUP Avrag of REE ovr all domains Wightd avrag of REE ovr all domains Education 0,08 0,039 0,07 0,03 0,04 0,005 0,069 0,096 No Education 0,08 0,048 0,095 0,035 0,04 0,03 0,09 0,005 Imputd Education 0,08 0,09 0,034 0,0 0,04 0,099 0,03 0,094 Imputd Education, Calibration Wights 0,038 0,073 0,034 0,0 0,059 0,00 0,03 0,094 Sourc: Own calculations. Similarly as in th simulation study for businss statistics, wighting th masurs of stimation prcision with domain siz, indicats on avrag highr quality assssmnt. It could b also noticd that stimators for small domains prform typically for linkd data qually as for ral data. Th prcision dpnds on th rlation of matchd variabl and th stimatd on. In prsntd study including imputd ducation into th modl slightly improvd stimats of th prcntag of conomically activ population. 5. Conclusions Data Intgration is usd to combin information from distinct sourcs of data which ar jointly unobsrvd and rfr to th sam targt population. Fusing distinct data sourcs to b availabl in on st nabls joint obsrvation of variabls from both fils. Th intgration procss is basd on finding similar rcords and th similarity is calculatd on th basis of common variabls in both datasts. Similarity of th ida concrning small domain stimation and data intgration tchniqus could b spcifid as follows :. Auxiliary information. Both tchniqus rfr to xtrnal data sourcs: - SDE in ordr to obtain auxiliary variabl that can hlp to improv stimation prcision for domains - DI to provid mor comprhnsiv data sts which allow for rducing th rspondnts burdn and bias rsulting. Joint application of both mthods might rsult in incrasing both: stimation prcision and th scop of information availabl, spcially in th contxt of small domains. But stimats on linkd data rquir good matching quality: - mthod for data intgration - dirct masur of consistncy of th distribution of matchd variabl is ndd This spcification is of cours, should not b considrd as full and final.

138 STATISTICS IN TRANSITION-nw sris, March arlir constrains hlp to avoid impropr valus - micro intgration procssing - calibration might b considrd as a mthod for adjusting sampl dsign to stimats for unplannd domains.. Corrlation and rgrssion. Th two data sourcs ar combind upon in-dpth corrlation analysis: - in SDE by modl-basd stimation for domains - in DI this corrlation is crucial in th matching procss for a common matching variabls and for b imputd - jointly unobsrvd variabl Z. Taking th abov into account, in both groups of mthods, variabl harmonisation is important. This involvs not only dfinition of th variabls, grouping and classification issus, but also dsignation of statistical units and rsulting aggrgation lvl for th analysis. Thus, th dangr of so calld cological fallacy or cological rror appars. Whn studying th rlationship btwn variabls that ar spcifid for diffrnt trritorial units, or at diffrnt lvls of aggrgation, th concpt of cological rror should b undrstood as taking th rlationship obsrvd at a highr lvl of aggrgation, as also valid at a lowr lvl. In practic, stimats for small aras frquntly usd rgrssion stimators, assuming tacitly that th tru valus of th paramtrs (β in th rgrssion quation at th lvl of individual units ar th sam as for th paramtrs obtaind from th man valus for th spatial units (Hady and Hnnl, 00, p. 5. But mpirical rsults show significant diffrncs. Typically, th corrlations obtaind at th aggrgat lvl ar much strongr than th ons obtaind for th individual units. This discrpancy in statistics is calld cological or nvironmntal ffct illusion (cological fallacy. Th possibility of rcognizing a varity of statistical units brings mthodological problm, namly how to stimat th rlation for a numbr of lvls simultanously. Application of th mixd modls might b considrd as on of th solutions suggstd to solv th problm and avoid th cological ffct. It should b strssd that th succss of any modl-basd mthod dpnds on distributions of stimatd variabls and covariats, corrlation analysis choic of good prdictors of th study variabls and modl diagnostic. 3. Sampling dsign. Oftn th two data sts ar obtaind from indpndnt sampl survys of complx dsigns, this raiss a numbr of mthodological problms: - in SDE with providing th sampling schma that would b optimal in stimation for domains and in assssing prcision of th stimats. According to Rao J.N.K. (003 most important dsign issus for small domain stimation ar th following: numbr of strata, construction of strata, optimal allocation of a sampl, slction probabilitis. This list can b nlargd by adding th problm of dfining th optimisation critria, possibilitis in obtaining strongly corrlatd

139 38 E. Gołata: Data intgration auxiliary information, choic of stimators taking into account thir fficincy undr spcific sampling dsigns. - in DI th sampling dsign cannot b ignord and diffrnt wights assignd to ach sampl unit must b considrd in ordr to prsrv th population structur and variabl distribution. In litratur Rubin s fil concatnation (986 or Rnssn s calibration (998 is proposd. Altrnativly Wu (004 suggsts mpirical liklihood mthod. 4. Stratification. In both mthods stratification has a significant maning. In SDE whr data ar drawn from population with no rspct to domains for which finally stimation is conductd, post-stratification could b considrd as a mthod of optimization th sampling schma. By introducing stratification in DI w optimiz th intgration procss by rducing th computing tim. 5. Thory & Practic. For both groups of mthods it is oftn obsrvd that situations obsrvd in practic do not corrspond to th thortical solutions. On th basis of th study conductd th following of thm could b mntiond: - High diffrntiation in corrlation across domains btwn variabls stimatd on th basis of DG- statistical rporting and auxiliary variabls from administrativ databass, including PIT and CIT - Th non-homognous distributions of stimatd variabls and covariat data may imply th nd for robust stimation (modifid GREG, Winsor and local rgrssion. This solution, howvr, is connctd with th highly complicatd and tim-consuming stimation tchniqus - Administrativ problms connctd with accss to auxiliary data, which limit thir usfulnss in short-trm statistics. 6. Estimats on linkd data. According to Rao (005, small ara stimation is a striking xampl of th intrplay btwn thory and practic. But h strsss that, dspit significant achivmnts, many issus rquir furthr thortical solutions, as wll as mpirical vrification. Among ths issus Rao points primarily on: a bnchmarking modl-basd stimators to agr with rliabl dirct stimators at larg ara lvls, b dvloping and validating suitabl linking modls and addrssing issus such as rrors in variabls, incorrct spcification of th modl and omittd variabls, c dvlopmnt of mthods that satisfy multipl goals: good ara-spcific stimats, good rank proprtis and good histogram for small aras. Similarly, Data Intgration is bcoming a major issu in most countris, with a viw to using information availabl from diffrnt sourcs fficintly so as to produc statistics on a givn subjct whil rducing costs and rspons burdn and maintaining quality. Howvr, th us of DI mthods rquirs not only furthr thortical solutions, but also many practical tsts. Typically, DI mthods sm to b undrstandabl and asy to us, but in practic significant complications occur.

140 STATISTICS IN TRANSITION-nw sris, March 0 39 Similarity of both mthods should b undrstood also as a st of common problms rquiring furthr rsarch and analysis that could nabl thir widr us in official statistics. REFERENCES BACHER, J. (00 Statistischs Matching - Anwndungsmöglichkitn, Vrfahrn und ihr praktisch Umstzung in SPSS, ZA-Informationn, 5. Jg. BALIN, M., D ORAZIO, M., DI ZIO, M., SCANU, M., TORELLI, N. (009 Statistical Matching of Two Survys with a Common Subst, Working Papr n. 4, Univrsita Dgli Studi di Trist, Dipartimnto di Scinz Economich Statistich. BRACHA, C z. (994 Mtodologiczn aspkty badania małych obszarów [Mthodological Aspcts of Small Ara Studis], Studia i Matriały. Z Prac Zakładu Badań Statystyczno-Ekonomicznych nr 43, GUS, Warszawa (in Polish. CHAMBERS, R., SAEI A. (003 Linar Mixd Modl with Spatial Corrlatd Ara Effct in Small Ara Estimation. CHAMBERS, R., SAEI A., 004, Small Ara Estimation Undr Linar and Gnralizd Linar Mixd Modls With Tim and Ara Effcts, Southampton Statistical Scincs Rsarch Institut. CHAMBERS, R.L, FALVEY, H., HEDLIN, D., KOKIC P. (00 Dos th Modl Mattr for GREG Estimation? A Businss Survy Exampl, in: Journal of Official Statistics, Vol.7, No.4, CHAMBERS, R.L. (996 Robust cas-wighting for multipurpos stablishmnt Survys in: Journal of Official Statistics, Vol., No., 3-3. CHOUDHRY, G.H., RAO, J.N.K. (993 Evaluation of Small Ara Estimators. An Empirical Study, in: Small Ara Statistics and Survy Dsigns, ds G. Kalton, J. Kordos, R. Platk, vol. I: Invitd Paprs, Cntral Statistical Offic, Warsaw. D ORAZIO, M., DI ZIO, M., SCANU, M. (006 Statistical Matching. Thory and Practic, John Wily & Sons, Ltd. DEHNEL, G. (00 Rozwój mikroprzdsiębiorczości w Polsc w świtl stymacji dla małych domn [Dvlopmnt of micro-businss in th light of stimation for small domains], Wydawnictwo Uniwrsyttu Ekonomiczngo w Poznaniu, Poznan (in Polish.

141 40 E. Gołata: Data intgration DEHNEL, G. (0 Us of Administrativ Data for Businss Statistics, Final Rport undr th grant agrmnt No , GUS, Warszawa. DEVILLE, J C. SÄRNDAL, C E. (99 Calibration Estimators in Survy Sampling, in Journal of th Amrican Statistical Association, Vol. 87, DI ZIO, M. (007 What is statistical matching, Cours on Mthods for Intgration of Survys and Administrativ Data, Budapst, Hungary. Eurara Projct Rfrnc Volum All Parts (004 Th EURAREA Consortium GHOSH, M., RAO J.N.K. (994 Small Ara Estimation: An Appraisal, Statistical Scinc vol. 9, no.. GOŁATA, E. (009 Opracowani dla wybranych mtod intgracji danych rguł, procdur intgracji danych z różnych źródł, [Dvlopmnt of slctd mthods for data intgration ruls, procdurs, data intgration from various sourcs]. GUS Intrnal matrials, Poznań, Poland (in Polish. GOLATA, E. (0 A study into th us of mthods dvlopd by small ara statistics in: Us of Administrativ Data for Businss Statistics (pp.84-, G. Dhnl (d., Final Rport undr th grant agrmnt No , GUS, Warszawa. HEADY, P., HENNEL S. (00 Small Ara Estimation and th Ecological Effct Modifying Standard Thory for Practical Situations, Offic for National Statistics, London, IST EURAREA, Enhancing Small Ara Estimation Tchniqus to Mt Europan Nds. HERZOG, T. N., SCHEUREN, F. J., WINKLER, W.E. (007 Data Quality and Rcord Linkag Tchniqus, Springr Nw York. KADANE, J.B. (00 Som Statistical Problms in Mrging Data Fils, Journal of Official Statistics, No. 7, LEHTONEN, R., VEIJANEN, A. (998 Logistics Gnralizd Rgrssion Estimators, Survy Mthodology, vol. 4. MŁODAK, A., KUBACKI, J. (00, A typology of Polish farms using som fuzzy classification mthod, Statistics in Transition nw sris, vol., No. 3, pp MORIARITY, C., SCHEUREN, F. (00 Statistical Matching: A Paradigm for Assssing th Uncrtainty in th Procdur in: Journal of Official Statistics, No. 7,

142 STATISTICS IN TRANSITION-nw sris, March 0 4 Multivariat analysis of systmatic rrors in th Cnsus 00, and statistical analysis of th variabls of NC 00 supporting th us of small ara stimats. J. Paradysz (d., Rport for Cntral Statistical Offic, Novmbr 008, Cntr for Rgional Statistics, Univrsity of Economics in Poznan (in Polish PARADYSZ, J. (00, Koniczność stymacji pośrdnij na użytk spisów powszchnych, [Ncssity of indirct stimation in national cnsus] in: Pomiar i informacja w gospodarc [Masurmnt and Information in th Economy] Gołata (d. publishd by Poznan Univrsity of Economics (in Polish. PFEFFERMANN, D. (999 Small Ara Estimation Big Dvlopmnts, in: Small Ara Estimation, Intrnational Association of Survy Statisticians Satllit Confrnc Procdings, Riga 0- August 999, Latvia. PIETRZAK-RYNARZEWSKA, B., JOZEFOWSKI, T. (00 Ocna możliwości wykorzystania rjstru PESEL w spisi ludności, [Assssmnt of th possibilitis of using population rgistr in th cnsus] in: Pomiar i informacja w gospodarc [Masurmnt and Information in th Economy], Gołata (d. publishd by Poznan Univrsity of Economics (in Polish. RAESSLER S. (00 Statistical Matching. A Frquntist Thory, Practical Applications, and Altrnativ Baysian Approachs, Springr, Nw York, USA. RAO, J.N.K. (999 Som Rcnt Advancs in Modl-Basd Small Ara Estimation in: Survy Mthodology, vol. 5, Statistics Canada. RAO, J.N.K. (003 Small Ara stimation, Wily-Intrscinc. RAO, J.N.K. (005 Intrplay Btwn Sampl Survy Thory and Practic: An Appraisal, Survy Mthodology, Vol. 3, No., RENSSEN, R. H. (998 Us of Statistical Matching Tchniqus in Calibration Estimation in: Survy Mthodology, Vol. 4, No., 7 83, Statistics Canada. ROSZKA, W. (0 An attmpt to apply statistical data intgration using data from sampl survys in: Economics, Managmnt and Tourism, South-Wst Univrsity Nofit Rilsky Faculty of Economics and Tourism Dpartmnt, Duni Royal Rsort, Bulgaria. RUBIN, D. B. (986 Statistical Matching Using Fil Concatnation with Adjustd Wights and Multipl Imputations, in: Journal of Businss and Economic Statistics, Vol. 4, No., 87 94, stabl URL: SäRNDAL, C.E., SWENSSON B., WRETMAN J. (99 Modl Assistd Survy Sampling, Springr Vrlag, Nw York. SÄRNDAL, C. E. (007 Th Calibration Approach in Survy Thory and Practic in: Survy Mthodology. Vol. 33, No., SÄRNDAL, C E., LUNDSTRÖM S. (005 Estimation in Survys with Nonrspons, John Wily & Sons, Ltd.

143 4 E. Gołata: Data intgration SCANU, M. (00 Introduction to statistical matching in: ESSNt on Data Intgration. Draft Rport of WP. Stat of th art on statistical mthodologis for data intgration, ESSNt. SCHEUREN, F. (989 A Commnt on Th Social Policy Simulation Databas and Modl: An Exampl of Survy and Administrativ Data Intgration, Survy of Currnt Businss, SKINNER, C. (99 Th Us of Estimation Tchniqus to Produc Small Ara Estimats, A rport prpard for OPCS, Univrsity of Southampton. SZYMKOWIAK, M. (0 Assssing th fasibility of using information from administrativ databass for calibration in short-trm and annual businss statistics in: Us of Administrativ Data for Businss Statistics (0 Final Rport undr th grant agrmnt No , GUS, Warszawa. Us of Administrativ Data for Businss Statistics (0 G. Dhnl (d., Final Rport undr th grant agrmnt No , GUS, Warszawa. VAN DER PUTTEN, P., KOK, J. N., GUPTA, A, (00 Data Fusion through Statistical Matching, Cntr for Businss, MIT, USA. VEIJANEN, A., DJERF, K., SŐSTRA, K., LEHTONEN, R., NISSINEN, K. (004 EBLUPGREG.sas, program for small ara stimation borrowing srngth ovr tim and spac using unit lvl modl, Statistics Finland, Univrsity of Jyväskylä. WALLGREN, A., WALGREN, B. (007 Rgistrd basd Statistics Administrativ Data for Statistical Purposs, John Wily & Sons Ltd. WINKLER, W.E. (990 String Comparator Mtrics and Enhancd Dcision Ruls in th Fllgi-Suntr Modl of Rcord Linkag, in: Sction on Survy Rsarch Mthods, , Amrican Statistical Association. WINKLER, W.E. (994 Advancd Mthods For Rcord Linkag, Burau of th Cnsus, Washington DC WINKLER, W.E. (995 Matching and Rcord Linkag, in: Businss Survy Mthods, B. Cox d , J. Wily, Nw York. WINKLER, W.E. (999 Th Stat of Rcord Linkag and Currnt Rsarch Problms, RR99-04, U.S. Burau of th Cnsus, WINKLER, W.E. (00 Quality of Vry Larg Databass, RR00/04, U.S. Burau of th Cnsus. WU, CH. (005 Algorithms and R Cods for th Psudo Empirical Liklihood Mthod in Survy Sampling in: Survy Mthodology, Vol. 3, No.,

144 STATISTICS IN TRANSITION-nw sris, March 0 43 STATISTICS IN TRANSITION-nw sris, March 0 Vol. 3, No., pp CUSTOMERS RESEARCH AND EQUIVALENCE MEASUREMENT IN FACTOR ANALYSIS Piotr Tarka ABSTRACT Factors Analysis is oftn tid to spcific proprtis of population and its cultur charactristics. If masurmnt is applid from population to anothr, thn xtractd factors may hard to b qually compard on th rflctiv basic lvl, unlss all conditions of invarianc masurmnt ar mt. Hnc, implmntation of customrs rsarch and any intr-cultural studis rquir a multi-cultural modl dscribing statistical diffrncs in both culturs with invarianc as undrlying assumption. In th articl w implmnt a modl for analysis of customrs prsonal valus prtaining to hdonic consumption aspcts in two culturally opposit populations. W conductd survy in two countris and th following citis: Poland (Poznan and Th Nthrlands (Rottrdam and Tilburg with randomly prpard sampls with youth rprsntativs on both sids. This modl prmittd us for tsting invarianc masurmnt undr cross-group constraints and thus xamining structural quivalnc of latnt variabls - valus.. Introduction On of th main problms in most of socio-conomic rsarch is th masurmnt of quivalnc prtaining to sampls drawn from th diffrnt populations. Equivalnc as a word rlats to on of th catgoris of quality assssmnt in studis whn scors obtaind from.g., two populations ar st for comparison. Equivalnc of a masurmnt is rlatd to th assssmnt of th xtnt to which masurmnts ar mad in th tstd groups using th sam units and masurs, distribution scors rlating to th sam charactristics of rspondnts according to various conditions and contxt of mad obsrvation (.g., basd on socio-conomic factors, or fram of tim. Th masurmnt is thrfor charactrizd by invarianc lvl. In th absnc of invarianc in Poznan Univrsity of Economics, Dpartmnt of Markting Rsarch, al. Nipodlgłości 0, Poland. [email protected].

145 44 P. Tarka: Customrs rsarch masurmnt, any diffrncs btwn individuals and populations cannot b rasonably intrprtd as comparisons in any multi-group studis. This is particularly important in studis whn w us units of masurmnt that ar rlativ and convntional, associatd with th rspondnts adoptd own indpndnt systm rfrnc (Sagan, 005; Tarka, 00.. Undrlying assumptions of invarianc masurmnt Tabl shows th main typs of invarianc rsarch occurring at all stags of th rsarch procss. Th issu of masurmnt invarianc is crucial for studis that ar aimd to invstigat group diffrncs. Cross-cultural mthodologists hav mphasizd that group comparisons assum invarianc of th lmnts of th masurmnt structur (i.., factor loadings and masurmnt rrors and of rspons biass (Billit, 00; Littl t al., 006. And group comparisons within a singl cultur also rquir masurmnt invarianc to insur that potntial diffrncs (.g., in th mans or rgrssion cofficints can b intrprtd rliably (Vandnbrg and Lanc, 000. Sub-groups within populations ar oftn htrognous with rgard to th paramtr valus of a modl. Nonthlss, most within-socity rsarch continus implicitly to assum homognity of th population (Muthén, 989. This is spcially happning in th fild rsarch prtaining to convninc sampls of social, ducational, or occupational sub-groups. Ths groups oftn diffr from on anothr or from th ovrall population with rgard to masurmnt or structural paramtrs. In th worst cas, rsarchrs masur diffrnt constructs in th groups. Hnc, within-socity studis should assss possibl lack of masurmnt invarianc, whn possibl, to uncovr potntial population htrognity. Rsarchrs usually assum invarianc of th structur of thir masurs as thy compar thm across th groups. Th validity of this assumption is critical for any conclusions about group rlatd diffrncs (Vandnbrg and Lanc, 000. If it is not tru, on cannot vn claim that th construct is th sam in th diffrnt groups (Littl t al., 006. Thus, lgitimat comparison of mans or structural rlations across groups rquirs invarianc of th masurmnt structurs undrlying th indicators (Ployhardt and Oswald, 004; Thompson and Grn, 006.

146 STATISTICS IN TRANSITION-nw sris, March 0 45 Tabl. Gnral catgoris for invarianc masurmnts in diffrnt populations Catgoris of intrcultural quivalnc tst Invarianc of th rsarch problm Translation invarianc Masurmnt invarianc Sampl invarianc Data collction invarianc Sourc: Sagan, 005. Typs of quivalnc in th catgory Concptual Functional Lxical Idiomatic Grammar Pragmatic Global Structural Mtric Scalar Masurmnt rrors Sampling units Rprsntativnss Communication with th rspondnt Contxt Styl and attitud rspons Dscription Th idntity of th constructs xamind Th similarity function of concpts and actions, prdictiv validity Th importanc of vocabulary trms Th importanc of mobil and customary trms Th adquacy of grammatical structurs Th importanc of colloquial words in vryday lif and action Th similarity of th covarianc matrix Th adquacy of masurmnt modls Comparability of masurmnt units Similarity masurmnt scal Homognity of th impact of spcific factors Comparability of sampling units Complianc oprational units, th dimnsions of socio-dmographic stratification Th similarity of bhaviour pattrns, th dfinition of privat and public sphrs Commonality of qustions of cultural contxt, th aras of social taboos and prmissions Consistncy and similarity of rsponss to th posd qustions and thms nonrspons 3. Procss of invarianc masurmnt Tabl shows th main typs of invarianc rsarch occurring at all stags of th rsarch procss. Th issu of masurmnt valuation basd on invarianc bgins with sris of conductd tsts whr on chcks th hypothss rlatd to disprsions among th groups. Ths tsts should b carrid out in a squnc, bcaus th bad modl fit, maks anothr baslss tsting masuring th lvl of cross-cultural quivalnc (Mrdith, 993; Sagan 005. As a rsult w obtain

147 46 P. Tarka: Customrs rsarch configural invarianc of th whol factorial structur and mtric invarianc of th factor loadings which ar critical for th intrprtation of constructs and ar rquisits for all othr masurmnt. Configural invarianc implis th sam numbr of factors in ach group and th sam pattrn of fixd and fr paramtrs. It is a prrquisit for th othr tsts. It is th vry basic form of invarianc and it asssss whthr w find th sam pattrns of loading btwn indicators and factors in both groups. Th paramtr rstrictions only rfr to th pattrns of loading and non-loading. Configural invarianc is assumd if th sam itms masur th sam factors in both groups. If configural invarianc is not supportd mpirically, thr ar fundamntal distinctions in th masurmnt structur, which mans that th manifst variabls masur diffrnt latnt variabl. Th mtric invarianc is mor stringnt in comparison to th configural invarianc, as additional rstrictions ar adoptd. Mtric invarianc mans that, in addition to th conditions of configural invarianc for all groups, th factor loadings ar quivalnt. If th modl of mtric invarianc is maintainabl, th manifst variabls masur th latnt variabls qually wll. If th modl fit of th mtric invarianc modl dos not dcras significantly, mtric invarianc of all itms can b assumd. Givn a mtric invarianc, th contnts of th factors ar assumd to b quivalnt. Likwis, th rlations of th variabls with othr variabls may b compard across th groups (Bolln, 989. Th tst of mtric invarianc is conductd by comparing th fit of th mtric and configural invarianc modls to th data with chi-squar statistics. Furthr modrn indications for invarianc ar diffrncs in th indics such as Comparativ Fit Indx (CFI, Root Man Squar Error of Approximation (RMSEA, and Standardizd Root Man Rsidual (SRMR. Mtric invarianc implis qual factor loadings across groups. For instanc, th paramtr λ ij - rprsnting factor loading must b th sam in groups.g., A and B. And this is tstd by imposing quality constraints on th Λ - matrics that contain th factor A B G loadings (i.., Λ =Λ =... Λ, whr suprscripts rfr to groups A to G. Equal factor loadings indicat that th groups calibrat thir masurs in th sam way. Hnc, th valus on th manifst scal hav th sam maning across groups. Mtric invarianc concrns a construct comparability that mtric invarianc is a strictr condition of construct comparability. According to th common factor prspctiv, th factor loadings indicat th strngth of th causal ffct of th latnt variabl ξ j on its indicators and can b intrprtd as validity cofficints (Bolln, 989. Significantly diffrnt factor loadings imply a diffrnc in th validity cofficints. This raiss concrns about whthr th constructs ar th sam across groups. Hnc, configural invarianc, by providing vidnc that th construct is rlatd to th sam st of indicators, is a prrquisit for infrring that th construct has th similar maning. Howvr, mtric invarianc is ncssary to infr that th construct has th sam maning, bcaus it provids vidnc about th quality of validity cofficints.

148 STATISTICS IN TRANSITION-nw sris, March 0 47 Additionally, scalar invarianc rfrs to invarianc of th itm intrcpts in th rgrssion quations that link th indicators g g x to thir latnt variabl ξ. i j Itm intrcpts can b intrprtd as th systmatic biass in rsponss of a group to an itm. As a rsult, th manifst man can b systmatically highr or lowr (upward or downward biasd than on would xpct du to th groups latnt man and th factor loading. Scalar invarianc is prsnt if th dgr of up- or downward bias of th manifst variabl is qual across groups. It is absnt if on of th groups diffrs significantly in on or mor of th itm intrcpts. To tst for scalar invarianc, on constrains th tau-vctors to b qual across groups τ A = τ B =... τ G. Thn, w follow invarianc of factor varianc / covarianc, which appars whn groups hav th sam variancs in thir rspctiv latnt variabls. This is A B G tstd by constraining th diagonal of th phi-matrics φjj = φjj =... φjj, to b qual. And invarianc of th factor covariancs rfrs to quality of th associations among th latnt variabls across groups. It is tstd by constraining th sub-diagonal lmnts of th phi-matrics φ A B... G jk = φjk = φjk, to b qual. Covariancs among constructs hav implications for th constructs maning or validity (Cronbach and Mhl, 955. Hnc, unqual covariancs rais concrns about th quality of construct manings (Col and Maxwll, 985. As far as th analyss of invarianc of th latnt mans ar concrnd, thy ar conductd in ordr to tst for diffrncs btwn groups (or points of tim in thir latnt mans. In contrast, traditional approachs to th analysis of man diffrncs us composit manifst scors and mploy t tsts, ANOVA, or MANOVA. Th validity of tsting group diffrncs in manifst scors dpnds on whthr th assumptions that undrli such comparisons ar corrct, spcifically, that both th factor loadings and th itm intrcpts ar qual (i.., mtric and scalar invarianc (Tarka, 0. Th rlationship btwn a latnt and obsrvd man or an xpctd obsrvd valu can b writtn as follows: g g g g E( xi = τi λκ i i. ( whr: g E x - xpctd valu of th i-th manifst indicator in group g, ( i g κ - is th man of factor i f in group g to b considrd in th tsts rlatd with latnt mans comparison of th particular groups. It shows that a manifst man dpnds not only on its latnt man but also on th factor loading and th itm intrcpt. Thus, a manifst man diffrnc can b causd ithr by a latnt man diffrnc or a diffrnc in th loadings, intrcpts, or both. Thrfor, a tst of latnt man diffrnc rquirs th quality of both th factor loadings and itm intrcpts. Th quality of th latnt mans is A B G tstd by constraining th kappa matrics κ = κ =... κ, to b qual across groups.

149 48 P. Tarka: Customrs rsarch Finally, a masurmnt of rrors invarianc concrns th hypothsis that A B G th masurmnt rror in th manifst indicators Θ =Θ =... Θ, is th sam across groups. 4. Factor analysis modl for two populations In factor analysis modl w considr a st of m populations Π, Π,..., Π m. Thy may b diffrnt nations, or culturally diffrnt groups, groups of individuals slctd on th basis of som known or unknown slction variabl, groups rciving diffrnt tratmnts, tc. In fact, thy may b any st of xclusiv groups of individuals that ar clarly dfind. And it is assumd that a battry of tsts has bn administrd to a sampl of individuals from ach population. Th battry of tsts nd not b th sam for ach group, nor nd th numbr of tsts b th sam. Howvr, sinc w shall b concrnd with charactristics of th tsts that ar invariant ovr populations, it is ncssary that som of th tsts in ach battry ar th sam or at last contnt-wis quivalnt. A gnral factor analysis modl in ach population will b as follows (Jörskog, 97: x = µ Λ f, ( whr: g g g g g x is random vctor with man vctor g µ g (and varianc-covarianc matrix of population Σ g in group g. As a rsult x g is xplaind by k g common factors f and uniqu factors g g. Furthrmor, w assum that ε ( f g = 0 and ε ( g = 0 and so th sam with Λ a factor pattrn. And this implis factor analytic solution g as follows (Jörskog, 97: whr: Φ - varianc covarianc matrix of g f g g g g g g g Ψ is th diagonal varianc covarianc matrix of. Σ =Λ Φ Λ Ψ, (3 In contrast to Jörskog gnral modl, Lawly and Maxwll proposd sparat modls for strictly two populations with varianc-covarianc matrics dnotd as Φ and Φ. Th cofficints of factor loadings, - if invariant undr th changs of populations will caus loading matrix Λ th sam for both populations. Thy also assumd that Ψ diagonal matrix of, will b th sam. Th modl can b gnralizd to som xtnt by allowing populations to hav diffrnt uniqu factors (rsidual variancs on varianc-covarianc matrics Ψ and Ψ, but this option complicats subsqunt stimation procdurs. Th g

150 STATISTICS IN TRANSITION-nw sris, March 0 49 population varianc-covarianc matrics for th givn x i ar thus givn as follows (Lawly and Maxwll, 963: Σ = ΛΦ Λ Ψ (4, Σ = ΛΦ Λ Ψ. (5 Such bing th cas, crtain loadings ar a priori zro, and that numbr of and positions of ths ar such as to dtrmin factors uniquly. Th factors ar arbitrary and for computational convninc, thy can b chosn in such a way that th matrix will b (Lawly and Maxwll, 963: ( nφ nφ Φ=. (6 ( n n and has unit diagonal lmnts. As a rsult thr ar k factors, whr crtain spcifid lmnts of th loading matrix Λ ar zro and that th population varianc-covarianc matrics satisfy assumptions of th Eq. (4 and (5. 5. From th modl of two populations towards th modl of two sampls For gnral modl, w hav N g rspondnts in th sampl from g -th population, x as th usual sampl man vctor and g S g - sampl varianccovarianc matrix with ng = Ng dgrs of frdom. Thus, w obtain indpndnt masurmnts for diffrnt groups. W may thus assum that S and S ar th sparat varianc-covarianc matrics for.g., two groups with rspctivly n and n dgrs of frdom, obtaind by taking a random sampl from ach population. Thn, gnral logliklihood function for S sampl will b: g log L { log tr ( } g = ng Σ g SgΣ g. (7 So, if th sampls ar indpndnt, th log-liklihood for all th sampls is: m log L = log L. (8 g And th log-liklihood function for two sparat groups will b (without function with obsrvations (Lawly and Maxwll, 963: n{ log tr ( S } { log tr ( } Σ Σ n Σ S Σ. (9 To stimat unknown paramtrs w should hav maximizd it with rspct that non-zro lmnts of Λ, th lmnts of Ψ, and th lmnts of Φ and Φ ar subjct to rstriction that Φ has diagonal lmnts. Th rsulting quations of stimations may b simplifid and solvd itrativly. Th hypothsis will b tstd by mans of th critrion (Lawly and Maxwll, 963: g = g

151 50 P. Tarka: Customrs rsarch Σˆ Σˆ log nlog. S S n which for larg sampls is distributd approximatly (0 χ with ( p k m dgrs of frdom, whr m is th numbr of non-zro loadings. If w want to administr th sam tst/masurmnt within diffrnt populations, w must follow conditions of invarianc as prviously discussd. In particular w nd to considr invarianc of: Λ in factorial pattrn ovr populations, ψ = ψ of with variancs of rgrssion. Thn, w idntify paramtrs whr Λ in Σ = ΛΦ Λ will b rplacd g g ψ g, * by Φ g = TΦ gt, g =,,..., m, and whr T is an arbitrary non-singular matrix of ordr k k. Thn, ach Σ g rmains th sam so that th function F is unaltrd. m F = n g log Σ g tr ( SgΣg log S p g. ( g = Sinc th matrix T has k indpndnt lmnts, this mans that at last k indpndnt conditions must b imposd on ΛΦ,, Φ,..., Φ to mak thm m uniquly dfind. And th most convnint way of doing this is to lt all th Φ, g b fr and to fix on non-zro lmnt and at last k zros in ach column of Λ. In an xploratory study on can fix xactly k zros in almost arbitrary positions. Jörskog (97 claims that on may choos zro loadings whr on thinks thr should b "small" loadings in th factor pattrn. Th rsulting solution may b rotatd furthr, if dsird, to facilitat bttr intrprtation. In a confirmatory study, on th othr hand, th positions of th fixd zros, which oftn xcd k in ach column, ar givn a priori by a hypothsis and th rsulting solution cannot b rotatd without dstroying th fixd zros. In ordr to mak obsrvabl variabls comparabl, according to diffrnt units of masurmnt in diffrnt sampls, on can rscal ths variabls bfor bginning th factor analysis. As a rsult w assum (Jörskog, 97: n= n, g = g whr: and m S= m ns g g, ( n g = ( ˆ D = diag Φ. (3

152 STATISTICS IN TRANSITION-nw sris, March 0 5 Thn, th varianc-covarianc for th rscald variabls is: * S g S * g = DS D. (4 Th wightd avrag of is a corrlation matrix. Th advantag of rscaling is that, whn combind with an option of rscaling th factors, factor loadings ar of th sam ordr of magnitud as usual whn corrlation matrics ar analyzd and whn factors ar standardizd to unit variancs. This maks it asir to choos starting valus for th minimization and intrprtation of th rsults. It should b indicatd furthr that it is not prmissibl to standardiz th variabls in ach group and to analyz th corrlation matrics instad of th varianc-covarianc matrics. This violats th liklihood function (7-8 which is basd on th distribution of th obsrvd variancs and covariancs. Invarianc of factor pattrns is xpctd to hold only whn th standardization of both tsts and factors ar rlaxd. g 6. Exampl: valus systm analysis in Polish and Dutch youth W drw basic idas and dvlopd our rsarch on Rokach (973 and Schwartz (99 dfinition of valus, dscribing thm as dsirabl, transsituational goals, varying in importanc, that srv as guiding principls in th lif of a prson or othr social ntity. As a rsult valus ar drivn by diffrnt motivations (Schwartz and Sagiv, 995 (Tabl. Th thory postulats 0 diffrnt typs of valus and two main valu dimnsions. Th 0 typs of valus ar arrangd in a circumplx structur around th following dimnsions: slf-transcndnc vrsus slf-nhancmnt and opnnss to chang vrsus consrvation. Figur displays th circular structur of th typs of valus as wll as th two dimnsions bhind thm (Schwartz and Bohnk, 004; Schwartz, 005. Th dimnsion of slf-transcndnc/slf-nhancmnt dscribs th possibl conflict btwn th accptanc of othrs as qual ntitis and th concrn for thir wll-bing (typs of valus: univrsalism and bnvolnc vrsus th tndncy to try to achiv prsonal succss as wll as prdominanc ovr othrs (typs of valus: powr and achivmnt. Th scond dimnsion rflcts th possibl conflict btwn indpndnt thought and action and prfrnc for an xciting lif (typs of valus: slf-dirction and stimulation vrsus th tndncy to sk stability, scurity, and attachmnt to customs, traditions, and convntions (typs of valus: scurity, conformity, and tradition. Virtually diffrnt typs of valus corrlat diffrntly. And th valu typ rlatd to hdonism, forms a link btwn opnnss to chang and slf-nhancmnt (Tarka, 00.

153 5 P. Tarka: Customrs rsarch Tabl. Th 0 typs of valus with motivational goals and th highr-ordr dimnsions Valu Motivation Dimnsion Slfdirctiochoosing, crating, xploring Indpndnt thought and action- Opnnss to chang Excitmnt, novlty, and challng in Stimulation Opnnss to chang lif Hdonism Achivmnt Powr Scurity Conformity Tradition Bnvolnc Univrsalism Plasur and snsuous gratification for onslf Prsonal succss through dmonstrating comptnc according to social standards Social status and prstig, control and dominanc ovr popl and rsourcs Safty, harmony, and stability of socity, of rlationships, and of slf Rstraint of actions, inclinations, and impulss likly to upst or harm othrs and violat social xpctations or norms Rspct, commitmnt, and accptanc of th customs and idas that traditional cultur or rligion provid th slf Prsrvation and nhancmnt of th wlfar of popl with whom on is in frqunt prsonal contact Undrstanding, apprciation, tolranc, and protction for th wlfar of all popl and for natur Sourc: Sagiv and Schwartz, 995. Mthod of data collction Btwn slfnhancmnt and opnnss to chang Slf-nhancmnt Slf-nhancmnt Consrvation Consrvation Consrvation Slf-transcndnc Slf-transcndnc Initially th 9-itm qustion battry was applid in th study to masur valu prioritis among Polish and Dutch youth rprsntativs in th acadmic nvironmnt. Th intrviw was confrontd with a fiv-point Likrt scal (whr: = totally disagr; 5 = totally agr. This typ of scal is a paralll in which ach itm rprsnts an altrnativ and quivalnt tool for masuring a latnt trait. Evaluation of rliability and masurmnt invarianc in scals of this typ is mad in contxt of classical thory of th tst. Data collction was basd on papr and pncil intrviws. In th cours of mpirical rsarch, printd qustionnairs had bn handd out to a numbr of

154 STATISTICS IN TRANSITION-nw sris, March 0 53 individuals (rspondnts at Univrsitis in Poland (in Poznan Univrsitis.g., Poznan Univrsity of Economics, Adam Mickiwicz Univrsity of Poznan and Poznan Univrsity of Tchnology and Univrsitis in th Nthrlands in Rottrdam and Tilburg for final valuation of th prpard sts of itms. Sampling fram was drivd and prpard according to intrnal univrsitis databas including complt list of participants attnding thr introductory classs of undrgraduat lvl. Rspondnts wr slctd on th ruls of simpl random sampling. Only a small prcntag (lss than 5% of thos contactd rfusd to participat in a study. Thus a collctd sampl was n = 85. Th data was collctd btwn May and Jun 009. Figur. Dimnsions of valu systms Opnss to chang Slf- Transcndnc Slf- Dirction Stimulation Univrsalism Bnvolnc Hdonism Powr Achivmnt Conformity Tradition Scurity Slf- Enhancmnt Consrvation Sourc: own construction Data analysis and mpirical rsults At first th factorial structur was tstd and thn masurmnt invarianc of th instrumnts that wr oprationalizd according to th valu thory. Somtims on may also apply th othr modl for comparison of masurmnts at diffrnt points in tim. Such bing th cas, growth curv modls of latnt dimnsion ar usd (.g. latnt growth curv modls. But th lattr option was byond objctiv of this articl. Th assumptions for th assssmnt of invarianc wr as follows: scal consistd of multipl itms,

155 54 P. Tarka: Customrs rsarch itms wr of rflctiv form (thy rflctd latnt dimnsion othrwis latnt variabl, th masurmnt was prformd in two groups at on tim. All analyss wr conductd using th computr program LISREL, whr a maximum liklihood was applid as th stimation mthod. Singl group analysis At first w masurd dirctly th highr-ordr dimnsions of th valus by thir corrsponding itms. Th two highr dimnsions slf-transcndnc/slfnhancmnt and opnnss to chang/consrvation constitutd four factors. Th rmaining 9 itms wr attributd to ths four factors. Th modls rquird svral modifications. At first, itms that did not achiv adquat factor loadings wr liminatd. Th critrion w st for an itm to load on a factor was 0.49 and highr. Som loadings wr too low for th consrvation, slf-transcndnc, and slf-nhancmnt factors. As th invarianc tst should b prformd on th sam masurmnt modl, w liminatd th sam itms in both sampls. Consquntly, th final modl that w tstd for invarianc includd 5 itms. Multi-group analysis Nxt w turnd to multipl-group comparison. This modl nabld us to tst to what xtnt th valu masurmnts wr invariant across th sampls. To tst it w usd th modl that includd 4 constructs, 5 itms, cross-loading and rrors. W compard two groups (.g. Polish and Dutch nationalitis. Th mpirical covarianc matrix of th itms for ach group srvd as th input. Varianc-covarianc matrix allowd for comparing outcoms in trms of intrgroup valu of th original units of masurmnt. If th varianc-covarianc matrics ar not significantly diffrnt in both groups, on can prform furthr analysis of individual aspcts of masurmnt invarianc. Th valuation of th structural invarianc of latnt variabls (also calld configural invarianc was conductd in both groups. This rflctd a tst of th hypothsis of quality varianc-covarianc matrix basd on th dgr of goodnss of fit of structural indpndnt modls mad on th basis of data from individual culturs. Good modls and thir fit to data provd th xistnc of a configuration invarianc and nabld us furthr comparison btwn th constructs. Th dgr of fit was tstd using th statistics such as χ indx, CFI Bntlr, PCLOSE probability of clos fit, cofficint RMSEA. Valus clos to.95 for CFI and blow.06 for RMSEA suggst a good fit (Hu and Bntlr, 993. Nxt, w assssd mtric invarianc,.g. th factor loadings of all itms that wr constraind to b idntical across two groups. This assssmnt was basd on a comparison of rlativ fitting btwn two structural modls. In th first modl, corrsponding factor loadings wr st as qual in all groups (factor loading λ in

156 STATISTICS IN TRANSITION-nw sris, March 0 55 th first group was qual to th valu of th factor loading λ in th scond group of rspondnts. In th scond modl, factor loadings in both groups wr th fr paramtrs. If th fit of th modl with dfind (fixd factor loadings was not significantly wors, as compard to modl with fr rlasd loadings, thn itms would masur th latnt variabls (factors in a comparabl way in both analyzd groups. Howvr, if th dgr of data fit in a modl, prtaining to fixd factor loadings was significantly wors, thn comparison of factor loadings btwn groups could b only mad on partial invarianc masurmnt btwn th groups. Tabl 3. Fit masurs for th modl assssing configural, mtric, and scalar invarianc Configural invarianc Mtric invarianc Scalar invarianc Chi-squar 79,56 9,0 05,60 CFI comparativ fit indx 0,935 0,940 0,948 RMSEA root man squar rror of approximation 0,046 0,049 0,040 PCLOSE probability of clos fit 0,495 0,55 0,540 SRMR standardizd root man squar of rsiduals 0,08 0,08 0,086 Sourc: own calculation in LISREL. Nxt, w turnd to th tst of scalar invarianc. It allowd us to compar th man valus for th latnt variabls, spcially to dtct:. intr-group diffrncs in th rsponss (according to particular statmnts which dtrmind latnt dimnsions and also. ffcts of rspondnts attituds and diffrncs in thir styl of giving rsponss to ths statmnts. Th global fit masurs of th configural invarianc modl, which ar displayd in Tabl 3, suggst that th modl should not b rjctd. Th rsults indicat that th mtric invarianc modl is supportd by th data. A chi-squar diffrnc tst btwn th configural and th mtric invarianc modl rvald that thr was no significant diffrnc in th modl fit. Also, th fit indics of CFI, RMSEA, and SRMR ar furthr indications for invarianc. In cas of scalar invarianc, w may obsrv that th constraind intrcpts of th itms ar qual across th sampls. As th rsults w cannot rjct th scalar invarianc modl. As configural, mtric, and scalar invarianc has bn confirmd, th comparison of latnt man valus btwn th two sampls was asy to conduct.

157 56 P. Tarka: Customrs rsarch And bcaus on intndd to compar th latnt mans in both groups, thrfor w addd a vctor of manifst mans as input. With rgard to th paramtr matrics, th τ x -vctor and th κ -vctor wr addd. Th rsults ar prsntd in Tabl 4. Tabl 4. Latnt man diffrncs of four constructs (rfrnc group: Polish sampl Mans for Polish group Mans for Dutch group Effct sizs (r Opnnss to chang 3,95 3,4,8 Slf-nhancmnt 4,87 4,0,3 Slf-transcndnc,67,65,00 Consrvation 3,6,53,* Not: Effct sizs of r in th latnt mans at p < 0,5; Sourc: own calculation in LISREL. Rsults show significant man diffrncs for th constructs opnnss to chang (stimat = 0,8, slf-nhancmnt (stimat = 0,3, and consrvation (stimat = 0,. For th construct slf-transcndnc w found no significant man diffrnc btwn groups (stimat = 0,0. As a rsult diffrncs hav bn found for th latnt mans of both sampls for th constructs opnnss to chang, slf-nhancmnt, th hypothsis that th latnt mans for valu qustions wr idntical in both groups must b rjctd. Individuals in th Dutch sampl displayd lowr lvls of opnnss to chang and slf nhancmnt (which wr also in thir own part of hdonic snslss and xcssiv consumption of th markt goods as compard to Polish sampl. From th abov rsults and application of modl it is quit intrsting to infr that Polish youth as compard to Dutch youth (bing drivd from agglomrations such as: Poznan, Rottrdam and Tilburg xposs mor intrst towards typs of valus such as Hdonism in gnral. Apparntly young Pols look now for mor plasur and njoyabl lif (also prtaining to products and srvics consumption than thir forign collagus from alrady dvlopd countris. Evnts from th past and hard ruls of socialism and limitation in accss for yars to fr markt goods lft thir strong impact on young popl s lif and bhaviour. Bing kpt too long away from opn markt sourcs, citizns of astrn block of Europ,.g. Poland, sm to rcoup thir dlays and catch up with latst trnds arising on th markt. In contrast, Dutch youth, bing too long xposd to wid markts, virtually grw accustomd to its products and srvics. As a rsult this situation

158 STATISTICS IN TRANSITION-nw sris, March 0 57 affctd thir lif styl, lowring also thir intrsts in Hdonism that is snslss and xcssiv consumption of th markt goods. And ths facts simply rval a nw prspctiv for companis businss activitis that is ithr to point on nw dirctions associatd with ntry on nw ascnding markts. 7. Conclusions Discussd in articl a modl of factor analysis modl was strongly basd on th xamination of masurmnt invarianc and spcifically, factor invarianc. Rsarchr whn using such a typ of modl avails of th opportunity to dtct invarianc for tstd itms and simultanously gnrat rliabl and valid constructs. If ths assumptions ar not satisfactory thn making furthr infrncs bcoms pointlss. In a consqunc th modl rquirs crtain paramtrs (.g., factor loadings to b constraind in th procss of idntification, which mans thy nd to b invariant across groups, and act as rfrnt variabls. If this invarianc assumption for som rason would b violatd, thn location of th paramtrs that actually diffr across groups would bcom difficult. In cas of th conductd analysis and implmntd modl, it simply turnd out to b a satisfactory solution rgarding th rsarchd problm and final calculatd scors. REFERENCES BILLIET, J. (00, Cross-cultural quivalnc with structural quation modling, [in:] Mohlr, P.P. (Ed. Cross-cultural survy mthods, Nw Jrsy: John Wily & Sons Inc., pp BOLLEN, K.A., (989, Structural quations with latnt variabls, Nw York: Wily. COLE, D.A., MAXWELL, S.E. (985, Multitrait-multimthod comparisons across populations: a confirmatory factor analytic approach. Multivariat Bhav. Rs. 0, pp CRONBACH, L.J., MEEHL, P.E. (955, Construct validity in psychological tsts, Psychol. Bull. 5, pp HU, L.-T., BENTLER, P.M., (999, Cut-off critria for fit indxs in covarianc structur analysis: convntional critria vrsus nw altrnativs. Structural Equation Modl. 6, pp. 55. JÖRESKOG, K.G. (97, Simultanous factor analysis in svral populations, Psychomtrika, 36, pp LAWLEY, D.N., MAXWELL, A.E. (963, Factor analysis as a statistical mthod. London: Buttrworths.

159 58 P. Tarka: Customrs rsarch LITTLE, T.D., SLEGERS, D.W., CARD, N.A. (006, A non-arbitrary mthod of idntifying and scaling latnt variabls in SEM and MACS modls, Structural Equation Modl, 3(, pp MEREDITH, W. (993, Masurmnt invarianc, factor analysis and factorial invarianc, Psychomtrika, Vol. 58, pp MUTHÉN, B., (989 Latnt variabl modling in htrognous populations, Psychomtrika, 54(4, pp PLOYHARDT, R.E., OSWALD, F.L. (004, Applications of man and covarianc structur analysis: intgrating corrlational and xprimntal approachs, Organ. Rs. Mthods, 7(, pp ROKEACH, M., (973, Th Natur of Human Valus, Nw York: Wily. SAGAN, A. (005, Analysis of quivalnc off masurmnt scals in intrcultural studis, Scintific Paprs, Vol. 659, pp SCHWARTZ, S.H. (99, Univrsals in th contnt and structur of valus: thortical advancs and mpirical tsts in 0 countris, [in:] Zanna, M. (Ed., Advancs in xprimntal social psychology, vol. 5, Orlando: Acadmic Prss, pp. 65. SCHWARTZ, S., SAGIV, L. (995, Idntifying cultur-spcifics in th contnt and structur of valus, J. Cross-Cult. Psychol. 6(, pp SCHWARTZ, S.H., BOEHNKE, K. (004, Evaluating th structur of human valus with confirmatory factor analysis, J. Rs. Prs. 38(3, pp SCHWARTZ, S.H. (005, Basic human valus: thir contnt and structur across countris, [in:] Tamayo, A., Porto, J.B. (Eds., Valus and Bhavior in Organizations,. Vozs, Ptrópolis, pp. 55. TARKA, P. (00, Masurmnt scals for customrs hdonic valus comparison of rliability tchniqus Scintific paprs Economtrics UE Wrocław, 9, pp TARKA, P. (00, Latnt variabl modls - issus on masurmnt and finding xact constructs in customrs valus Polish Statistical Rviw (Przgląd Statystyczny, 4, pp TARKA, P. (0, Statistical analysis of youth s valu systms in Poland and Nthrlands an approach to LOV and RVS scal [in:] Józf Pocicha (Ed. Mthods of data analysis, Acadmic paprs UE Kraków, 0, pp THOMPSON, M.S., GREEN, S.B. (006, Evaluating btwn-group diffrncs in latnt mans. [in:] Hancock, G.R., Mullr, R.O. (Eds. Structural Equation Modling: A Scond Cours, Grnwich: Information Ag, pp VANDENBERG, R.J., LANCE, C.E., (000, A rviw and synthsis of th masurmnt invarianc litratur: suggstions, practics, and rcommndations for organizational rsarch, Organ. Rs. Mthods 3(, pp

160 STATISTICS IN TRANSITION-nw sris, March 0 59 STATISTICS IN TRANSITION-nw sris, March 0 Vol. 3, No., pp EDITOR S NOTE ON THE STATISTICAL CONGRESS SECTION Th main objctiv of vry statistical congrss can prhaps b said as xclling at profssional languag for quivalnc and comparisons. In doing so, statisticians act in th vin of Adolph Qutl s tradition, who (as th prsidnt of th Cntral Committ of Statistics in Blgium organizd th first such a congrss, hld in Brussls in 853 (though, as an intrnational vnt, and who strssd th nd to stabiliz th languag of statistics spcifically to promot th unification of official statistics that th govrnmnts publishd, providing comparabl rsults. Similar ida has guidd th fforts of th Polish Statistical Association that at th outst of rsumption of its activity in th lat 930s stablishd two scintific committs: on for statistical vocabulary, othr for prparing guidlins for xploring statistical rsourcs. And this typ of ida contributing to stabilization of th broadly concivd languag of statistics, not only cross-nationally but also across sctors and across disciplins continus to also guid th mission of our Journal, th intrnational scop of which is mphasizd in its sub-titl an intrnational journal. Th upcoming congrss to clbrat 00th Annivrsary of th Polish Statistical Association dsrvs highlighting for both rasons: (i as th scintific mting of rprsntativs of th community of statisticians, and of usrs of statistics; and (ii to undrli th importanc of on of th most activ country s scintific association, which continus to promot and ncourag awarnss of th statistical profssion and shaping svral aras of application of statistics, including rsarch, ducation and dissmination of statistical information. Thrfor, I hav askd lading rprsntativs of this community, both rsarchrs and practitionrs, who act as mmbrs of th Journal s Editorial Board, to commnt on th occasion of this annivrsary. Espcially, to addrss som issus thy considr of particular intrst to thm, and to th disciplin as a fild of dynamic dvlopmnt. This sction contains an array of such occasional statmnts, from historical rmarks on th Polish Statistical Association (C. Domański and W. Łagodziński, through som challngs of public statistics (M. Szrdr, to origin and dvlopmnt of th Journal (J. Kordos and W. Okrasa. This part is, howvr, prcdd by two biographical nots, dvotd to two ky figurs in modrn statistics in gnral Jan Czkanowski and Jrzy Nyman. Thy both, for somwhat diffrnt rasons (.g., J. Czkanowski was also on of th ladrs of th Polish Statistical Association bfor World War II, ar to som

161 60 W.Okrasa: Editor s not... xtnt although not bing formally dclard as such considrd spiritual (scintific patrons of th congrss. This sction is compltd by th congrss organizational matrials: th Announcmnt of th Congrss and th Congrss Agnda. Włodzimirz OKRASA Editor-in-Chif

162 STATISTICS IN TRANSITION-nw sris, March 0 6 STATISTICS IN TRANSITION-nw sris, March 0 Vol. 3, No., pp JAN CZEKANOWSKI ( Jan Czkanowski was born into a landowning family, on 6 Octobr 88 in Głuchów, nar Grójc in th Masovia rgion. His fathr Wincnty ( was th ownr of th stats of Głuchów and narby Kośmin. His mothr, Amlia von Guthk, was Grman. Jan had four ldr brothrs and sistrs: Natalia, Alksandr, Stanisław and Maria. H was initially ducatd at hom, but in autumn 894 h bcam a third-yar pupil at th wll-known ral school run by Wojcich Górski in Warsaw. In autumn 898 h movd to th ral school in Libava (Lipaja in Latvia, whr h passd his matura school-laving xam in Jun 90. On Sptmbr 90 h joind th army as a voluntr. Through an ovrsight, in contravntion of an instruction of 888, h was accptd in spit of his Catholicism into th dfnsiv artillry of th thn military port of Tsar Alxandr III in Libava. Unabl as a privat to b movd to anothr unit without a Suprm Ordr, and unabl as a Catholic to rmain in th dfnsiv artillry of th Vilnius district to which Libava blongd, on 6 Dcmbr 90 h was dischargd from th army as unfit du to ovrstraining of th hart. H wnt abroad, laving th Russian Empir without th appropriat documnts, and with his hart in his mouth. H crossd th bordr in a saloon car occupid by a highranking imprial officr and his wif, which nabld him to avoid any bordr chcks. Aftr journying to Italy, in spring 90 h was accptd into th mathmatics and natural scinc sction of th Philosophy Faculty at th Cantonal Univrsity of Zurich. Thr h studid anthropology undr th suprb anthropologist Rudolf Martin, anatomy undr Gorg Rug, and mathmatics undr Hinrich Burghardt. It was to ths subjcts that h would dvot his long, hard-working lif. H undrstood anthropology in a broad sns, from a humanist standpoint as ncompassing knowldg about man and his functions. Anatomy was a part of that knowldg, along with thnography, anthropognsis and typology, gntics, linguistics and statistics. Czkanowski saw th human bing as a cratur charactrizd by a larg numbr of connctd and corrlatd faturs. H undrstood that to study only a fw of ths faturs must ncssarily lad to a limitd, fragmntary, on-sidd pictur which would obscur or vn falsify th ral human bing as an objct of study.

163 6 Jan Czkanowski ( At th bginning of th 0th cntury, whn Czkanowski was studying in Zurich, a multifactd analysis of th human bing was not yt fasibl. Th English statistical school (Parson, Yul, Fishr, Studnt was just bginning its activity. Czkanowski quickly apprciatd th rol that statistics could play for anthropology and th mpirical scincs, and bcam a studnt and pionr of th nw disciplin. Jan Czkanowski s first acadmic work was a short monograph on statistics, writtn in th scond smstr of his univrsity studis. It dmonstrats th us of Parson s corrlation cofficint to valuat various mthods of masuring skull hight. It should b notd that his was 90, and Karl Parson had introducd th corrlation cofficint in 90. With this initial work, Czkanowski travlld in 903 to a congrss of Grman anthropologists in Worms, accompanying his profssor Rudolf Martin. H applid too lat to b includd on th list of spakrs, but h mad such an imprssion with his thorough knowldg of th latst mthods of English mathmatical statistics, which wr not yt known among Grman anthropologists, that Flix von Luschan, dirctor of th African and Ocanic dpartmnts of th Royal Anthropological Musum in Brlin, offrd him a rsarch assistant s position with prospcts of bing snt to Africa or Ocania. Czkanowski agrd to tak up th position, but only aftr complting his studis in Zurich. Th monograph, which had provd so significant for Czkanowski s futur dstiny, vntually appard in print in Archiv für Antropologi in 904. In 903 Czkanowski wrot a papr on th application of th corrlation cofficint to th study of muscular anomalis, for which h collctd matrial whil working as dputy assistant in th anatomy laboratory. This attmpt to apply modrn statistical mthods in anatomy was publishd in 906 in a mmorial volum to th Amrican anthropologist Franz Boas. Czkanowski s work to populariz biomtrics is wll known. Whil still a studnt in Zurich h wrot a papr on th subjct, which appard in 904 as an introduction to Rudolf Martin s anthropology txtbook Lhrbuch dr Anthropologi, which is still widly known among anthropologists today, and in 907 was publishd in Czkanowski s doctoral dissrtation. In it h givs a short dscription of th statistical mthods which had bn introducd to anthropology by English biomtricians. H compltd his studis in July 906, obtaining th dgr of doctor of philosophy (his crtificat is datd 907. In th following wintr smstr Czkanowski furthrd his ducation by studying mathmatics at Brlin Univrsity. As a frsh graduat from Zurich, starting from Novmbr 906 h took up th position of assistant at th Royal Anthropological Musum in Brlin. That post providd th possibility of travlling to Africa undr a scholarship from th Prussian govrnmnt. Thus his youthful drams of an xotic trip to Africa wr to b ralizd. Th young Czkanowski was invitd by Princ Adolf Frdrick of Mcklnburg to join a scintific xpdition to th Nil-Congo rgion in Cntral Africa. H spnt mor than two yars (from May 907 to 7 July 909 in Sudan, th Congo, Uganda

164 STATISTICS IN TRANSITION-nw sris, March 0 63 and Grman East Africa, rturning to Brlin via Egypt, Syria and th Balkans. His dutis includd producing an thnographic map. Th ntrpris was a hug on. A total of 30 portrs wr mployd, and svn stations wr prpard along th rout quippd with food, drink, mdicins, tools, clothing, tnts, camp bds, firarms, and vn folding bathtubs mad of a crumpling imprmabl matrial in short, vrything that th xplorrs would nd. Whr possibl, xpdition mmbrs stayd with missionaris, at colonial bordrland fortrsss or at th courts of African rulrs. Czkanowski crossd north-wstrn Tanzania, Rwanda and two xtnsiv bordrlands: btwn Uganda and Zair, and btwn Zair and Sudan. Th undrtaking took plac in quit xcptional conditions; th trritory xplord, with an ara almost twic that of Switzrland, covrd a rgion that had bn inaccssibl to Europan colonialists and to Arab, Indian and vn African mrchants. Both th tims and th placs visitd rmaind politically unstabl and of uncrtain futur. Spnding mor than two yars on th xpdition, Czkanowski collctd vast amounts of somtims uniqu matrials from parts of Africa which at that tim wr ntirly unknown. Th matrials wr rlvant to both anthropological and thnological or thnographic qustions, and vn to som xtnt to sociological topics. H publishd thm ovr many yars, som of thm vn aftr World War II, in 95. Th first fiv volums wr publishd in Lipzig from 9 to 97 in th form of a vast monograph titld Forschungn im Nil-Kongo Zwischngbit. For th rsults achivd on th African xpdition h was dcoratd with th ordrs of th Blgian Crown and th Mcklnburg Griffon, and with a Mcklnburg Mmorial Mdal. Czkanowski achivd his most important rsults in studis of racial classification and population structur. Th rvolution brought about by Jan Czkanowski in human classification was chifly basd on th introduction of a nw taxonomic mthod for racial analysis. This was introducd in 909 as Czkanowski s diagraphic mthod. It was publishd in Czkanowski s fundamntal mthodological papr Zur diffrntialdiagnos dr Nandrtalgrupp, which rmaind a standard work for his pupils for many yars aftrwards. On March 90 Jan Czkanowski marrid Elizavytą (Elizabth Srgiyvska, daughtr of an Orthodox parish prist in Tula. Th coupl had mt in Zurich, whr Elizabth was studying mdicin. Thy would hav two daughtrs: Zofia Trsa (born 5 Sptmbr 97 and Anna Katarzyna (born 5 Jun 99. On Octobr 90 Jan Czkanowski was appointd curator of th Ethnographic Musum of th Imprial Acadmy of Scincs in St. Ptrsburg. H movd thr at th start of 9, and rmaind in th post until th nd of Sptmbr 93. Whil h was at St. Ptrsburg th wll-known zoologist Józf Nussbaum-Hilarowicz mad a proposal to Czkanowski that h should complt his habilitation dgr in anthropology and tak a univrsity chair at Lvov (Lwów, Lmbrg. Aftr a fairly long priod of hsitation and dlay, h dcidd to mov to Lvov. By a lttr of th Imprial Ministry of Dnominations and

165 64 Jan Czkanowski ( Enlightnmnt in Vinna, datd August and with ffct from Octobr 93, h was appointd assistant profssor of anthropology and thnology in th Philosophy Faculty of Lvov Univrsity. H was appointd on his mrits, without having gaind his habilitation. H bgan lcturing at th start of th 93/94 acadmic yar, and would spnd th longst priod of his lif in Lvov, until 944. Apart from his lcturs h also organizd th anthropology and thnology dpartmnt and ngagd in rsarch on national anthropology. Howvr that work was suspndd as a rsult of th outbrak of th First World War. As a Russian subjct bing in th stat srvic of Austria, h was complld to mak a hasty scap from th Russian army. In lat August 94 h travlld to Krynica, and latr to Busko. On 30 Sptmbr 94 h sttld in Luhačovic in Moravia, whr h continud writing up th matrials collctd during his African xpdition. With th issuing of a dcr rcognizing citizns of th Polish Kingdom, h obtaind a passport, and on 0 Octobr 96 h rturnd to Lvov. At th start of th 96/97 acadmic yars h rnwd his lcturs at th univrsity as a full profssor. His work at th univrsity was again intrruptd on Novmbr 98, aftr Lvov had bn capturd by Ukrainian forcs. On 0 Dcmbr Czkanowski travlld to Paris via Warsaw and Pragu. Thr h workd for th Polish Dlgation at th Vrsaills pac confrnc, acting as an xprt and latr as a mmbr of th Dlgation Council. From March to May 99 h srvd as political scrtary on th Polish National Committ, from May to 5 Jun h workd for th Polish Dlgation, and from 5 Jun to Octobr 99 h hadd th offics of th Dlgation, in Sptmbr rplacing th Dlgation s scrtary gnral Stanisław Kozikry. Rcalld to Paris, h actd as scintific xprt to th Polish Dlgation until 5 March 90. By a dcision of th Chif of Stat datd 9 April 90, Jan Czkanowski was appointd full profssor of thnology and anthropology at Jan Kazimirz Univrsity in Lvov, with ffct from January 90. H rturnd to Lvov, and on 5 April 90 h again bgan lcturing at th univrsity. In 93 th Warsaw Scintific Socity had publishd a book by Jan Czkanowski titld Zarys mtod statystycznych w zastosowaniu do antropologii ( Outlin of statistical mthods in application to anthropology. This was th first statistical txtbook writtn in Polish to dscrib modrn mthods of handling mpirical data and propr intrprtation of rsults. It was publishd just two yars aftr th apparanc of th world s first txtbook of modrn mathmatical statistics, An Introduction to th Thory of Statistics by Gorg Yul, and it playd a grat rol in making biomtrics bttr known among Polish scholars bfor World War I and in th intrwar priod. Bsids dscriptiv statistics, this thoroughly modrn and prcis txtbook covrs th topics of rasoning basd on th corrlation cofficint, multipl rgrssion with workd xampls, as wll as th diagraphic taxonomical mthod of Czkanowski. I would ncourag any authors undrtaking work on a modrn txtbook of statistics to study Czkanowski s xampl from almost a hundrd yars ago.

166 STATISTICS IN TRANSITION-nw sris, March 0 65 It is incontstabl that Czkanowski mad a hug contribution to statistics. This suprb scholar also mad a gratr contribution than anyon ls to th flourishing of Polish anthropology, and causd it to gain worldwid rnown. Profssor Czkanowski was th foundr of th Lvov School of anthropology, which st th ton for all rsarch carrid out in Poland ovr many yars. It is thrfor also rfrrd to as th Polish School of anthropology, distinguishd by a totally original approach to individual intrapopulational taxonomy of humans. Profssor Jan Czkanowski was a mmbr of th Lvov Scintific Socity. Activ local mmbrs of th third sction, dvotd to mathmatics and natural scinc, also includd Stfan Banach and Hugo Stinhaus, whil mmbrs activ lswhr includd Mari Curi (Paris, Wacław Sirpiński (Warsaw and Stanisław Zarmba (Cracow. In th yars Czkanowski hld th post of rctor of Jana Kazimirz Univrsity in Lvov. Aftr th arrival of Grman forcs in Lvov, on 30 Jun 94 Jan Czkanowski was dprivd of th ability to continu work at his blovd Anthropology Dpartmnt. Thanks to a Ukrainian doctoral studnt his nam was rmovd from th list of Lvov profssors who wr shot by th Grmans on 4 July 94. Bcaus h kpt his most important matrials and books at hom, h was abl to carry on intnsiv scintific work vn during th occupation. H obtaind formal protction from th Arbitsamt by taking up th administration of th stats of Kośmin nar Grójc, basd on a notarizd powr of attorny. This also nabld him to plac his family in th villag of Głuchów and to travl thr and also to Warsaw, whr h took part in undrground ducational activitis. Th Kośmin stats wr ownd at that tim by his ldr brothr Stanisław, who had formally rcivd thm from his fathr Wincnty in 895. On 8 May 944, Jan Czkanowski and his family lft Lvov and, until 4 Sptmbr of that yar, stayd as gusts with Profssor Jrzy Fuhrich at Broniszów nar Ropczyc. Latr, taking advantag of a chang in situation causd by th movmnt of Sovit forcs to th Wisłoka lin, h movd to th villag of Cmolas nar Kolbuszowa, and taught at th scondary school in Kolbuszowa until th nd of April 945. (Th primary school in Cmolas now bars th nam of Jan Czkanowski as its patron. Thanks to th intrvntion of th Education Ministry, and having rcivd a truck from th Provincial Offics in Rzszów, h movd to Lublin, whr h lcturd in anthropology at th Catholic Univrsity of Lublin h had rcivd an appointmnt from that institution in Novmbr 944, but was not abl to travl thr arlir bcaus of lack of mans of transport. By lttr of th Prsidnt of th National Council, Bolsław Birut, datd 8 Fbruary 946, Czkanowski was appointd full profssor of anthropology in th Faculty of Mdicin at Poznań Univrsity. H took up th dutis of profssor and th chair of anthropology on March 946. Aftr that faculty was transformd into th indpndnt Collg of Mdicin, h joind th Faculty of Mathmatics and Natural Scinc, and latr, whn that faculty was dividd, th Faculty of Biology and Earth Scincs.

167 66 Jan Czkanowski ( Whil holding his chair at Poznań h continud to lctur at th Catholic Univrsity of Lublin until 949, whn th Ministry rfusd to allow him to continu working at two univrsitis. Dscribd blow ar a fw pisods of intrst from th carr of Jan Czkanowski:. During World War I h producd statistics on nationality and rligious dnomination in th Polish lands for th us of th futur Polish Dlgation at th Vrsaills pac confrnc, which h attndd as an xprt and as had of its offics. H prsntd to Prsidnt Wilson a concpt for th positioning of th astrn bordr which would hav placd th sam numbr of Orthodox Christians on th Polish sid of th bordr as Catholics on th Russian sid.. In th Grman Nazi priod, Czkanowski challngd as Utopian th ida that in prhistory thr xistd pur racial typs such as Grmanic, Slav and Ugro- Finnish. H dmonstratd this by making masurmnts on Polish army conscripts. H showd that th highst contribution of th Nordic lmnt, and thus th gratst closnss to th Nazis Aryan idal, was found in young Jws who cam from Warsaw. 3. Th Karaim national minority was spard th fat of th Jws and Gypsis only bcaus, whn qustiond by th Grmans in 94, Jan Czkanowski gav authoritativ confirmation of thir Turkish origins. In 960, on grounds of ag, Jan Czkanowski wnt into rtirmnt. Howvr h continud to giv a sminar in anthropology for mastr s dgr studnts spcializing in that fild. Profssor Jan Czkanowski s scintific work was xcptionally wid-ranging. H had a multifactd mind, intrstd in many diffrnt issus rlating to human lif and to human bings thmslvs. Howvr h was abl to achiv his gratst succsss in thortical anthropology, by applying statistical mthods to anthropomtric matrials, in thnography and thnology, and in Slavic studis, whr h providd strong justification for th thory that th original Slavic homland was situatd btwn th Vistula and Odr rivrs. This viw was opposd most strongly by Grman and to som xtnt by Czch scholars, and vn by som from Poland, who wr not convincd by th rasoning and documntation put forward by Czkanowski. Poland rcognizd his achivmnts. H was a full mmbr of th Polish Acadmy of Scincs. Two univrsitis Wrocław in 959 and Poznań in 96 awardd him th highst availabl titl, that of doctor honoris causa. Th Polish govrnmnt awardd him th honours of Commandr s Cross of th Ordr of Polish Rbirth and th Ordr of th Standard of Labour, First Class. H was an honorary mmbr of th Polish Anthropological Socity, and also honorary mmbr of th anthropological socitis of Brno and Zurich, and corrsponding mmbr of th Paris Anthropological Socity and th Royal Anthropological Institut of Grat Britain and Irland. In h chaird th Coprnicus Polish Socity of Natural Scintists. H was a mmbr of th Polish Statistical Socity, srving as its vic-chairman in H was

168 STATISTICS IN TRANSITION-nw sris, March 0 67 mmbr, vic-chairman and chairman of th Polish Folk Studis Socity and a mmbr of th Polish Orintalist Socity. H was a founding mmbr and chairman of th Scintific Council of th Polish Biomtric Socity, from th Socity s founding in 96 until his dath. Jan Czkanowski did on 0 July 965 in Szczcin. H is burid on th Avnu of Distinguishd Citizns in Warsaw s Powązki cmtry. As a rsult of fforts by th anthropology community, th nam of Jan Czkanowski has also bn givn to on of Poznań s strts. Th following dscription of Czkanowski coms from an xtnsiv articl dvotd to th history of anthropology in Poland (T. Bilicki, T. Krupiński, J. Strzałko, Historia antropologii w Polsc. Przgląd Antropologiczny 987, 53(, pp.3-8: Czkanowski was a scholar in th old, grat, profssorial styl: a man of wisdom adord by som, admird by many and rvild by a fw. This tall, grandly built man, with th pntrativ gaz of his pal blu ys, with an insparabl cigartt stuck to th cornr of his mouth, could b sductivly courtous and gntl-mannrd, but also had a sharp tongu and could b caustic in polmics and discussions. H was a polyglot, who bsids his nativ Polish had prfct mastry of Grman, Frnch and Russian, and could also convrs frly in English, Italian and Czch. Coming from th landowning classs, h was a man of th world, clos to a dozn Europan princs and princsss, and according to lgnd vn to on crownd had. H was charming in company, and in his old ag h likd to dlight his listnrs with spicy ancdots, such as thos about th partis hld in privat swimming baths in Zurich at th bginning of th cntury, or thos about th rvlris of th Russian cavalry stationd in Kalisz whn it was a bordr town of th Russian Empir. H was an rudit prson who was abl in his tim to spak authoritativly about mattrs of anthropology, Mndlian gntics, Europan archaology, Slav linguistics, Slav and African thnography, and mathmatical statistics. Sourcs: Th Archivs of Adam Mickiwicz Univrsity in Poznań. Chodzidło T., Wspomnini pośmirtn. Śp. prof. Jan Czkanowski ( Zszyty Naukow KUL 966, 9(3, pp Ćwirko-Godycki M., Profsor Jan Czkanowski. Przgląd Antropologiczny 965, XXXI(, pp. 33. Gajk J., Jan Czkanowski. Sylwtka uczongo. Nauka Polska 958, 6(, pp Malinowski A., Życi i działalność Jana Czkanowskigo, in: J. Piontk t al. (ds., Toria i mpiria w polskij szkol antropologicznj. W 00-lci urodzin Jana Czkanowskigo. Poznań 985, pp

169 68 Jan Czkanowski ( Prkal J., Jan Czkanowski ( Listy Biomtryczn, 965, 9, pp. III IV. Szląg Z., Grójcki w wspomniniach. Sris IV, Adam Mickiwicz Litrary Socity, Grójc Branch, 004. Wank A., Szśćdzisiąt lat pracy naukowj Jana Czkanowskigo. Matriały I Prac Antropologiczn 964, 70, pp Wokroj F., 50-lci promocji doktorskij prof. dra Jana Czkanowskigo, Życi Szkoły Wyższj 957, 7/8, pp Mirosław Krzyśko Adam Mickiwicz Univrsity in Poznań Faculty of Mathmatics and Computr Scinc Umultowska 87, 6-64 Poznań [email protected]

170 STATISTICS IN TRANSITION-nw sris, March 0 69 STATISTICS IN TRANSITION-nw sris, March 0 Vol. 3, No., pp JERZY NEYMAN ( Th Russian priod, Jrzy Spława-Nyman was born on 6 April 894, into a nobl family, in th town of Bndry on th rivr Dnistr. H dislikd th prfix Spława, and xcpt for som arly works h publishd undr th nam Nyman. Out of rspct for that dcision, w us only th shortnd form of his surnam hr. Kloncki (995 rports that, according to his sourcs, th Nyman family cam to Poland in th 7th cntury from Grman or Dutch lands. Nyman was th grandson of a participant in th uprising of 863. For his part in th insurrction his grandfathr had bn burnd aliv in his own hous, his proprty confiscatd, and his tn (according to J. Nyman sons snt to Sibria. Only his youngst son Czsław who would b Jrzy s fathr was allowd to sttl in Bndry in th Europan part of Russia. Czsław Nyman graduatd in law in Kiv. Thr h also marrid Kazimira Lutosławska. Jrzy Nyman, whos fathr was a succssful man, was initially ducatd at hom. H had a govrnss, and also attndd an unofficial Polish school which opratd in privat homs. Whn at th ag of tn h wnt to th scondary school in Simfropol, h knw fiv languags (Frnch, Grman, Polish, Russian and Ukrainian and was ahad of his collagus with his knowldg in many filds, with th xcption of Russian history and gography. In 906 Nyman s fathr did, and his family movd to Kharkov, whr thy had rlativs. Aftr h compltd scondary school in 9 his mothr snt Jrzy with a group of studnts on a rail journy around Europ. In autumn of 9 Nyman bgan his studis at Kharkov Univrsity. At first h was intrstd in physics, which was a rsult of th publication at that tim of th thory of rlativity and th rcnt Nobl Priz awardd to Mari Curi. In 94 h wnt on H dislikd th prfix Spława, and xcpt for som arly works h publishd undr th nam Nyman. Out of rspct for that dcision, w us only th shortnd form of his surnam hr. Kloncki (995 rports that, according to his sourcs, th Nyman family cam to Poland in th 7th cntury from Grman or Dutch lands.

171 70 Jrzy Nyman ( a studnts acadmic xpdition to Mongolia. Howvr, bcaus h had no talnt for manual laboratory work, h droppd physics that sam yar and bgan to study Lbsgu s book Lçons sur l'intégration t la rchrch ds fonctions primitivs. This rsultd in a papr on th Lbsgu intgral (530 pags of tiny dns manuscript in th Russian languag, for which Nyman rcivd a gold mdal in 96. During his studis Nyman attndd S. Brnstin s lcturs in probability and mathmatical statistics. In his introduction to Early Statistical Paprs of J. Nyman (Univrsity of California Prss, 967, thir author bgan by giving thanks to Brnstin, from whom h had larnt to concntrat on gnuinly difficult problms. In 97 Nyman compltd his studis and bcam a rsarch assistant in th univrsity s mathmatics dpartmnt, as wll as a lcturr at Kharkov polytchnic and assistant to A. Przborski. Th yars wr xtrmly difficult. Th First World War, th Bolshvik rvolution and th civil war wr not conduciv to work and ld to a markd dtrioration in living conditions. In 99 Nyman was diagnosd with tubrculosis and snt to th Caucasus. Thr h mt th Russian paintr Olga Solodovnikova, whom h marrid in 90. Tn days aftr th wdding Nyman was arrstd by th Russians and imprisond for svral wks. In 90 Nyman passd his mastr s dgr xam and bcam a univrsity lcturr. H also workd with Profssor M. Ygorov in th fild of agricultural xprimntation. Th Polish-British priod, Following th Riga Traty of 9, undr an xchang of familis, Nyman wnt with his mothr and grandmothr to Poland. Thus h saw that country for th first tim at th ag of 7. Thy sttld in Bydgoszcz, in th hous of Nyman s brothr Karol. His wif, who had typhus, rmaind for th tim bing in Russia. Nyman mad contact with Profssor W. Sirpiński, who studid th rsults from Nyman s aformntiond manuscript, and suggstd snding on of thm, which turnd out to b a nw rsult, to th journal Fundamnta Mathmatica. Th papr was accptd and appard in 93 undr th titl Sur un théorèm métriqu concrnant ls nsmbls frmés. Sirpiński hopd that, starting from th nw acadmic yar, it would b possibl to obtain a post for Nyman at a Polish univrsity. Th most likly institution was th univrsity in Lvov (Lwów. Howvr Nyman wantd to bgin working straight away, and bcam a snior statistical assistant at th National Scintific Agricultural Institut in Bydgoszcz, which was hadd by Profssor K. Bassalik. Initially h ngagd in intns furthr studis of statistics and agricultural xprimntation. Around th nd of 9 h obtaind funds for a journy to Brlin and for th purchas of statistical journals and books thr. Nyman spnt mor than a yar in Bydgoszcz, and whil thr wrot svral paprs on applications of probability thory to agricultural xprimntation. In Dcmbr 9 Nyman bgan working for th National Mtorological Institut in Warsaw, whr h lookd aftr quipmnt and collctd data. Also, in

172 STATISTICS IN TRANSITION-nw sris, March , probably thanks to A. Przborski, who had also com to Poland from Kharkov, Nyman bcam his assistant at Warsaw Univrsity. At th sam tim h bgan giving classs as a lcturr in mathmatics and statistics at th Cntral Agricultural Collg (SGGW. H thn had a total of 5 taching hours a wk at thos two institutions. From 94 h gav additional classs at th Jagillonian Univrsity in Cracow, and from 97 h also workd for th bt producrs K. Buszczyński and Sons. In 98 h organizd a Biomtrical Laboratory at th M. Nncki Institut. In ordr to nabl his pupils and collagus to publish thir work, and to populariz his own idas, h foundd th journal Statistica and publishd it from 99 to 938. H also workd with th Institut of Social Affairs, th Cntral Statistical Offic and othr institutions. Basd on his paprs on agricultural xprimntation writtn in Bydgoszcz, in 94 Nyman rcivd th titl of doctor of mathmatics from Warsaw Univrsity. His xaminrs wr th profssors T. Kotarbiński, S. Mazurkiwicz, A. Przborski and W. Sirpiński. It should b notd that a part of his doctoral thsis, which was publishd in Roczniki Nauk Rolniczych (Annals of Agricultural Scincs in 93, was translatd into English and publishd in 990 with xtnsiv commntary in th journal Statistical Scinc. In 98 Nyman gaind his post-doctoral habilitation dgr at Warsaw Univrsity. In 94, thanks to K. Bassalik and W. Sirpiński, Nyman rcivd a onyar Polish govrnmnt scholarship for a stay at Univrsity Collg London, with Karl Parson. Among th rsults was th publication of vrsions of thr arlir works of Nyman in th journal Biomtrika. Nxt, with th support of Parson and Sirpiński, Nyman rcivd a scholarship from th Rockfllr Foundation, which h usd for a yar s stay in Paris, with Borl at th Sorbonn and with Lbsgu at th Collèg d Franc. In 96 h bgan working with Egon Parson, th son of Karl. Thir contacts wr intnsiv, and in 934 Nyman gaind th post of lcturr at Univrsity Collg London, which solvd his problm of having no prmannt mploymnt and no ral prospcts of obtaining a profssorship in Poland, which had mad his matrial situation vry difficult. In spit of living and working in London, Nyman maintaind contact and coopration with his Polish tam. H workd at Univrsity Collg until 938. It should b pointd out that Nyman wantd to work in Poland. Rid (98, p. 7 cits dramatic fragmnts of Nyman s corrspondnc in th mattr of finding a suitabl post for him at any institution in Poland. In th cours of thos 8 vry difficult yars, Nyman managd to achiv an unimaginably grat amount. A list of his works, includd in th abov-mntiond volum of arly works of J. Nyman, includs 65 paprs from , on txtbook giving an introduction to probability thory, and two monographs writtn in Polish in 933 and 934. And ths ar not all of his publications, as can b sn from th bibliography drawn up by B. Łazowska (995. Many of th works ar xtrmly substantial, which somtims vn ld to problms publishing thm.

173 7 Jrzy Nyman ( Th list of his works naturally includs publications motivatd by currnt application problms arising in connction with Nyman s work at th institutions mntiond arlir. Thy includd in particular agricultural xprimntation, biomtrics, sampling mthods and problms rlatd to insuranc. As a rsult of qustions askd by E. Parson, Nyman bcam intrstd in th issu of hypothsis tsting. In 98 his first joint work with Parson appard, titld On th us and intrprtation of crtain tst critria for purposs of statistical infrnc, publishd in th journal Biomtrika in two parts (pags and Th work concrns mainly th liklihood ratio tst, and introducs th concpt of a st of altrnativs, rrors of th first and scond typ, th powr function, and a dfinition of th liklihood ratio statistic. It is thn shown that diffrnt known tsts can b obtaind by this gnral mthod, and an invstigation is mad of th asymptotic quivalnc of th liklihood ratio tst and th chi-squard tst. As a rsult of furthr discussions with Parson, Nyman formulatd a problm of tsting in th languag of problm of optimization, and in 930 provd th basic Nyman Parson lmma. This was includd in 93 in a papr of Nyman and Parson concrning uniformly most powrful and uniformly bst tsts in a class of similar tsts. That work, titld On th problm of th most fficint tsts of statistical hypothss, was accptd by th Royal Socity, prsntd by Karl Parson at th Socity s mting in Novmbr 93, and publishd in 933 in Philosophical Transactions of th Royal Socity (pp Th papr is of fundamntal importanc in th thory of th tsting of hypothss givn a fixd sampl siz. As is notd by L Cam and Lhmann (974, by introducing tsts as solutions to clarly dfind optimization problms, Nyman and Parson providd a modl for gnral dcision thory, latr dvlopd by A. Wald, and for mathmatical statistics in gnral. In 99 that work was slctd for inclusion in a volum of th most important achivmnts in fundamntals of statistics in th 0th cntury (Brakthroughs in Statistics, Vol. I, Springr. A similar distinction wnt to Nyman s work On th two diffrnt aspcts of th rprsntativ mthod: th mthod of stratifid sampling and th mthod of purposiv slction, prsntd in 934 at a mting of th Royal Statistical Socity and publishd in th Journal of th Royal Statistical Socity (934, pp , which was includd among th gratst 0th-cntury achivmnts in statistical mthodology (Brakthroughs in Statistics, Vol. II, 99, Springr. This work was basd on a monograph of 933, writtn in Polish and rsulting from Nyman s work for th Institut of Social Affairs. In 935, in Annals of Mathmatical Statistics (pp. 6, Nyman publishd th papr On th problm of confidnc intrvals. In th summr of 936 h continud to work intnsly on confidnc intrvals, and prsntd his rsult on th duality of intrval stimation and tsting. E. Parson rjctd it for Biomtrika as bing too long and mathmatical, but th work appard undr th titl Outlin of a thory of statistical stimation basd on th classical thory of probability in 937 in Philosophical Transactions of th Royal Socity (pp It was prsntd at a mting of th Royal Socity by Jffrys. In 935, at a mting of th

174 STATISTICS IN TRANSITION-nw sris, March 0 73 Industrial and Agricultural Sction of th Royal Statistical Socity, Nyman prsntd a joint papr writtn with K. Iwaszkiwicz and S. Kołodzijczyk on orthogonal dsigns and randomizd blocks. This was printd in 935 in a supplmnt to th Journal of th Royal Statistical Socity (pp Th papr, along with th work of R.A. Fishr, had grat importanc in th dvlopmnt of xprimntal planning. In 937 Nyman publishd a papr in Skandinavisk Aktuaritidskrift (pp titld 'Smooth' tst for goodnss of fit, which provd anothr milston in th dvlopmnt of statistics. In it h gav an asymptotically optimal solution to th problm of tsting th fit of a st of obsrvations to a fully known continuous distribution. In this work Nyman introducd squncs of local altrnativs (contiguous distributions, which in th 960s bcam a standard tool of asymptotic statistics. Th tst introducd in that papr rmaind almost compltly forgottn for yars, although that has changd radically in rcnt dcads. In 935 Nyman and E. Parson foundd a nw journal calld Statistical Rsarch Mmoirs. In 936 Nyman s son Michal was born. In 937 Nyman was invitd to an intrnational probability congrss in Gnva. In addition S. Wilks invitd him to giv a sris of lcturs in th Unitd Stats. On his travls in th Stats his work arousd much nthusiasm, and th visit itslf was a hug succss. In Novmbr 937 G. Evans snt Nyman an invitation to st up a statistical cntr in Brkly, California. H was also offrd a profssorship at Ann Arbor, Michigan. In 938, a fw days aftr his 44th birthday, Nyman accptd th Brkly offr. Among othr things, this dcision mant that h would scap th consquncs of th Scond World War in Europ. It should b rmmbrd that many of Nyman s Polish collagus and studnts did during th war. E. Scott (006 writs that in 95 Nyman ddicatd to thm an xtndd dition of a volum of his thoughts on statistics, titld Lcturs and Confrncs on Mathmatical Statistics and Probability, listing thir nams and how ach of thm did. Th first dition of th volum (ditd with th assistanc of W. Dming had appard in 938 undr th titl Lcturs and Confrncs on Mathmatical Statistics. Th book gaind grat rnown in th Unitd Stats, and hlpd to populariz Nyman s idas and rsults. Th Amrican priod, On August 938 Nyman arrivd in Brkly and st to work with grat vigour. H workd on stting up th Statistical Laboratory and giving numrous lcturs (for xampl, in h lcturd for 5 hours a wk. H bgan gradually to assmbl a tam. Elizabth Scott, an astronomy graduat, bcam his assistant. H also mployd E. Fix, but unfortunatly was not abl to obtain a post for A. Wald, who had scapd from Nazi prscution in Europ. Nyman gaind his first distinctions from th Amrican statistics community: h was invitd to giv a lctur at a joint confrnc of th Amrican Statistical Association and th Intrnational Statistical Institut, and bcam a mmbr of th organizing

175 74 Jrzy Nyman ( committ of th 0th Mathmatical Congrss and an ditor of th journal Annals of Mathmatical Statistics. Th outbrak of war and aggrssion towards Poland distrssd him dply. H mad fforts to hlp his fllow Pols. Among othr things, through th Kosciuszko Foundation, h arrangd a scholarship for A. Zygmund, which nabld th lattr to migrat with his family to th Unitd Stats and probably savd his lif. In 94 E. Lhmann bcam Nyman s assistant. Howvr racial problms mant that h was not abl to mploy D. Blackwll. Nyman not only st up th Laboratory, but also bgan to work closly with many univrsity facultis at Brkly (Gntics, Gology, Hygin, Agricultur, and this activity was valud vry highly. In Fbruary 94 Nyman was ngagd to solv optimization problms for th military. Th projct was carrid out at th Brkly Statistical Laboratory, with varying intnsity, until th nd of th war. In Octobr 944, togthr with a group of Amrican mathmaticians, h was snt to England for th purpos of rsarching th ffctivnss of crtain bombs. Also in 944 h gaind Amrican citiznship. H was also abl to bring P. Hsu to work for a tim at Brkly. In 945 Nyman organizd a symposium in statistics and probability, at which h prsntd a papr titld Contribution to th thory of th chi-squar tst, which among othr things introducd th class of bst asymptotically normal (BAN stimators, which ar much mor convnint to us than th classical stimators obtaind by th mthod of maximum liklihood, and ar usful in many complx problms. Th symposium was a grat succss. Th holding of th symposium was motivatd by a dsir to clbrat th nd of th war and to facilitat a rturn to thortical rsarch following svral yars of work on applications for th Amrican military. In 946 Nyman was invitd by Prsidnt Truman to join a tam of intrnational obsrvrs for th Grk lctions. That summr h was invitd to spnd a smstr at Columbia Univrsity, whr A. Wald workd, and whr Nyman was offrd a profssorship and numrous privilgs. Ths offrs provd ffctiv as a mans of applying prssur to gain significant advantags for his Laboratory at Brkly. In particular, posts wr found thr for M. Loèv and C. Stin. In 947 Nyman was lctd vic-prsidnt of th Amrican Statistical Association, and in 948 h bcam prsidnt of th Intrnational Statistical Institut. Rcognition for his achivmnts can also b sn in th fact that most of th paprs apparing in Annals of Mathmatical Statistics at that tim rlatd to problms which had bn st and considrd in arlir works by Nyman. In 948 Nyman and Parson rnwd publication of Statistical Rsarch Mmoirs; th sris continus to b publishd today undr th nw titl Univrsity of California Publications in Statistics. Aftr tn yars of Nyman s activitis Brkly had bcom on of th two strongst cntrs for statistics in th Unitd Stats, th othr bing Columbia Univrsity. In 949 Nyman took his first sabbatical to Europ. First h visitd London, whr h gav lcturs and had discussions with Parson. Nxt h lcturd in Paris. Whil thr h mt L. L Cam, and rcruitd him to th Laboratory. H also rcivd a grat distinction whil in Paris: h bcam th first non-frnch author

176 STATISTICS IN TRANSITION-nw sris, March 0 75 to b askd to work on a volum in th Borl Sris. Aftr Paris h visitd Warsaw and many othr Polish citis. H also mt with his brothr Karol. In 950, aftr Nyman s rturn from Europ, a scond Brkly Symposium took plac. Nyman was constantly fighting for th Laboratory s funding and position. Th situation was so difficult that Nyman gav up his work on his contribution to th Borl Sris. Problms wr multiplid by th dath of A. Wald in an air crash, and th consqunt attmpts by Columbia Univrsity and othr institutions to tak ovr part of Nyman s group. In 95, in rspons to qustions put by th astronomr C. Shan, Nyman and Elizabth Scott bgan a long priod of intns collaboration on th dynamics of galaxis. This ld to a sris of around twnty paprs, which ar rgardd as bing among Nyman s most important works on applications. For svral months in th acadmic yar 95/953 Nyman workd in Bangkok, hlping P. Sukhatm to organiz a cntr for training in sampling mthods. In 953 Nyman mployd D. Blackwll and H. Schffé. Also in 953 h sparatd from his wif Olga. In 954 a dcision was takn to st up a Dpartmnt of Statistics at Brkly. Nyman prpard th third Brkly Symposium, whr alongsid work on probability and statistics thr wr paprs prsntd in th filds of astronomy, physics, biology and halth issus, conomtrics, industrial mathmatics and psychomtrics. This trnd was continud at subsqunt Symposia. In th sam yar Nyman, A. Tarski and thr othr Amrican mathmaticians wr invitd to th Mathmatical Congrss in Amstrdam to giv lcturs on th futur of mathmatics. In 955 th Dpartmnt of Statistics bgan its work, undr Nyman s dirction. A yar latr Nyman rsignd from that position, whil rtaining th liftim post of had of th Statistical Laboratory. In 958 h took anothr sabbatical. H travlld widly, including to Poland. H also wrot his fundamntal work on C(α tsts, which appard in a volum ddicatd to H. Cramér. Until th nd of his lif Nyman rmaind bittr that this work had not gaind du rcognition. Rid (986, pp. 5 5 quots a diplomatic statmnt of Nyman on that subjct. Th construction of C(α tsts, initiatd by a modst publication by Nyman in 954 in Trabajos d Estadistica (pp. 6 68, was ky to th dvlopmnt of adaptiv mthods and asymptotically fficint smiparamtric statistics. Unfortunatly most works on ths subjcts mak no mntion of th originator of th significant ida bhind thm. E. Scott (006 nots that during Nyman s liftim his fundamntal rsults quickly cam into practic and found a plac in basic txtbooks, bcoming classical knowldg in a sns, and for many it was no longr clar who thir originator was. Nyman rconcild himslf to th situation. In 960, although h had rachd rtirmnt ag, Nyman continud to work intnsivly and obtaind significant funds for furthr projcts. H was awardd an honorary doctorat by th Univrsity of Chicago, bcam an honorary mmbr of th Royal Statistical Socity, and togthr with Elizabth Scott rcivd a priz from th Amrican Association for th Advancmnt of Scinc. In 960 th fourth Brkly Symposium took plac. In th following yar Nyman spnt

177 76 Jrzy Nyman ( much tim travlling; h visitd Lningrad, wnt to Moscow for a mting with Brnstin, and also rachd Kiv and Kharkov. A dirct rsult of that visit was th arrangmnt of th translation into English of E. Dynkin s book on Markov procsss. In 963 Nyman travlld in th southrn stats of th USA. Movd by th problms of rac, h organizd a collction of funds for scholarships, and wrot a lttr to H. Cramér in th mattr of a Nobl Pac Priz for Martin Luthr King. In 964 Nyman clbratd his 70th birthday. In rcognition of that occasion h was givn an ntry in th Grat Book of th National Acadmy of Scincs, and rcivd an honorary doctorat from Stockholm Univrsity. In 965 a volum of paprs ddicatd to Nyman was publishd, ditd by F. David. In 966 h bcam th first non-briton to b awardd th gold mdal of th Royal Statistical Socity, and th Univrsity of Brkly publishd thr volums of work by Nyman and Parson. Also in 966 h bcam an ovrsas mmbr of th Polish Acadmy of Scincs. W should also not that th fifth Brkly Symposium took plac in 965. In 968 Nyman and L Cam organizd protsts against th war in Vitnam. In spit of this, in 969 Nyman bcam on of twlv Amricans to rciv th country s highst scintific award, th Mdal of Scinc, for laying th foundations of modrn statistics and dvising tsts and procdurs that hav bcom ssntial parts of th knowldg of vry statistician. Th yar 970 saw th holding of th sixth Brkly Symposium, with an xtnsiv programm rlatd to biology and nvironmntal pollution. Th symposium was supplmntd by thr confrncs hld in spring 97. It should b rmmbrd that procdings wr printd for ach of th six symposia, and Nyman was th ditor or co-ditor of ach on of ths vr mor voluminous works. Also in 97 Nyman and A. Zygmund bgan work on a collction of ssays on various rvolutionary changs in scinc, which thy rfrrd to as Coprnican. Th volum, prpard for th 500th annivrsary of th birth of Coprnicus, and titld Th Hritag of Coprnicus: Thoris Mor Plasing to th Mind, was publishd in 974 on th occasion of Nyman s 80th birthday. In 974 a mting To Honour Jrzy Nyman took plac in Warsaw, and a collction of th paprs prsntd thr was publishd in 977. Nyman rcivd honorary doctorats from Warsaw Univrsity and th Indian Statistical Institut. Volums of Annals of Statistics and Intrnational Statistical Rviw wr ddicatd to him. Thr was also foundd a Jrzy Nyman Lcturship in Mathmatical Statistics. In 979 Nyman bcam an ovrsas mmbr of th Royal Statistical Socity. Nyman s Amrican priod producd svral works of grat importanc for th dvlopmnt of asymptotic statistical mthods, such as BAN stimators and C(α tsts. Howvr th main topic of intrst for Nyman in that priod was th building and vrification of probabilistic modls for a numbr of natural phnomna. Th first papr in that sris was publishd in Annals of Mathmatical Statistics in 939 (pp with th titl On a nw class of

178 STATISTICS IN TRANSITION-nw sris, March 0 77 `contagious' distributions, applicabl in ntomology and bactriology, and concrnd th modlling and analysis of clustrs. Subsqunt work concrnd mattrs of th formation of clustrs with rgard to modlling of th sprad of pidmics and modlling of th distribution of galaxis in th univrs. For mor than twnty yars Nyman workd on problms of wathr modification. H was also intrstd, among othr things, in carcinognsis, th dynamics of population growth, and analysis of compting risks. Analysing his paprs writtn in Poland and during th Amrican priod, w find that mor than a half of Nyman s approximatly 00 publications rlat to mattrs of applications. Mor dtails concrning th ntirty of Nyman s work can b found in rports by Kloncki and Zonn (973, L Cam and Lhmann (974, L Cam (995 and Scott (006. J. Nyman did at Brkly on 5 August 98. H had rmaind activ until th vry nd of his lif. In Jun 98 h had attndd a confrnc on cancr, organizd jointly with L Cam. Evn th day bfor his dath h was working in hospital on a book on th subjct of wathr modification. Finally w rcall th viw xprssd by Elizbth Scott (006, who knw Nyman wll sh wrot that Nyman always spok of Poland with tndrnss, and that h was proud of its hritag, although somtims h could b critical of th actions of th Polish authoritis. Sourcs: Kndall D.G., Bartltt M.S., Pag T.L. Jrzy Nyman Biographical Mmoirs of Fllows of th Royal Socity 98, 8, pp Kloncki W. Jrzy Nyman ( Probability and Mathmatical Statistics 995, 5, pp Kloncki W., Zonn W. Jrzy Spława-Nyman. Wiadomości Matmatyczn 973, XVI, pp L Cam L., Lhmann E.L. J. Nyman. On th occasion of his 80th birthday. Annals of Statistics 974,, pp. vii xiii. L Cam L. Nyman and stochastic modls. Probability and Mathmatical Statistics 995, 5, pp Lhmann E.L. Jrzy Nyman In: Biographical Mmoir. National Acadmy of Scincs. Washington, D.C. 994, pp Łazowska B. Bibliografia prac prof. dr Jrzgo Nymana ( Zstawinia Bibliograficzn. Cntralna Bibliotka Statystyczna im. Stfana Szulca. Warsaw 995. Rid C. Nyman from lif. Springr. Nw York 98.

179 78 Jrzy Nyman ( Scott E.L. Nyman Jrzy. In: Encyclopdia of Statistical Scincs 8. Wily- Intrscinc. Nw York 006, pp Trsa Ldwina Institut of Mathmatics of th Polish Acadmy of Scincs Branch in Wrocław Dpartmnt of Mathmatical Statistics Koprnika 8, 5-67 Wrocław

180 STATISTICS IN TRANSITION-nw sris, March 0 79 STATISTICS IN TRANSITION-nw sris, March 0 Vol. 3, No., pp YEARS OF THE POLISH STATISTICAL ASSOCIATION Czsław Domański. Th origins of statistics in Poland Th bginning of statistics in Poland is connctd with th following facts: first stimats and population cnsuss; first publications in th fild of statistics ; initiation of statistical litratur; formation of statistical administration; first lcturs in statistics. Th first vr stimations of population of Poland wr supplid by a numbr of authors: Józf Wybicki stimatd th numbr of population in 777 at th lvl of popl; Alksandr Busching in 77 gav th numbr of 8.5 million, Stanisław Staszic in th yar 785 providd th stimatd numbr of 6 million; Frydryk Moszyński in 788 r. producd th numbr of popl.. Statistical Institutions Th bginnings of statistical activitis on th Polish trritoris coincid with th procdings of th so-calld Four Yar Parliamnt Sssion, i.. th yars Th Parliamnt adoptd a rsolution on carrying out in 789 th first national population cnsus combind with smok rgistration. Th cnsus rsults wr to hlp th Parliamnt to pass a law on a nw tax, which was supposd to provid mony towards xpnss on a prmannt, on hundrd thousand army. Th author of th statistical tabls of th 789 cnsus and a statistical mthod of th military tax calculation was th dputy Frydryk Józf arl Moszyński ( In 864 an organizational unit of th Warsaw Municipal Council calld th Statistical Sction was stablishd. Until th yar 876 its primary objctiv was to prpar matrials which would appar in an annual publication ntitld: Obzor goroda Warszawy. Sinc 877, aftr th Sction had incrasd th rang of its statistical activitis, it startd to act as a statistical offic of th city of Warsaw. Sinc its foundation th Statistical Sction was hadd for ovr 30 yars by an

181 80 Cz. Domański: 00 yars of conomist and a statistician Profssor Witold Załęski. His scintific output rlatd to th dvlopmnt of th statistical thought includs th following works: An Outlin of th Thory of Statistics (884, Rmarks on th Thory of Statistics (888, Th Kingdom of Poland a statistical approach (900-90, On Comparativ Statistics of th Polish Kingdom (908. Załęski s handbook An Outlin of Thory of Statistics, ncompasss fiv chaptrs: Statistics as a mthod and scinc, Th history of statistics, Th history of administrativ statistics, Congrsss of statistics, Statistics organization. Th book can b considrd th first Polish handbook of statistics. In 866 in National Dpartmnt a projct was concivd on stablishing a statistical offic in Galicia. Th projct was prsntd by Miczysław Marass ( th author of, among othrs, a dissrtation ntitld On Concption and Aim of Statistics (Kraków, 866, which was th first Polish publication dvotd to th thory of statistics. Th author dfins thr th tasks of statistics, which is subdividd into gnral and dtaild, dscribs mthods of statistics and prsnts thr ways of statistical data compiling: tabular, graphic and dscriptiv. A fw yars latr in 873 th National Statistical Offic for Galicia was st up in Lvov and its activity continud until 98. Th founding fathr and th longtrm had of th offic was Tadusz Pilat (844-93, a Profssor of statistics and administration at th Univrsity of Lvov; also h was a co-foundr (885 and th first Pol among 00 mmbrs of th Intrnational Statistical Institut. Pilat was th first statistician who usd stimations in statistical analysis and statistical infrnc. Th Cracow Municipal Statistical Offic was st up in 884. Its foundr was Józf Klczyński (84-900, a Profssor of statistics and administrativ law at th Jagillonian Univrsity who had workd in th National Statistical Offic in Lvov in th yars J. Klczyński publishd in Polish Rviw a lngthy articl ntitld Intrnational Statistical Institut, on of th arlist publications dvotd to this institution. In 89 h bcam th scond Polish citizn to bcom a mmbr of ISI. Klczynski, who xrtd a significant influnc on th dvlopmnt of Polish statistics, publishd th following paprs: On calculating population numbr btwn cnsuss (879, and Municipal Statistical Offics. Anothr scholar who mad a grat contribution to th dvlopmnt of Polish statistical thought was a philosophr and an conomist Augustyn Ciszkowski ( H participatd in th Scond Intrnational Statistical Congrss in 855 r. in Paris as th only Polish rprsntativ and th spakr of on of th sctions. During th Congrss a statistics of forsight and futur protction was introducd. This was mant to assist popl in making savings and insuring thm against consquncs of unfortunat vnts in futur. Th Congrss awardd, among othrs, th following institutions: Savings Banks, Providnt Socitis, Pnsion Funds and Insuranc Funds.

182 STATISTICS IN TRANSITION-nw sris, March 0 8 Th first statistician who clarly dfind th tasks of statistics was Ignacy Franciszk Stawiarski ( H prcivd statistics as th scinc which includs all th wishs, dmands and xpctations of politicians and political conomists, and using all availabl ways and mthods provids a dtaild dscription of th country s physical and moral powrs. Morovr, using comparisons, calculations and probabilitis draws conclusions aimd at improvmnt in th country s gnral wll-bing. Statistics of Poland, following th xampl of Statistiqu gnral d la Franc (806, was to b publishd in thr volums. Although th book was not compltd, th tasks of statisticians dscribd almost 00 yars ago, rmain basically th sam. Bfor th World War I a bold initiativ of a group of Polish scintists was launchd almost simultanously in Cracow and Warsaw. Th initiativ was aimd at compiling a statistical publication which would b thmatically, mthodologically and organizationally indpndnt of th partitioning countris: Russia, Prussia and Austria. Th publication, which would ncompass th whol trritory of th partitiond Poland, was to b publishd in Cracow. For that purpos th first profssional association of statisticians Polish Statistical Association was stablishd in 9. Th Prsidnt of th Association bcam Juliusz Lo (86-98 Profssor of financ at th Jagillonian Univrsity, and at th sam tim th Mayor of Cracow. In 95 Polish Statistical Association publishd Statistics of Poland ditd by Profssor Adam Krzyżanowski ( and Profssor Kazimirz Władysław Kumanicki ( Th publication was th first comprhnsiv study which prsntd socio-conomic dvlopmnt of th Polish trritoris from th bginning of th 9th cntury until th outbrak of th World War I. Kumanicki, who was on of th foundrs of th Association and its Scrtary, wrot Studis in Migration Statistics (9, Probability in Statistics (90, and many othr works. In th yars Profssor of gography and cartography of Lvov Univrsity - Eugniusz Romr (87-954, carrid out works on compiling Gographic and Statistical Atlas of Poland. Th atlas, publishd in Vinna in 96 in thr languags: Polish, Frnch and Grman, containd 3 tabls and 69 maps rlatd to gography, history, dmography, industry, agricultur, ducation and administrativ and political ntitis. Morovr, abundant statistical matrial collctd by Romr during his work on th atlas nabld him to dit, in coopration with Ignacy Winfld, anothr important statistical publication ntitld Polish Yarbook. Statistical Tabls (Cracow 97. Th book, which cam out in Polish, Grman and Frnch, was comparabl in siz to Krzyżanowki and Kumanicki s Statistics of Poland as it prsntd in numrical approach th conomic situation and social lif in thr sctors of th partitiond Poland from th turn of th cnturis until World War I.

183 8 Cz. Domański: 00 yars of Statistical yarbooks, Gographic and Statistical Atlas of Poland as wll as othr statistical and historical studis publishd in wartim provd to b xtrmly usful for th dlgation rprsnting Poland during pac ngotiations in Paris (99 and in Riga (9. 3. Association of Polish Economists and Statisticians. Th Association of Polish Economists and Statisticians was foundd in Warsaw in 97. Th activitis of th Association wr dividd into fiv sctions: conomic thory, financ, statistics, conomic policy and social policy. Th initial mting of th Statistics Sction was hld on 4 January, 98. Th ntir board of th Sction consistd of th following mmbrs: th chairman Profssor Ludwik Krzywicki, th dputy Profssor Edward Grabowski, and th scrtary Stfan Szulc, MSc. In 9 th Association Council acknowldgd th quartrly Th Economist to b th official organ of th Association of Polish Economists and Statisticians. Thrfor, Th Economist can b assumd th first Polish statistical priodical with an conomic angl. In August 99 Warsaw was hosting th 8th Sssion of th Intrnational Statistical Institut. Th fact that Polish scholars wr ntrustd with th task of organizing th sssion was a sign of rcognition for th rol that Polish statistics playd on th intrnational arna. Th activitis of thmatic sctions of th Association wr put into a halt in th yars Howvr, on May 9, 933 th following sctions wr ractivatd: thory of conomics, conomic policy, statistics and agricultur conomics. Th Statistics Sction consistd of 4 mmbrs: Jan Drngowski, Michał Kalcki, Ignacy Krautlr, Ludwik Landau, Zygmunt Limanowski, Stfan Moszczński, Jrzy Spława-Nyman, Jan Pikałkiwicz, Franciszk Piltz, Edward Strzlcki, Edward Szturm d Sztrm, Stfan Szulc and Jan Wiśniwski. 4. Furthr activity of Polish Statistical Association. Th Statistics Sction working within th framwork of Association of Polish Economists and Statisticians was dissolvd in Dcmbr 937 du to rstablishing of th Polish Statistical Association. Th mmbrs of th Statistics Sction of SPES bcam th founding mmbrs of th PSS. Th rsolution on stablishing of th Polish Statistical Association was adoptd during a mting of th Statistics Sction of SPES hld on Dcmbr 6, 936. Th activity that PSS was ngagd in at that tim was vry intns and

184 STATISTICS IN TRANSITION-nw sris, March 0 83 fruitful. Polish Statistical Association publishd two priodicals: Statistical Rviw and Statistics in Businss. Its activitis wr carrid out by four rgional branchs: Silsia-Dąbrowa most activ, Poznan, Vilnus and Lvov. Morovr, thr wr four sctions: Mathmatical Statistics, Statistics in Businss, Economic Statistics and Population Statistics. In 938 thr volums of Statistical Rviw cam out togthr with fiv volums of Statistics in Businss and som othr publications. Th mmbrs of th board of th PSS includd th following minnt scholars: Profssor Stfan Szulc, Profssor Edward Szturm d Sztrm, Profssor Ludwik Krzywicki, Profssor Edward Grabowski, assistant Profssor Jan Wiśniwski, Profssor. Jan Czkanowski and Jan Drngowski, MSc. Within th framwork of PSS thr wr two Scintific Commissions working: for th statistical trminology and for dvising a guidbook of statistical sourcs. Th lattr on workd undr th suprvision of Wacław Skrzywan and succdd in prparing a dtaild plan and contnts of th guidbook. Unfortunatly, th ffct of th commission s work was dstroyd as a rsult of th outbrak of war. In 939 two volums of Statistical Rviw cam out in print and a numbr of matrials wr gathrd for subsqunt volums. Also, two volums of Statistics in Businss wr publishd. In Volum II of th Statistical Rviw a list of PSS mmbrs was includd (as of Jun 5, 939 and it comprisd, 9 nams of full mmbrs and 30 nams of supporting mmbrs. Numrous mmbrs of PSS who wr not killd as a rsult of war activitis, wr dprivd of th possibility of prforming thir normal scintific and profssional dutis. Thy got ngagd in clandstin ducation activitis and carrid on som rsarch gtting rady for th aftr-war priod. Many studis which wr writtn by PSS mmbrs at that tim wr uniqu and had a lasting valu. g. Th Chronicls of War and Grman Occupation Yars by Ludwik Landau. Othr mmbrs, who found mploymnt in Statistical Offic of th Govrnor Gnral in Cracow, managd to sav rsarch matrials of th Cntral Statistical Offic. Aftr th war Profssor Stfan Szulc, th had of th Cntral Statistical Offic, undrtook th task of r-activating th Polish Statistical Association, which took plac in 947. H was lctd th Chairman of th Association. Dspit incrasingly unfavourabl conditions rsulting from political situation, PSS managd to continu its activitis up to th nd of 950. In 949 Volum III of th Statistical Rviw was publishd. In th yars to follow ( thr was a long brak in th xistnc of a sparat organization of statisticians aftr PSS had bn dissolvd. Btwn 953 and 980 Polish statisticians conductd thir activitis in th Statistics Sction of th Polish Economic Socity.

185 84 Cz. Domański: 00 yars of Th highlight of th priod was th yar 975 whn Polish statisticians wr givn a task of organizing 39th Sssion of Intrnational Statistical Institut.(ISS. 5. Ractivation of th Polish Statistical Association. Anothr initiativ aimd at ractivating th organization of Polish statisticians was takn in 980 by a group of workrs of th Cntral Statistical Offic. At th initial stag a tam rsponsibl for carrying out th task was slctd. Th tam was ld by Doctor Jan Kordos and Profssor Lszk Zinkowski, and th tam mmbrs wr: Lucjan Adamczuk, Kazimirz Latuch and othrs. Th foundrs mting was hld on 6 of April 98 and was attndd by 40 statisticians from Białystok, Lublin, Łodz, Olsztyn, Poznan, Rzszow Szczcin, Torun, Warsaw and Wrocław. Th rsolution on stablishing Polish Statistical Association was passd unanimously. Polish Statistical Association strngthnd its position on th intrnational arna and sinc 994 it has bn affiliatd with th Intrnational Statistical Institut. It has also achivd a prominnt position at hom and it is sn as a vry activ organization whos activitis influnc both scintific and social nvironmnt. Evry yar th Association is th organizr of two or thr scintific confrncs attndd by mmbrs of intrnational statistical community. PSS has a long tradition of organizing sminars and confrncs dvotd to discussing problms important for both statisticians and local communitis. Th paprs prsntd at confrncs ar subsquntly publishd in priodicals issud by th Polish Statistical Association and th Cntral Statistical Offic: Statistics in Transition, Statistical Nws, Statistical Quartrly or in spcial monothmatic volums. At prsnt th main activitis of th Association ar oftn supportd by assistant bodis: Historical Sction, Classification and Data Analysis Sction, Mathmatical Statistics and Burau of Statistical R6sarch and Analysis. In 990 Taxonomy Sction, which latr changd its nam into Classification and Data Analysis Sction of PSS, originatd and sinc thn it has organizd its annual confrncs. Th most important rsults of scintific rsarch prsntd during th confrncs wr publishd in 7 volums ntitld Classification and Data Analysis Thory and Application. Classification and Data Analysis Sction organizd in 00 in Cracow was on of thos confrncs, i.. Th Eighth Confrnc of th Intrnational Fdration of Classification Socitis - (IFCS. In 006 Polish Statistical Association was th co-organizr of 6th Europan Mting of Statisticians, which took plac in Torun. Sinc 980 PSS has bn organizing jointly with Th Univrsity of Lodz th intrnational confrnc Multivariat Statistical Analysis MSA. Th confrnc procdings hav bn publishd in 0 volums of Acta Univrsitatis Lodzinsis. PSS also cooprats with th Economic Univrsity of Katowic on organizing intrnational confrnc Survy Sampling in Economic and Social Rsarch.

186 STATISTICS IN TRANSITION-nw sris, March 0 85 Burau of Statistical Rsarch and Analysis plays an important rol in th activity of Polish Statistical Association. It is an indpndnt rsarch unit which carris out statistical rsarch commissiond by various scintific institutions and institutions of highr ducation. Th profits gnratd by th Burau go towards organizational and programm activitis of th Polish Statistical Association. Th financial mans arnd by th Burau nabld th Association to undrtak nw tasks, improv th quality of audio-visual quipmnt, produc training films, organiz scintific confrncs, financ publications, tc. 6. Congrss of Polish Statistics. To clbrat th on hundrdth annivrsary of th Polish Statistical Association th Congrss of Polish Statistics will b hld on 8-0 April 0 in Poznan, combining this vnt with th clbration of Polish Statistics Day in 0. Th prliminary programm of th Congrss compriss a numbr of thmatic sssions, including th annivrsary (historical sssion, as wll as othrs dvotd to th mthodology of statistical rsarch, rgional statistics, population statistics, socio-conomic statistics, th problms of statistical data and th statistics of halth, sport and tourism. Th Congrss will also host two panl discussions on: fundamntal problms of statistics in th modrn world, and th futur of statistics. 7. Summary. Lt us now turn our attntion to th most important achivmnts of two minnt mmbrs of th Polish Statistical Association, who playd an activ part in th scintific lif of th Association - Jan Czkanowski ( and Jrzy Nyman ( Rsarchs aimd at finding a mthod in multi-fatur analysis (909 rsultd in dvloping a diagraphic mthod (Czkanowski mtod. Th mthod nabls to group and ordr a st of multi-fatur individuals (ach lmnt is dfind by a numbr of faturs. It includs two stps: a matrix is introducd to th st of individuals, i.. th distanc btwn ach two individuals of th st is calculatd, which givs th distanc tabl calld Czkanowski tabl; th numbrs in Czkanowski tabl ar rplacd by corrspondingly blacknd filds, and columns and rows ar movd in such a way as to gt a diagram which would b possibly most blacknd at th main diagonal. Th obtaind rsult is calld Czkanowski diagram (J. Prkal, 965. This simpl mthod of multi-fatur analysis was usd for ovr half a cntury to solv problms in anthropology, thnography, psychology mdicin, linguistics, musicology, botany and othr filds. Th mthod offrs a numbr of variations (man diffrncs, faturs hirarchy for distanc calculation. Thanks

187 86 Cz. Domański: 00 yars of to this mthod Czkanowski bcam a rnownd biomtrician. In 904 h publishd in introduction to biomtrics in anthropology handbook by R. Martin and in 907 it cam out in print as his doctoral dissrtation. In 93 Czkanowski wrot An outlin of statistical mthods applid in anthropology. It was th first Polish handbook on modrn mthods of compiling numrical data and intrprtation of findings. It is worth noting hr that G. U. Yul publishd his handbook of mathmatical statistics ntitld An introduction to th thory of statistics just two yars arlir. In th yars Czkanowski was a Profssor and th had of Chair of Anthropology at th Univrsity of Lvov. Jrzy Nyman arrivd in England in 938 and aftr som tim h sttld in Brkly, USA. At that tim statistics was not in th cntr of intrst of Brkly Univrsity, howvr Nyman was dtrmind to st up a Dpartmnt of Statistics, which h latr dvlopd and changd th nam into Laboratory of Statistics. H organizd famous Brkly Symposiums and showd grat intrst in astronomy and advancd statistics in lss dvlopd countris. This contributd to intnsiv dvlopmnt in scintific contacts at intrnational lvl and in th sat of ISI in Holland. Th Intrnational Association of Statistics in Physical Scincs was foundd (I.A.S.P.S.. In 975 I.A.S.P.S. was dissolvd and rplacd by Brnoulli Association which constitutd a sction of ISI. Brnoulli Association absorbd as its sub-sction two othr major groups of statisticians: Th Europan Mting of Statisticians (in th USA basd on th Institut of Mathmatical Statistics, and th intrnational group cooprating on th organization of Confrnc of Stochastic Procsss. All th abov mntiond activitis aimd at dvlopmnt of statistical movmnt on an intrnational scal wr inspird by Nyman. Jrzy Nyman bcam a Profssor of Statistics at Brkly Univrsity and his discipls can b mt all ovr th world. His magnum opus was th Nyman- Parson thory of tsting statistical hypothss. BIBLIOGRAPHY DOMAŃSKI CZ. (0, Stna rocznica powstania Polskigo Towarzystwa Statystyczngo, Wiadomości Statystyczn nr 9, s. -0. KRZYŚKO M. (00, Jan Czkanowski antropolog i statystyk, Kwartalnik Statystyczny nr 4, s PERKAL J. (965, Jan Czkanowski, Listy Biomtryczn nr 9-, s. - ;.OKTAWA W. (00, Probabiliści, statystycy, konomtrycy i biomtrycy, Lublski Towarzystwo Naukow, Lublin.

188 STATISTICS IN TRANSITION-nw sris, March 0 87 STATISTICS IN TRANSITION-nw sris, March 0 Vol. 3, No., pp THE POLISH STATISTICAL ASSOCIATION (PTS RE-ESTABLISHING Władysław Wisław Łagodziński For th hundrd-yar history of xistnc and activity of th Polish Statistical Association th yar 98 was an xcptional on sinc th Association for th first tim in its history bcam part of th procss of crating th basis of official statistics for a dmocratic socity. W wr st up both by th public dmand and how painful nd to clans scinc and statistical practic of th prvious 5-35 yars of availability, dpndncy, dpndncis, buraucracy, but also of conformism and opportunism to authoritis. Using th privilg of "an y-witnss" I wish to rcall how th Association was stablishd for th third tim in its history. Bfor r-stablishing Polish statistics startd its official activity immdiatly aftr th Scond World War, as th statisticians from Warsaw bgan to oprat two days aftr th libration of th city (9 January 945, and CSO startd its activity on March, 945, whn th front was still in th country, and thr wr two months lft to th nd of th war. Th Association took action two yars latr, and on March 5, 947 th Polish Statistical Association was r-ntrd into th rgistr of associations and unions. Stfan Szulc, th Prsidnt of th CSO, was lctd th Chairman, and Dr. Kazimirz Romaniuk his dputy 3. Short was th joy of th activity of both CSO and indpndnt PTS. Alrady in 949, Prof. S. Szulc rtird, and Dr. K. Romaniuk movd to th Planning Committ, Cntral Statistical Offic withdrw its grant and rsignd its position of a supporting mmbr. PTS lost its rasons to xist. Polish statistics wr dominatd by Vic-Prsidnt of th Main Council of PTS. Chairman of th Council of Warsaw Dpartmnt of PTS. S "Polish Statistical Association 9-0". Joint publication ditd by Kazimirz Kruszka, Warsaw 0. Polish Statistical Association Gnral Council.; spcially Part I, Chaptrs 4,5,6 and 7. 3 S Lucjan Adamczuk and Kazimirz Latuch, "Raktywowani Polskigo Towarzystwa Statystyczngo" In: Wiadomości Statystyczn, 98, No.8.

189 88 W. W. Łagodziński: Th polish statistical conomists and plannrs. Th final blows for PTS wr inflictd by I Congrss of Polish Scinc (95, and I Scintific Confrnc of Statistics Dpartmnts of Highr School of Economics (95. Th spcialists in political conomics of socialism and plannrs put thn th finishing touch and consntd to th cration of th Sction of Statistics in th Warsaw Dpartmnt of PTS. Th final blow was th formal liquidation of PTS on April 4, 955. And this is how PTS casd to xist for 6 yars. In rtrospct, it is difficult for m to find a good trm for what actions w took in 98. Was it an "stablishing of th nw PTS", "ranimation" or finally "rstablishing"? For m, it will always b a r-stablishing, as in th minds and activity of Polish statisticians an xtrmly strong survival gn was always prsnt, th gn of th public and scinc srvic. This was in th priod of th Partitions of Poland, bfor and aftr World War I, bfor, during and aftr World War II, as wll as in th yars Statisticians ar rluctant to talk about this, bcaus statistics is ssntially th scinc of th country and it is intndd to srv th stat in accordanc with th principls of scinc, truth and thics of th profssion. Th yar 98 again st bfor us th qustions of whr w ar in this country and in this scinc, what this statistics should look lik and how w ar to srv thir country. Th nxt dcad showd that ths qustions wr rpatdly rturning and ar still valid. First stag of r-stablishing Th priod in th Cntral Statistical Offic, and consquntly in th whol Polish statistics was vry livly in political and union sns. Th NSZZ "Solidarność", th most powrful trad union of all cntral govrnmnt institutions (mor than 500 mmbrs was activ in th CSO. But bfor th association "Solidarność" was stablishd, w had trid to st up an Indpndnt Slf-Govrning Trad Union of Polish Statisticians, and only th grat mphasis of th crw causd th cration of th circl "Solidarność". Latr th ida of ractivating th PTS dvlopd. Many mmbrs of th founding group of th "Solidarność" was also among th foundrs of th PTS. But whil th popl of Solidarność" wr a group of vry radical viws and vn mor radical actions, th group of founding mmbrs of th PTS was mor modrat in gnral and rprsntd a full cross-sction of socio-profssional prsonnl of statistics, that is official posts, viws, political options, intrst groups, acadmic intntions and prhaps also idological ons.

190 STATISTICS IN TRANSITION-nw sris, March 0 89 Founding mmbrs - who wr thy? Th list of founding mmbrs who compltd th Founding Dclaration of Polish Statistical Association includd 4 prsons, but not all wr prsnt at this mting. Currntly, only som of thm ar living, although th author, dspit strnuous fforts, was not abl to contact all living founding mmbrs. Two groups prvaild: rsarchrs and statisticians practitionrs. Among th first ons wr mn of grat statur such as profssors Lszk Zinkowski, Wisław Sadowski, Jrzy Holzr, Zdzisław Hllwig, Mikołaj Latuch, Zbigniw Pawłowski, Stanisław Wirzchosławski and Jan Kordos. Among th founding mmbrs wr mn who workd in th CSO in th thirtis (Stanisław Róg, Maria Czarnowska, Józf Wojtyniak. Th majority wr hads of dpartmnts of statistical organizational units, lcturrs from univrsitis and middl-ranking managmnt staff of statistical offics. To dat, th following prsons ar activly participating in th activitis of PTS authoritis: W. Łagodziński as Vic Prsidnt of th Gnral Council, K. Kruszka, J. Brgr and T. Jurk as mmbrs of th Main Council of PTS. Th founding mting On , at th hadquartrs of on of th musums in Warsaw th founding mting was hld. Th abov mntiond founding mmbrs signd th following dclaration: "Aftr rviwing th Programm Dclaration and th Statut of th Polish Statistical Association prsntd at th Founding Mting hld on 6 April 98 in Warsaw I confirm participation in th r-stablishing of activity of th Polish Statistical Association. At th sam tim I apply for mmbrship in th Polish Statistical Association as an ordinary mmbr. I agr to comply with provisions of th Statut and th Ruls, th Rsolutions of Gnral Mtings of Mmbrs (Dputis, to mak rgular paymnts of mmbrship fs and to implmnt th goals and tasks of th Polish Statistical Association". Each dclaration was confirmd by a signatur. Th dclaration was a carful compromis for thos tims. What is important is that w did not obtain thn any dclaration of support from th CSO. This significantly influncd th nxt 0 yars. Th Assmbly passd th statut, lctd provisional govrnmnt, adoptd a programm dclaration, approvd th stablishmnt fund and adoptd a rsolution on th activity and th organizational ruls of th Association. W also dcidd that w ar a hir to th traditions and achivmnts of th Association. Th dscription of th history of th Association and photocopis of original documnts can b found in th mntiond publication, ditd by Kazimirz Kruszka. Full list of founding mmbrs in PTS 9-0, Op. Cit.

191 90 W. W. Łagodziński: Th polish statistical What is worth rmmbring today whn rfrring to th 98 convntion? Whn dciding on th r-stablishmnt of th PTS, w knw that: most acadmic and profssional circls in th yars lost th ability to dtrmin dirctions of its dvlopmnt and articulation of intrsts. This ld to th suprficial actions, loss of prstig and public confidnc, statistics dprivd of broadr social support and subjctd to incrasing prssur from th authoritis lost systmatically th status of social srvic transforming itslf in a govrnmnt agncy, 3 statistical information bcam mor and mor widly th subjct of manipulation. Thr wr attmpts at th cntral lvl to us it to bolstr th idology of succss and prosprity of th Pols by using cnsorship and slction of statistical data far mor than was rasonabl, by running psychological mchanisms of slf-cnsorship, blurring of prsonal rsponsibility for th contnt and quality of information and studis (on was also dprivd of mrit and job satisfaction for th accuracy of rsarch and dvlopmnt, as wll as high quality of publications W. L, 4 du to ngativ phnomna causing statistical information to fail to mt th rality, a crisis of public confidnc in statistics startd to grow. All this mant a dramatic crisis in th social situation and th position of statistics, thus...ovrcoming this crisis, rstoring confidnc in th statistics, rstablishing its status of a nationwid social srvic, raising its rnown and prstig as a scinc... wr th most urgnt goals of th PTS in 98. Aftr yars, whil rporting th vnts from th history of th PTS RE- ESTABLISHING in 98, I cannot rsist th imprssion that many of th obsrvations and findings mad back thn rtaind its validity and its rlvanc to th prsnt day.

192 STATISTICS IN TRANSITION-nw sris, March 0 9 STATISTICS IN TRANSITION-nw sris, March 0 Vol. 3, No., pp NEW ECONOMY NEW CHALLENGES FOR STATISTICS Mirosław Szrdr. Introduction Congrss of Polish Statistics organizd in April 0 sms to b a good opportunity for analyzing and valuating procsss to which statistics in Poland was xposd ovr th last yars, during th priod of building dmocracy and th markt conomy. Fundamntal changs in politics and conomics commncd in 989 hav strongly influncd not only Polish public statistics, its institutions and activitis, but also hav bcom a nw challng for th scinc of applid statistics, and for th practic of statistical survys. This papr involvs a condnsd dscription of nw tasks which wr takn up by Polish statisticians in nw circumstancs of th markt conomy, and givs an outlin of som nw challngs which thy will fac in th nar futur. Spcial attntion is paid to statistical survys.. Origins and dirctions of changs in statistical survys Considring sourcs of th volution in dsigning and conducting statistical survys in Poland ovr th last yars on should tak into account two important procsss. Th first on covrs dp changs that affctd political, social and conomic livs causd by transition from th cntrally plannd conomy to th markt conomy. Th othr procss, acting indpndntly of th formr on, was th gnral dvlopmnt of th thory of statistics and applid statistics, which in this priod was spcially fast, and was strongly supportd by th progrss in IT. An analysis of particular ffcts of changs which took plac in th practic of statistical survys in Poland, nabls on vry rarly to idntify th singl rason. Mor frquntly, a combination of th two dscribd procsss, and som othr factors, account for thos changs. Univrsity of Gdańsk.

193 9 M. Szrdr: Nw conomy Th main rsults of th volution in statistical survys in Poland aftr 989 can b classifid into thr groups which involv:. significant incras in th aras of conomic and social activitis whr quantitativ (statistical rsarch gaind th prdominant position among all rsarch works applid in thos filds;. strongr harmonization of dvlopmnts of th thory of statistics with practical nds of statistical survys; 3. incrasing fforts of statisticians aimd at providing high quality rsults of conductd survys to larg parts of th socity, spcially in topics which attract attntion of many popl. In my opinion, th abov thr groups of th ffcts of Poland s transformation in statistics hav had som impact on th conomy and th social lif, as a kind of fdback, and additionally thy hav influncd statistical ducation within th socity. 3. Statistical survys in nw aras of conomic and social activitis A systm of dmocracy and principls of th markt conomy rquird ssntial changs in th ruls of political and conomic livs. Th transformation also causd nw institutions which wr stablishd and nw filds of social and conomic activitis to nd mor advancd statistical dscriptions and analyss. Soon aftr th bginning of transformation procsss in 989, many conomists and markt analysts ralizd that thr was a growing dmand for markting survys and also for rliabl markt forcasts both at macro- and micro lvls. It was connctd, among othrs, with th nds for prparing businss plans for various purposs, including ntrpris rstructuring and nw invstmnts. A dvlopmnt of markt rsarch and markting survys attractd a gnuin intrst in statistical survys, and in statistics as a whol, among incrasing numbr of markt spcialists. Consumrs nds and prfrncs constitutd a nw fild of application of statistical survys which virtually did not xist in th cntrally plannd conomy. Initially, simpl statistical tchniqus wr mployd in this kind of rsarch, howvr in rspons to mor complx and mor dynamic markt phnomna which gradually startd to appar, mor advancd mthods wr usd. Markting rsarch cratd a strong stimulus for including mor statistics in univrsity curriculums for studnts studying conomics and managmnt. This, in turn, was accompanid by incrasing amount of rsarch output focusd on quantitativ masurmnts of markt procsss. Anothr ara of conomic activity, which succdd to attract attntion of many statisticians was financial markt with all its componnts, including stock xchang, banking systm, and rapidly dvloping procsss on this markt. That was a nw rality in Poland s conomic lif aftr 45 yars of anothr conomic systm which did not nd an xchangabl currncy or financial markts.

194 STATISTICS IN TRANSITION-nw sris, March 0 93 Particularly intrsting for statisticians bcom problms connctd with stock xchang, invstmnt funds, currncy markts, and insuranc. Th amount of nw issus which rquird profssional analyss was so larg that many scintists spcializing in mathmatics and physics joind th group of conomists and statisticians who dalt with th nw challngs. Majority of thm gaind nw qualifications and rmaind in this circl for long, as Poland bcom a part of th intrnational financial markt, and had to cop with all nw procsss which dvlopd thr in th following yars. Nowadays, it is difficult to imagin analyss of financial phnomna without applying adquat statistical tchniqus and tools. And although th applid mthods and tchniqus ar somtims calld financial rathr than statistical, it is obvious that statistics is th scinc which works out and dvlops mthods of discovring rgularitis or pattrns in mass phnomna, including th ons which ar hiddn in financial sris. It is worth noting that many advancd mthods of conomic modlling or statistical infrnc finds thir initial applications in th fild of financ. Rcnt turbulncs on th world s financial markts nhancd th dmand for propr standards and high quality of statistical analyss concrning procsss dvloping on th domstic financial markt. This is a challng for Polish statisticians for today, and no doubt, also for tomorrow. Out of many aras of social lif, whr statistical masurmnts and rsarch play a crucial rol, th most spctacular incras of intrst in statistics has occurrd in opinion polls. In dmocracy, th voic of public opinion is important not only for th socity but for thos who govrn th country as wll. It is ssntial that both ths groups obtain rliabl and accurat masurmnts of th stat of public opinion, mainly xprssd by opinion polls. Opinion polls nabl popl to count thmslvs, in ordr to find out how many (or how fw of thm ar thr, and th awarnss of th numbr is a starting point for building public opinion says Profssor A. Sułk, a Polish sociologist (s Sułk [0], p. 33. In first svral yars aftr 989, th fild of opinion polls was lft in Poland ntirly to sociologists and pollstrs. It did not manag to attract much intrst of statisticians. This attitud has changd gradually, whn th conscutiv national lctions brought campaigns with a larg numbr of poor quality polls and disappointing lction forcasts. Widsprad criticism of th mthodology usd in opinion polls rfrrd also to statisticians, who vntually took up th challng. Common fforts mad by sociologists and statisticians to improv th quality of opinion polls rsultd in mor accurat and mor prcis polls in following yars. Highr standards in dsigning and prforming polls hav bn adaptd by majority of pollstrs oprating in Poland. Thr ar som masurabl ffcts of improvd mthodology usd in opinion polls, which involv dcrasing amounts of rrors in lction survys and forcasts. For instanc, th total rror in xit poll conductd during th 0 parliamntary lction was fiv tims smallr than th corrsponding rror in xit poll prformd during th EU rfrndum in 003. It sms vry likly that in th following yars ahad opinion polls will rmain an intrsting ara for statisticians whos comptncs will b ngagd in solving

195 94 M. Szrdr: Nw conomy nwly arousd mthodological or practical problms, such as incrasing proportion of non-rspons. 4. Adquat rspons of th thory of statistics to th nds of practic A nwly stablishd political and conomic systm in Poland aftr 989 causd an incras in th numbr of statistical survys prformd byond th systm of public statistics. Nds of conomic practic hav bcom an important factor which dtrmins dirctions of th dvlopmnt of applid statistics, and dfins spcific issus which ought to b solvd in various kinds of statistical survys. This rfrs particularly to problms that appard in quantitativ markt survys, in analyss of financial phnomna, and in studis of th activitis of small and mdium-sizd ntrpriss. Many statistical survys rlatd to social or conomic issus hav bn carrid out for local authoritis. As a rspons to practical nds on could obsrv an incrasing intrst of Polish statisticians in small domain infrnc (including small ara stimation. This is on of th issus which hav attractd rsarch intrsts of statisticians rprsnting both official and commrcial statistics. A numbr of valuabl scintific achivmnts in this fild hav thir roots in original works carrid out in Poland s Cntral Statistical Offic (GUS. Thrfor, som initial applications of nw tchniqus rprsnting small domain statistics can b found in survys dsignd by institutions of public statistics. Thr also xist svral acadmic institutions in Poland which hav bn succssful in dvloping small domain mthods and tchniqus. Taking into account incrasing information nds xprssd by many institutions and ntrpriss, including local authoritis, on should xpct furthr dvlopmnt of this branch of statistics in th futur. On of th crucial challngs for th practic of statistical survys rmains th problm of nonrspons which incrasingly strongly affcts th rsults of many survys. This is th problm which rfrs to all kinds of statistical survys, in vry country. Efforts of statisticians focusd on carful dsigning of a survy is frquntly wastd du to larg proportion of rspondnts who rfus to cooprat, as a rsult th obtaind obsrvations may crat th sampl structur which is significantly diffrnt from th dsignd on. Furthrmor, a larg proportion of nonrsponss undrmin rationality of applying classical infrnc basd on this kind of data. It sms that many profssionals who dal with dsigning and conducting survys, and also statisticians who try to find fficint tchniqus which would compnsat for th lack of obsrvations raliz that Today, nonrspons is a normal (but undsirabl fatur of th survy undrtaking (C.E. Särndal, S. Lundström [005], s. IX. If this is th cas, on can xpct that th problm of daling with nonrsponss will rmain on of important challngs for statisticians in th futur. Thr has bn a grat dal of rsarch output obtaind in this fild, including intrsting proposals of nw imputation and calibration tchniqus prsntd by Polish statisticians.

196 STATISTICS IN TRANSITION-nw sris, March 0 95 Evntually, howvr, additional non-sampl information sms to b a dcisiv factor for th fficincy of all thos tchniqus. In my opinion, furthr studis in this ara will concntrat on sarching for mthods and tchniqus which would b combin th incrasing amount of information, prior and sampl on, about various populations that ar invstigatd. I think that th markt conomy in Poland, unlik th cntrally plannd conomy, has inspird rsarchrs to rspond with nw statistical idas and nw solutions to th nds of practic. Morovr, during th last yars thr has bn a tndncy for widning th ara of social and conomic livs, in which statistical survys hav bn succssfully usd on a rgular basis. This procss is likly to b continud, as th conomic and social ralitis gnrat nw information nds. 5. Statistical ducation in th socity On of th important challngs for statistics is to work out such masurmnt and dscription tchniqus which would, on th on hand, b adquat to incrasingly mor complx phnomna, and on th othr, b asily and proprly undrstood within th socity. Rliabl and good quality statistical data ar sought not only by ntrpriss or administration units. In dmocratic socitis, statistics should support nw popl s initiativs with data and mthods of data analysis. It rlats, among othrs, to activitis of non-govrnmnt organizations in such aras as: nvironmnt protction, labour markts, vocational ducation, halth-car and povrty. Promotion of high quality data and rsults of statistical analyss rprsnting ths aras can ssntially hlp popl or civic organizations rach th goals in thir voluntary activitis. Without a clar and crdibl dscription of th particular problm which thy want to solv, thir fforts ar likly to b lss productiv. Quantitativ dscriptions ar prfrrd at first stags of daling with a problm, bcaus numbrs ar abl to dfin th problm mor prcisly and unambiguously. Polish statistics has bn mor accssibl than in th past, and much has bn don in ordr to provid th rquird statistical information to various organizations and groups of popl whos intntion is to do somthing good for a crtain community. Howvr, mor can b don in this fild, spcially by official statistics. Statistical ducation which would nabl citizns to us and intrprt quantitativ facts proprly is anothr important challng. Unprpard popl confrontd with incrasing amount of statistical information in mass mdia and lswhr can fl lost or confusd, if thir individual obsrvations do not confirm th data. This, as a consqunc, can crat suspicion that statistics gnrats inadquat picturs of th rality. Lack of confidnc, which in such cass can b xplaind by lack of statistical ducation, may intrfr communication within th socity. In th long run, possibl lack of trust in statistical data, or in mthods of gathring and analyzing thm, would b a srious

197 96 M. Szrdr: Nw conomy problm in communication btwn dmocratic institutions and mmbrs of th socity. Thrfor, th problm of statistical ducation is now, and likly is going to b in th futur, a challng not only for statisticians but also for political and govrnmnt bodis. 6. Conclusions Nw challngs for statistics in Poland aftr 989 hav bn cratd by procsss connctd with building dmocracy and th markt conomy, and also by world-wid tndncis lik globalization and fast dvlopmnt of IT, which acclratd th nd for highr standards of statistical rsarch and survys. In th last yars statistical rsarch and survys hav com up in many nw filds of social and conomic activitis. Statistical dscription and quantitativ xplanation of many procsss in thos filds hav bcom mor popular than qualitativ ons, which wr prfrrd in th past. Th nw circumstancs constantly crat nw challngs for th applid statistics and for th thory of statistics. Spcial car should b paid to statistical ducation in th socity which hlps popl undrstand quantitativ dscription of th nvironmnt to which thy blong. REFERENCES SÄRNDAL C.E., S. LUNDSTRÖM, Estimation in Survys with Nonrspons, John Wily & Sons, Ltd., 005. SUŁEK A., Obrazy z życia socjologii w Polsc, Wyd. Oficyna Naukowa, Warszawa 0.

198 STATISTICS IN TRANSITION-nw sris, March 0 97 STATISTICS IN TRANSITION-nw sris, March 0 Vol. 3, No., pp STATISTICS IN TRANSITION" AND "STATISTICS IN TRANSITION - NEW SERIES " - FIRST FIFTEEN YEARS Jan Kordos How did w in Poland start prparing a statistical journal in English? I rmmbr that w discussd this issu, aftr th ractivation of th Polish Statistical Association (PTS in April 98, among mmbrs of th PTS and som collagus in GUS. I also discussd this with Prof. Ryszard Zasępa and nxt with Prof. Wisław Sadowski, who was at that tim th Prsidnt of th Cntral Statistical Offic of Poland (GUS and th formr Editor-in-Chif of Przgląd Statystyczny (Statistical Rviw. H advisd us to stablish a statistical journal in English as th journal of th Polish Statistical Association, and Przgląd Statystyczny would rmain as it was, th journal of th Committ of Statistics and Economtrics and th Polish Acadmy of Scincs. Profssor Sadowski supportd that ida fully, and promisd som assistanc from GUS. W accptd th approach of Profssor Sadowski, and discussd it with som collagus from th PTS. W ralizd that thr wr svral problms to b solvd, and on of thm was a financial support of such an undrtaking. In Dcmbr 985, whn I was lctd th Prsidnt of th Polish Statistical Association 3, w startd activitis in diffrnt filds, and among othrs, w discussd how to gt a prmannt financial support for th Association s activitis. W ralizd that th contribution of GUS was important but not sufficint. In 986 th Main Council of PTS dcidd to stablish th Burau of Statistical Rsarch and Analysis (BSRA to gt from that activity financial sourcs for diffrnt projcts undrtakn or supportd by th Association. W prpard appropriat documnts and snt thm to th Ministry of Intrnal Affairs for approval. It was not an asy task, and Dr. Lucjan Adamczuk, a mmbr of th Main Council of PTS, and I, had to convinc th appropriat An intrnational xprt in sampling; Profssor at Warsaw School of Economics; an author of th first Polish handbook in sampling; a chairman of th Mathmatical Commission of GUS; coopratd with FAO and othr intrnational organization; coopratd with Prof. Jrzy Nyman. Th Prsidnt of th Cntral Statistical Offic of Poland in ; Editor-in-Chif of Przgląd Statystyczny (Statistical Rviw in 970s; Chairman of th Committ of Statistics and Economtrics of th Polish Acadmy of Scincs; Rctor of Warsaw School of Economics ( , author of svral books on mathmatical statistics (translatd also in English, Italian and Slovakian, thory of dcision taking (translatd in English and Grman. 3 Prof. Jan Kordos was th Prsidnt of th Polish Statistical Association in

199 98 Jan Kordos: Statistics in Transition officials at th Ministry of Intrnal Affairs that th Burau would b involvd in statistical activity only. W should rmmbr that in was bfor 989, whn th changs of th systm bgun. Finally, in March 987 w got approval of th appropriat officials, and startd diffrnt projcts approvd by th Main Council of PTS. Th possibility of issuing a statistical journal in English by th Polish Statistical Association was rpatdly discussd among mmbrs of th Association. W got financial support from activitis of th Burau of Statistical Rsarch and Analysis of PTS. Finally, in April 99, th Main Council of PTS dcidd to st up a Working Group chaird by Prof. Alksandr Zliaś (Univrsity of Economics, Crakow, for prparing dtaild proposals to start a nw journal. Initially, th working titl of th journal Th Polish Statistician was adoptd. Dcision of th Main Council of PTS Thr wr diffrnt idas for th journal. Finally, w dcidd togthr with th statisticians from othr countris, that it should b an intrnational statistical journal publishd by our Association but ditd by statisticians from diffrnt countris. Th final nam of th journal was stablishd in Octobr 99 during th intrnational confrnc on small ara statistics. I discussd this issu with a numbr of intrnational statisticians, with Prof. Graham Kalton (USA, and Dr. Richard Platk (Canada, as my main advisors. W cam to th conclusion that th most appropriat nam would b Statistics in Transition, which ssntially corrspondd to th journal s initial aim to srv mainly countris undrgoing transition. Bsids, statistics is always "in transition" in a sns. Th cration of "Editorial Board" Th Working Group chaird by Prof. Alksandr Zliaś suggstd m as an Editor-in-Chif of th Journal. First, I had som objctions to that suggstion sinc I was alrady involvd in diffrnt activitis. Finally, aftr som discussion, I accptd it, and th Main Council of PTS appointd m to ths dutis, and w startd, ovrcoming som difficultis, to implmnt this task. Th rol of Coditors was accptd by Prof. Tomasz Pank and Prof. Adam Szulc of Warsaw School of Economics. It was ncssary to slct appropriat collagus from Poland and abroad, i.. Associat Editors (AE. First, w chos Polish AE, which was not asy, and thn th AE from abroad. Th lattr cam from Blgium, Canada, Holland, India, Italy, Japan, Mxico, th Unitd Kingdom, and th Unitd Stats, as wll as from countris in transition, namly Bulgaria, Czch Rpublic, Estonia, Latvia, Small Ara Statistics and Survy Dsigns, Intrnational Scintific Confrnc, Warsaw, Poland, 30th Sptmbr 3 rd Octobr 99.

200 STATISTICS IN TRANSITION-nw sris, March 0 99 Lithuania, Romania, Russian Fdration, Slovakia and Ukrain. I was abl to stablish coopration with thm du to my long-trm (mor than ight yars work abroad, participation in various intrnational confrncs and acquaintanc with many minnt statisticians. I must admit that I had no xprinc in running such a srious journal, but I rcivd a considrabl assistanc in th arly yars of my work from my collagus, hr I would lik to mntion: Dr. Richard Platk from Canada, formrly Statistics Canada, Dr. M.P. Singh from Canada, th Editor-in-Chif of "Survy Mthodology", and as wll from Dr. Lars Lybrg, Swdn, th Editor-in- Chif of "Official Statistics". Ovr th cours of th yars natural changs followd and svral of our clos collagus passd away. I shall mntion hr, abov all, our Associat Editors: Prof. Ryszard Zasępa (Poland, Prof. Alksandr Ryszard Wójcik (Mxico, Dr. M.P. Singh (Canada, Prof. Kn Takuchi (Japan, Prof. A. Rvnko (Ukrain and Prof. Alksandr Zliaś (Poland. Th first issu of th journal I would lik to mntion hr only th first issu of th journal publishd in Jun 993 which was dvotd to various aspcts of Polish statistics. That yar w clbratd two hundrd yars of Polish statistics, and 75 yars of stablishmnt of th Cntral Statistical Offic of Poland (GUS. Th first papr, prpard by Dr. J. Olński, Prsidnt of GUS, dalt with diffrnt problms connctd with transition of Polish statistics to th rquirmnts of markt conomy. Prof. T. Walczak dscribd svnty fiv yars of official statistics in Poland on background of two hundrd yars of th Polish statistics. Prof. W. Wojcichowski prpard a not on th Committ of Statistics and Economtrics of th Polish Acadmy of Scincs. Prof. W. Wlf dvlopd th concpt of th computrizd systm of macroconomic short and mdium-trm forcast and conomic policy simulation for th priod of transition towards th markd conomy. Prof. Z. Hllwig considrd stimation of linar rgrssion paramtrs undr scarcity of data. Prof. R.. Zasępa dscribd sampling mthods usd in diffrnt houshold survys in Poland, including application of sampling mthods in population cnsuss in Poland as a mans of spding up tabulation in 950 and 960, and to broadn th scop of th cnsuss. Dr. J. Wywiał dscribd th stimation of a man for thr sampling dsigns in a fixd population. Thr wr also thr nots on th following topics: Th Polish Statistical Journal, by Prof. Cz. Domański, A short not on Small Ara Statistics and Survy Dsigns, Intrnational Scintific Confrnc, hld in 30 th Sptmbr 3 rd Octobr 99, by Mr. W. Łagodziński, Th Rsarch Bulltin of th Rsarch Cntr for Economic and Statistical Studis which was launchd 99, by Dr. A. Szulc. I dscribd th activitis of th Polish Statistical Association foundd in 9.

201 00 Jan Kordos: Statistics in Transition Ovr th5 yars of my work as th Editor-in-Chif of SIT and SIT-ns, w publishd 46 issus, i.. ovr thr issus pr yar, in ight volums, comprising th total of about 800 pags, 505 articls, 55 rports, 6 book rviws, and ight obituaris. W hav publishd fiv spcial issus dvotd to statistics of small aras, a numbr of articls on sampl survys in various countris, th mthodology of houshold survys, data quality and th mthodology of th population cnsus 00. W also raisd svral statistical aspcts obsrvd in countris in transition and prsntd a lot of paprs discussd at intrnational confrncs, som of thm organizd by th PTS. W promotd Polish statistics in th intrnational arna, and nabld statisticians from othr countris to prsnt thir achivmnts. In 006 w rcivd a proposal for coopration with Springr Publishing Company, and I rgrt to say w faild to tak advantag of this offr. Th first vrsion of th journal, known as Statistics in Transition (SIT, was publishd in th yars twic a yar, with additional "spcial issus" publishd oftn as wll. Th journal providd a forum for xchanging viws and xprinc in various filds of statistics, at th bginning rgarding mainly th countris in transition from cntral planning to th markt conomy. Gradually th scop of our intrsts was xtndd to includ widr aras of application of statistical mthods, and prparation for a nw sris of th journal bgan. Statistics in Transition - nw sris (SIT-ns, was launchd in 007 as an lctronic vrsion of th Polish Statistical Association journal, publishd by th Cntral Offic Statistics. W agrd that th journal should b publishd thr tims a yar (April, August, Dcmbr. Th nw dition is to som xtnt a continuation of th prvious rlas, rgarding th numbring of volums and th logo. Howvr, SIT-ns is now taking a broadr policy of prsnting th application of statistical mthods, ducational statistics and its dvlopmnt. Aftr finishing my work as th Editor-in-Chif at th nd of 007, my dutis ar now limitd to thos of th Foundr/Formr Editor. I still continu to follow carfully th dvlopmnt of th journal and provid assistanc as far as I can. In 008 Prof. Włodzimirz Okrasa was appointd a nw Editor-in-Chif of Statistics in Transition - nw sris, Dr. Mark Cirpiał-Wolan was approvd a nw Scintific Scrtary, and Dr. Roman Popiński bcam th Scrtary. Th issus publishd sinc 000 ar availabl on-lin at th addrss: Th yar 0 is not only th hundrdth annivrsary of th Polish Statistical Association, but also th twntith yar of th journal bing issud. I hop that th journal will continu to b publishd in th futur, srving Polish statistics and giving statisticians from othr countris th chanc to prsnt thir contributions to th dvlopmnt of statistics. Jan Kordos Editor-in-Chif in

202 STATISTICS IN TRANSITION-nw sris, March 0 0 STATISTICS IN TRANSITION-nw sris, March 0 Vol. 3, No., pp. 0 0 STATISTICS IN TRANSITION NEW SERIES TODAY As a kind of post scriptum to th abov not by Profssor J. Kordos (Foundr Editor, it sms worth mntioning that sinc th nd of 007 th Journal has bn ditd by a nw Editor-in-Chif, with th hlp of also thn nwly appointd staff of th Editorial Offic and with th support of th Editorial Board. Som innovations that hav bn introducd ovr that priod sms to b worthwhil mntioning. Rsponding to growing intrst in public statistics, a nw sction dvotd to Currnt Issus in Public Statistics was stablishd in ordr to rport on ky issus rlatd to th functioning of official statistics intrnationally, on subjct mattrs that gain incrasing importanc in a country s data systm and ar appaling to community of producrs and usrs of statistics, as wll as to othr partis concrnd about th ovrall quality of public data, including policy makrs and practitionrs. It is notworthy that it was commncd by addrssing on of th issus of th most quintssntial and vital problm in public statistics that concrns data accss whil protcting individual ntitis data fil against disclosur for non-statistical purposs, following th lttr of th Polish Statistical Association on rportd accidnts of braching th principl of statistical confidntially. In 00 Profssor Vijaj Vrma of th Univrsity of Sina, who visitd Warsaw on th occasion of intrnational confrnc on EU-SILC, submittd a proposal to introduc a Journal s nw sction on Comparativ Survys. Th ida, which also was supportd by Profssor Kordos, was to strss th fact that growing dmand for a mor systmatic prsntation of hug works bing don in th ara of multipopulation survys might b sn as a nw hallmark for th contnts of th trm statistics in transition. Profssor Vrma kindly accptd to srv as a co-ditor of this sction. Th paprs includd in this sction ar supposd to discuss issus rlating to th maning, gnration and us of comparabl data, cross countris, rgions, sub- or supr-populations or tim. W ncourag our collaborators and potntial authors to submit such paprs. Currntly, th Editorial Offic of Statistics in Transition nw sris includs: Włodzimirz Okrasa, Editor-in-Chif Profssor and chair of mthodology at th Institut of Sociology of th Univrsity of Cardinal Stfan Wyszynski in Warsaw (UKSW, Advisor to th Prsidnt of th Cntral Statistical Offic of Poland/GUS. H srvd as a Had of Unit at th Europan Scinc

203 0 Statistics in Transition nw sris Foundation/ESF (Strasbourg ( aftr his work for th World Bank in Washington DC ( , and for th Social Scinc Rsarch Council N.Y., ( H was an ASA/NSF (Amrican Statistical Association and National Scinc Foundation Snior Rsarch Fllow at th US Burau of Labor Statistics (990-9, following taching in Amrican univrsitis (Univ. of Maryland and Univ. of Mississippi, and rsarching at th Institut of Economic Scincs of th Polish Acadmy of Scincs. Rsarch Scholar at th London School of Economics (Th British Acadmy, at th Univrsity of Oxford, and othrs; author of mor than 00 publications (most of thm in English in, among othrs, Europan Economic Rviw, Rviw of Incom and Walth, Rsarch on Economic Inquality; World Bank Working Paprs. Mark Cirpiał-Wolan, Scintific Scrtary Ph.D. of Warsaw School of Economics, lcturr in conomtrics and macroconomics at th Univrsity of Rzszów and th Rzszów School of Businss, Dirctor of Statistical Offic in Rzszów; author of mor than 50 publications in domstic and intrnational journals. Roman Popiński, Editorial Scrtary Ph.D., Political Scinc in Polish Institut of Intrnational Affairs, Lad Spcialist of CSO/P Information Division (sinc April 0, part-tim. Bata Witk, Editorial Scrtary, graduatd in sociology (UKSW, joind th SiTns Offic in April, 0.

204 STATISTICS IN TRANSITION-nw sris, March 0 03 STATISTICS IN TRANSITION-nw sris, March 0 Vol. 3, No., pp Information on th Congrss of Polish Statistics to Clbrat th 00 th Annivrsary of Th Polish Statistical Association In 0 w will b clbrating th 00 th annivrsary of th Polish Statistical Association (PSA, an organization cratd to intgrat spcialists involvd in public statistical srvics as wll as rprsntativs of th acadmic community, local and conomic govrnmnt and agncis of stat administration intrstd in th thory and implmntation of statistical rsarch. Th Association contributs to th dvlopmnt of thortical, mthodological and practical aspcts of statistical rsarch and tris to promot statistical knowldg in socity. It maintains coopration with statistical associations in othr countris and such organizations as Brnoulli - Socity for Mathmatical Statistics and Probability, Intrnational Socity for Quality of Lif Rsarch, Intrnational Socity for Quality-of-Lif Studis or Intrnational Fdration of Classification Socitis. Polish Statistical Association is an affiliatd mmbr of Intrnational Statistics Institut. To clbrat th 00 th annivrsary of Th Polish Statistical Association w dcidd to hold th Congrss of Polish Statistics on 8 0 April 0 in Poznan and combin this vnt with th clbration of Polish Statistics Day. Th Annivrsary of th Polish Statistical Association, as wll as th Congrss of Polish Statistics ar undoubtdly major vnts. It is our grat honour to inform that th Prsidnt of th Rpublic of Poland, Mr Bronisław Komorowski has xtndd his Honorary Patronag ovr th Congrss, whil numrous prominnt scintists and conomists hav bcom mmbrs of its Honorary and Scintific Committs.

205 04 Congrss In 08 w will clbrat 00 th Annivrsary of rcovry of indpndnc. Th Cntral Statistical Offic was th first unit of cntral administration of th indpndnt Polish stat. It was stablishd by Rgulation of th Rgncy Council alrady in July 98. And it is worth to not that Polish statisticians stablishd thir official association vn six yars arlir, bfor rcovry of th stat! And now th Polish Statistical Association can boast 00 yars of history and rich tradition. Th Polish Statistical Association was stablishd in Cracow in 9 and its main objctiv in th pr-war priod was to prpar a statistical dscription of th traditionally Polish trritoris from th arlist tims ( It was publishd in Cracow in 95 and titld Statistics of Poland ( Statystyka Polski. Juliusz Lo, its first Prsidnt, was a profssor of Jagillonian Univrsity and th thn Prsidnt of th city of Cracow. Mmbrs of th PSA wr famous Polish statisticians and conomists, among othrs profssors: Józf Buzk, Ludwik Landau, Jan Pikałkiwicz, Jrzy Spława-Nyman, Stfan Szulc. Contributors of th PSA ar not only minnt Polish statisticians, but also a larg numbr of anonymous popl ddicatd to srv scinc and th stat. In th intrwar priod th prsidnt of th Polish Statistical Association was Profssor Edward Szturm d Sztrm and th dputy prsidnt was Profssor Jan Czkanowski. Th association was mainly a scintific and rsarch on at that tim. Th official journal of th PTS was th quartrly Statistical Rviw. Aftr World War II, in 947 th PTS startd its activity undr th ladrship of Profssor Stfan Szulc. But in 953 th dcision on its liquidation was takn and ntrd in forc in 955. A part of th PSA mmbrs has bcom mmbrs of th Polish Economical Association, whr th Sction of Statistics was cratd. Th last ractivation of PTS took plac in April 98. In 993, following th initiativ of Profssor Jan Kordos (th Prsidnt of PSA in and undr his dition, th journal of th PSA ditd in

206 STATISTICS IN TRANSITION-nw sris, March 0 05 English was fundd. It is ntitld Statistics in Transition. Currntly th Polish Statistical Association has about 750 mmbrs organizd in 7 rgional branchs. Th PSA publishs jointly with th Cntral Statistical Offic th monthly journal Statistical Nws ( Wiadomości Statystyczn and th scintific journal of an intrnational charactr ntitld Statistics in Transition Nw sris. In rcognition of xcptional activitis of statisticians form Poznan, th Gnral Assmbly of Polish Statistical Association, appointd Poznan as th localisation of th Congrss. Acknowldgd Poznan Univrsitis, city and rgional authoritis wr invitd to participat in organization of th Congrss. In ordr to organiz th Congrss of Polish Statistics a spcial rsolution was adoptd by: Polish Statistical Association, Cntral Statistical Offic, Poznan Univrsity of Economics and Statistical Offic in Poznan: Polish Statistical Association Cntral Statistical Offic Poznan Univrsity of Economics Statistical Offic in Poznan Congrss of Polish Statistics is on of th most significant vnts in th history of Polish scintific thought and statistical practic. It marks th clbration of th 00th annivrsary of th Polish Statistical Association, in rcognition of its lading rol and lgacy. Th organizrs of th Congrss of Polish Statistics hop that it will provid a spcial opportunity for th xchang of idas and xprinc btwn rprsntativs of public statistics, rsarch cntrs as wll as othr partnrs involvd in invstigating and monitoring social, conomic and dmographic procsss. This form of discussion should also hlp to dirct mthodological and rsarch work to b undrtakn by th Polish statistical community in th yars to com. Th Congrss of Polish Statistics will hav an intrnational scop mainly by focusing on th prsntation of th Polish contribution to th world rpository of statistical knowldg. Th intrnational charactr of th Congrss will also b highlightd by th participation of numrous rprsntativs from forign institutions and th promotion of its idas and contributions outsid Poland. W also look forward to th participation of lading statisticians, who will nrich th Congrss with advancs in rsarch and applications. Numrous wll-known scintists in th ara of statistical rsarch wr invitd to participat in and

207 06 Congrss contribut to th Congrss. Th following rspctd statisticians hav announcd thir participation in th Congrss: Raymond Chambrs, Malay Ghosh, Lornzo Fattorini, Jan-Claud Dvill, Rinhold Dckr, Patrick Gronn, Wojcich Krzanowski, Nico Kilman, Francsco Billari, Achill Lmmi, Ann Valia Goujon and Li-Chun Zhang. Th Congrss programm compriss a numbr of thmatic sssions, including an annivrsary (historical sssion, a mthodological sssion dvotd to th mthodology of statistical rsarch, rgional statistics, population statistics, socioconomic statistics, statistical data and statistics of halth, sport and tourism. Th Congrss will also host discussion panls focusing on fundamntal problms of statistics in th modrn world and th futur of statistics. Th task of organizing th various sssions and panls has bn undrtakn by Polish most distinguishd statisticians, rcognisd both at th national and intrnational lvl. Plas s th a dtaild Congrss programm attachd. Congrss procdings will tak plac in th plnary halls (aula of Adam Mickiwicz Univrsity in Poznan and Poznan Univrsity of Economics. Th Organizing Committ would lik to invit vryon to join in th uniqu clbration of Polish statistics and tak part in th Congrss of Polish Statistics. Updatd information about th confrnc ar publishd on th Congrss wbsit: Chairprson of th Organizing Committ of th Congrss: Assoc. Prof. Elżbita Gołata, UEP: -mail: [email protected] Scrtariat of th Organizing Committ of th Congrss: Statistical Offic in Poznan, ul. J. H. Dąbrowskigo 79, Poznań: -mail: [email protected] tl (Mo-Fr: 8-5, (Mo: 9-, Tu: 7-0,W: 7-0, fax

208 STATISTICS IN TRANSITION-nw sris, March 0 07 Plnary sssions: Annivrsary sssion Th Programm of th Congrss of Polish Statistics Poznań 8 0 April 0 Plnary sssion Dvlopmnt of Polish statistical rsarch. Prsntation of th achivmnts of Polish statistics, organizr prof. dr hab. M.Krzyśko Walnty Ostasiwicz (Uniwrsytt Ekonomiczny w Wrocławiu, Dvlopmnt of statistical rsarch in Poland Jan Milniczuk, Polish Contributions in th dvlopmnt of mathmatical and applid statistics Tadusz Caliński, Dvlopmnt of Polish Statistical Rsarch Advancs in biomtrics Krzysztof Jajuga (Uniwrsytt Ekonomiczny w Wrocławiu, Dvlopmnt of Polish statistical rsarch in conomic scincs Janusz Witkowski, Tadusz Walczak, Jan Brgr (GUS, Public statistics historical dvlopmnt and modrn challngs Plnary sssion Dvlopmnt of Polish statistical rsarch. Eminnt Polish statisticians Trsa Ldwina (Instytut Matmatyczny PAN, Jrzy Nyman invitd papr Mirosław Krzyśko (UAM, Jan Czkanowski - invitd papr. Stanisława Bartosiwicz (Wyższa Szkoła Bankowa w Wrocławiu, Stańczyk Elżbita (Urząd Statystyczny w Wrocławiu, A short ovrviw of th socio-conomic history of Poland in th yars Jan Kordos (Wyższa Szkoła Mndżrska, Warszawa, Intrdpndnc btwn th dvlopmnt of thory and practic in survy mthodology in Poland Discussion Panl Th Futur of Statistics Janina Jóźwiak (Szkoła Główna Handlowa w Warszawi, Population statistics Janusz Witkowski (GUS, Social statistics Tomasz Pank (Szkoła Główna Handlowa w Warszawi, Social statistics Jrzy Wilkin (Uniwrsytt Warszawski, Economic statistics Jan Paradysz (Uniwrsytt Ekonomiczny w Poznaniu, Rgional statistics

209 08 Congrss Jrzy Andrzj Moczko (Uniwrsytt Mdyczny w Poznaniu, Halth statistics Mirosław Szrdr (Uniwrsytt Gdański, Statistical data Jack Koronacki (Instytut Podstaw Informatyki PAN, Warszawa, Mthodology of statistical rsarch Paralll Sssions: History and Dvlopmnt of Polish Statistics. Józf Pocicha (Uniwrsytt Ekonomiczny w Krakowi, Circumstancs surrounding th foundation of th Polish Statistical Association and its first Prsidnt invitd papr. Bożna Łazowska (Cntralna Bibliotka Statystyczna, Th lgacy of profssor Władysław Bortkiwicz 3. Czary Kuklo (Uniwrsytt w Białymstoku, Th family and houshold in Poland in th pr-industrial ag myths and facts invitd papr 4. Witold Zdaniwicz (Intytut Statystyki Kościoła Katolickigo, Warszawa, Contribution of th Statistical Institut of th Catholic Church to Polish public statistics Mathmatical statistics. Tadusz Bdnarski (Uniwrsytt Wrocławski, A statistical analysis of causs of bias in labour markt survys invitd papr. Wioltta Grznda (Szkoła Główna Handlowa w Warszawi, Using a smiparamtric Baysian Cox modl to study dtrminants of long-trm unmploymnt among young popl 3. Jan W. Owsiński (Instytut Badań Systmowych PAN w Warszawi, An optimal partition of mpirical distribution (and som problms assiociatd with it Mathmatical statistics. Lsław Gajk (Komisja Nadzoru Finansowgo i Politchnika Łódzka, Modlling insolvncy risk of invstmnt companis using statistical mthods invitd papr. Danil Kosiorowski (Uniwrsytt Ekonomiczny w Krakowi, Masurs of position and disprsion in robust analysis of conomic data strams 3. Pawł Kobus ( Szkoła Główna Gospodarstwa Wijskigo w Warszawi, Th us of th Baysian approach to stimat distributions of variabls for slctd units in a population using aggrgat data Mathmatical statistics 3. Jack Koronacki (Instytut Podstaw Informatyki PAN w Warszawi, Analysing multivariat data givn a small sampl siz invitd papr. Tomasz Górcki, Mirosław Krzyśko (Uniwrsytt im. Adama Mickiwicza w Poznaniu, Krnl principal componnt analysis

210 STATISTICS IN TRANSITION-nw sris, March Bronisław Cranka, Małgorzata Graczyk (Uniwrsytt Przyrodniczy w Poznaniu Estimating th total wight of objcts in wighing dsigns Mathmatical statistics 4. Zbigniw Szkutnik (Akadmia Górniczo-Hutnicza w Krakowi, EM algorythm and its modifications invitd papr. Jan Milniczuk (Instytut Podstaw Informatyki PAN w Warszawi i Politchnika Warszawska, Małgorzata Wojtyś (Politchnika Warszawska, Post-modl stimation of grad dnsity 3. Trsa Ldwina, Grzgorz Wyłupk (Instytut Matmatyczny PAN, Oddział Wrocław, A tst for two sampls givn on-sidd altrnativs Survy sampling and small ara statistics - English languag sssion. Malay Ghosh (Univrsity of Florida, Finit population sampling: modldsign synthsis - invitd papr. Ray Chambrs, Gunky Kim (Wollongong Univrsity, Rgrssion analysis using data obtaind by probability linking of multipl data sourcs - invitd papr 3. Imbi Traat (Univrsity of Tartu, Domain stimators calibratd on rfrnc survy Survy sampling and small ara statistics - English languag sssion. Jan-Claud Dvill, Danil Bonnéry, Guillaum Chauvt (ENSAE, Nyman typ optimality for marginal quota sampling - invitd papr. Janusz L. Wywiał (Katowic Univrsity of Economics, Estimation of population man on th basis of a simpl sampl ordrd by an auxiliary variabl 3. Wojcich Ziliński (Warsaw Univrsity of Lif Scincs, Statistical proprtis of a control dsign of controls providd by Suprm Chambr of Control 4. Wojcich Gamrot (Katowic Univrsity of Economics, On mpirical inclusion probabilitis Survy sampling and small ara statistics 3 - English languag sssion. Lornzo Fattorini (Univrsity of Sina, Dsign-basd infrnc on cological divrsity - invitd papr. Tomasz Żądło (Katowic Univrsity of Economics, On prdiction of totals for spatially corrlatd domains 3. Tomasz Klimank (Poznań Univrsity of Economics, Poznań Statistical Offic, Using indirct stimation with spatial autocorrlation in social survys in Poland 4. Tomasz Józfowski (Poznań Statistical Offic, Using a SPREE stimator to stimat th numbr of unmployd across subrgions Survy sampling and small ara statistics 4 - English languag sssion. Li-Chun Zhang (Statistics Norway, Micro calibration for data intgration - invitd papr

211 0 Congrss. Sara Francschi (Univrsity of Tuscia, Lornzo Fattorini (Univrsità di Sina, Maffi D. (Univrsità di Firnz Dsign-basd tratmnt of unit nonrspons by mans of th calibration approach 3. Marcin Szymkowiak (Poznań Univrsity of Economics, Construction of calibration stimators of total for diffrnt distanc masurs 4. Jan Kubacki (Łódź Statistical Offic, Estimation of paramtrs for small aras using th hirarchical Bays mthod in th cas of known modl hyprparamtrs Population statistics - English languag sssion. Nico Kilman (Univrsity of Oslo, Challngs for statistics on housholds and familis - invitd papr. Irna E.Kotowska (Warsaw School of Economics, Evolving population structurs and thir rlvanc for dmographic and social chang - invitd papr 3. Marta Styrc, Anna Matysiak (Warsaw School of Economics, Socioconomic status and marital stability Population statistics - English languag sssion. Francsco Billari (Bocconi Univrsity, Milan, Challngs for nw mthods in dmographic analysis (tntativ - invitd papr. Ewa Frątczak (Warsaw School of Economics, Tradition and modrnity in dmographic analysis. From Graunt and Lxis to longitudinal modls with fixd and random ffct 3. Mark Kupiszwski (CEFMPR, What drivs population chang? - invitd papr Population statistics 3. Elżbita Gołata (Economic Univrsity Poznań, Population cnsus and truth. Lucyna Nowak (GUS, Dvlopmnt of statistical rsarch in th fild of dmography and migration 3. Wiktoria Wróblwska (SGH, Changs in maximum lif span and longvity challngs for statistics 4. Jrzy T.Kowalski, Anna Majdzińska (Uniwrsytt Łódzki, Population aging in EU countris th nar futur and projctions 5. Jadwiga Borucka Joanna Romaniuk, Ewa Frątczak (SGH, Duration of first (marital and cohabiting unions in birth cohorts Social Statistics - English languag sssion. Achill Lmmi (Sina Univrsity, Dipartimnto di Economia Politica Dimnsions of povrty. thory, modls and nw prspctivs - invitd papr. Anna Szukiłojć-Bińkuńska (Główny Urząd Statystyczny, Dpartamnt Badań Społcznych i Warunków Życia, Masurmnt of povrty and social xclusion in Polish public statistics

212 STATISTICS IN TRANSITION-nw sris, March 0 3. Stanisław Macij Kot (Politchnika Gdańska, Wydział Ekonomii i Zarządzania, Zakład Statystyki, Stochastic quivalnc scals for Poland 4. Krystyna Hanusik, Urszula Łangowska-Szczęśniak (Uniwrsytt Opolski, Wydział Ekonomiczny, Dtrminants of variation in th lvl and structur of consumption of Polish housholds Social Statistics. Walnty Ostasiwicz (Uniwrsytt Ekonomiczny w Wrocławiu, Lif quality as a subjct of statistical rsarch invitd papr. Jolanta Prk-Białas (Szkoła Główna Handlowa, Instytut Statystyki i Dmografii, Th situation of oldr gnrations in Cntral and Eastrn Europ on th basis of EU-SILC data 3. Anna Szukiłojć-Bińkuńska (Główny Urząd Statystyczny, Dpartamnt Badań Społcznych i Warunków Życia, Lif quality in GUS survys 4. Krzysztof Szwarc (Uniwrsytt Ekonomiczny w Poznaniu, Katdra Statystyki i Dmografii, Th standard of living and variation in th dmographic situation at NUTS 4 lvl in th Wilkopolska provinc Social Statistics 3. Urszula Sztandrska (Uniwrsytt Warszawski, Wydział Nauk Ekonomicznych, Katdra Makrokonomii i Torii Handlu Zagraniczngo, Polish public statistics as a sourc of inspiration for and an obstacl to th dvlopmnt of labour markt rsarch invitd papr. Pawł Ulman (Uniwrsytt Ekonomiczny w Krakowi, Katdra Statystyki, Th influnc of conomic activity of th disabld on th conomic situation of thir housholds 3. Dominik Śliwicki (Urząd Statystyczny w Bydgoszczy, Using a logit modl in conomtric analysis of gross salary 4. Alksandra Matuszwska-Janica (Szkoła Główna Gospodarstwa Wijskigo w Warszawi, Katdra Ekonomtrii i Statystyki, Statistical analysis of th gndr wag gap in Poland as compard to th EU countris by ag, company typ and occupational group Social Statistics 4 - English languag sssion. Ann Valia Goujon, Ramon Baur, Samir K.C., Michala Potančoková (Vinna Institut of Dmography (VID of th Austrian Acadmy of Scincs, Th human capital puzzl: why it is so hard to find good data on ducational attainmnt? - invitd papr. Marcin Stonawski (Cracow Univrsity of Economics, Human capital and population aging in Poland 3. Agniszka Chłoń-Domińczak (Warsaw School of Economics, Th us of indicators in th contxt of dvlopmnt of vidnc-basd social policy

213 Congrss 4. Dominik Rozkrut (Urząd Statystyczny w Szczcini, Diffrntiation of innovation stratgis Economic statistics. Włodzimirz Siwiński (Uniwrsytt Warszawski, Akadmia L. Koźmińskigo, A statistical ovrviw of th 008 crisis invitd papr. Eugniusz Gatnar (Narodowy Bank Polski, Th rol of th National Bank of Poland in th systm of Polish public statistics 3. Barbara Pawłk (Uniwrsytt Ekonomiczny w Krakowi, A study of th usfulnss of conomic situation tst rsults publishd by GUS for short-trm projctions of changs in conomic activity in Poland using vctor autorgrssion 4. Andrzj Czyżwski, Alksandr Grzlak (Uniwrsytt Ekonomiczny w Poznaniu, Possibilitis of using input-output statistics for macroconomic assssmnt in conomy Economic statistics. Barbara Librda (Uniwrsytt Warszawski, Gnrational accounting by mans of masuring th walth of conscutiv gnrations invitd papr. Krzysztof Malaga (Uniwrsytt Ekonomiczny w Poznaniu, Dilmmas of modrn statistics of conomic growth 3. Stanisław Lwiński Vl Iwański, Zofia Wilimowska (Politchnika Wrocławska w Wrocławiu, Financial structur of Polish companis: statistical modlling 4. Maria Parlińska, Robrt Babiak (Szkoła Główna Gospodarstwa Wijskigo w Warszawi, Scrning and risks of information asymmtry Economic statistics 3. Elżbita Mączyńska (INE PAN, Przs PTE, Statystyka jako źródło danych w badaniach naukowych. Dylmaty i nidostosowania - invitd papr. Monika Natkowska, Jack Kowalwski (Urząd Statystyczny w Poznaniu, Using a map of short-trm statistics in th procss of organizing businss survys conductd by public statistics 3. Grażyna Dhnl (UE Poznań, Indirct micro-stimation in businss statistics 4. Anta Ptak-Chmilwska (Szkoła Główna Handlowa, Conditions of th businss sctor in Poland. Statistics of businss survival Economic statistics 4. Andrzj P. Wiatrak, Contmporary problms of agricultural statistics invitd papr. Robrt Pacuszka (Główny Urząd Statystyczny, Mthods of agricultural production and thir classification. An ida for a GUS mthodological study

214 STATISTICS IN TRANSITION-nw sris, March Rnata Bilak (GUS Th rol of statistics in th procss of planning dvlopmnt policis prioritis and challngs 4. Grzgorz Kowalwski (Uniwrsytt Ekonomiczny w Wrocławiu, Mthodology of conomic situation survys Rgional statistics. Jan Paradysz (Cntrum Statystyki Rgionalnj, Uniwrsytt Ekonomiczny w Poznaniu, Rgional statistics: th currnt stat, problms and dirctions invitd papr. Dominika Rogalińska (Główny Urząd Statystyczny, Challngs of rgional statistics in th contxt of th dbat about policy cohrnc 3. Danuta Strahl, Małgorzata Markowska (Uniwrsytt Ekonomiczny w Wrocławiu, Possibilitis of assssing th lvl of innovation in NUTS rgions in th light of Eurostat information rsourcs 4. Ewa Kamińska-Gawryluk (Urząd Statystyczny w Białymstoku, Rgional variation in Poland and slctd EU countris (UE- 5 Rgional statistics. Tadusz Borys (Uniwrsytt Ekonomiczny w Wrocławiu, Tomasz Potkański (Związk Miast Polskich, Monitoring rgional and local dvlopmnt. Dorota Donic (Urząd Statystyczny w Katowicach, Rgional accounts mthodological problms and practic 3. Bartosz Bartniczak (Urząd Statystyczny w Wrocławiu, Th modul of sustainabl dvlopmnt indicators in th local databank 4. Dorota Wyszkowska (Uniwrsytt w Białymstoku, US w Białymstoku, Rgional statistics as an instrumnt of supporting th dvlopmnt of Polish provincs 5. Jack Batóg, Barbara Batóg, Magdalna Mojsiwicz (Uniwrsytt Szczciński, Katarzyna Wawrzyniak (Zachodniopomorski Uniwrsytt Tchnologiczny w Szczcini, A statistical systm of monitoring th implmntation stag of th city dvlopmnt stratgy Rgional statistics 3. Janusz Dygaszwicz (Główny Urząd Statystyczny, Th agricultural cnsus of 00, th national cnsus of 0 and th us of GIS in public statistics. Pawł Chlbicki, (ESRI Polska, ArcGIS as a powrful took for statistical data visualization and analysis 3. Sylwia Filas-Przybył, Macij Kaźmirczak Dorota Stachowiak (Urząd Statystyczny w Poznaniu, Ośrodk Statystyki Miast, Th us of administrativ data in urban statistics 4. Robrt Buciak, Mark Piniążk (Główny Urząd Statystyczny, Uniwrsytt Warszawski, Spatial classification of rural aras in Poland

215 4 Congrss 5. Roma Ryś-Jurk (Uniwrsytt Przyrodniczy w Poznaniu, Rgional variation in agricultural production in EU countris (UE-7 Data analysis and classification - English languag sssion. Rinhold Dckr (Univrsität Bilfld, Modl-basd analysis of onlin consumr rviws mthods and applications - invitd papr. Patrick Gronn (Erasmus Univrsity Rottrdam, Th support vctor machin as a powrful tool for binary classification - invitd papr 3. Andrzj Sokołowski (Cracow Univrsity of Economics, Bata Basiura (AGH Univrsity of Scinc and Tchnology in Cracow Ward s agglomrativ mthod Data analysis and classification - English languag sssion. Wojtk Krzanowski (Univrsity of Extr, Classification: som old principls applid to nw problms - invitd papr. Justyna Wilk (Uniwrsytt Ekonomiczny w Wrocławiu, Th symbolic approach in rgional analyss 3. Marcin Płka (Wrocław Univrsity of Economics, Th nsmbl approach for clustring intrval-valud symbolic data 4. Justyna Brzzińska (Univrsity of Economics in Katowic, Indpndnc analysis of nominal data with th us of R softwar Data analysis and classification 3. Dorota Rozmus (Univrsity of Economics in Katowic, Th nsmbl approach in taxonomy. Małgorzata Markowska, Bartłomij Jfmański (Uniwrsytt Ekonomiczny w Wrocławiu, Assssing th dynamics and dirction of changs in th dvlopmnt of intllignt spcialization of Europan rgions using fuzzy classification 3. Kamila Migdał-Najman (Uniwrsytt Gdański, Th structur of a slforganizing hybrid nural ntwork basd on th SOM-GNG algorithm 4. Krzysztof Najman (Uniwrsytt Gdański, Slf-organizing ntworks in clustr analysis Data analysis and classification 4. Alksandra Łuczak, Fliks Wysocki (UP Poznań, Assssing th lvl of socio-conomic dvlopmnt of NUTS 4 units (poviats of th Wilkopolska provinc. Katarzyna Kopczwska (Uniwrsytt Warszawski, Rgions in spac. Dos location and accssibility mattr for socio-conomic dvlopmnt? 3. Robrt Pitrzykowski (Szkoła Główna Gospodarstwa Wijskigo w Warszawi, Th us of quantil rgrssion in spatial analyss of arabl land prics 4. Marzna Piotrowska-Trybull, Stanisław Sirko (AON Th influnc of a military bas on th dvlopmnt of th surrounding NUTS 5 unit (gmina

216 STATISTICS IN TRANSITION-nw sris, March Joanna Zyprych-Walczak, Alicja Szablska, Idzi Siatkowski (Uniwrsytt Przyrodniczy w Poznaniu, Mthods of gn slction that account for Intr-gn corrlation Statistical data. Jan Zawadzki, Maria Szumksta-Zawadzka (Zachodniopomorski Uniwrsytt Tchnologiczny w Szczcini, On mthods of prdicting missing data in tim sris with priodical (sasonal fluctuations. Jadwiga Suchcka, Emilia Modranka (Uniwrsytt Łódzki, Spatial statistics mthods and applications 3. Ewa-Zofia Frątczak, Adam Korczyński (Szkoła Główna Handlowa w Warszawi, Tradition and modrn trnds in data imputation mthods. An ovrviw of thoris slctd xampls of applications 4. Maja Rynko (GUS, Indx and aggrgation thory dtaild analysis 5. Czary Głowiński (SAS Institut sp. z o.o., Using social ntworks to modl th bhaviour of customrs of tlcommunications companis Statistical data. Grażyna Trzpiot, Agniszka Orwat-Acdańska (Uniwrsytt Ekonomiczny w Katowicach, Th classification of mutual funds basd on th managmnt styl th quantil rgrssion approach. Tadusz Kufl (Uniwrsytt Mikołaja Koprnika, Marcin Błażjowski, Pawł Kufl (Wyższa Szkoła Bankowa w Toruniu, Th cration of databanks as th basis of socio-conomtric analyss in GRETL softwar 3. Zbigniw Augustyniak, (Główny Urząd Statystyczny, Onlin prsntation of statistical data as an lmnt of implmnting th SISP projct 4. Arlta Olbrot-Brzzińska (Urząd Statystyczny w Poznaniu, Social functions of statistical information and th rsponsibility of public statistics 5. Katarzyna Wawrzyniak (Katdra Zastosowań Matmatyki w Ekonomii Wydział Ekonomiczny Zachodniopomorski Uniwrsytt Tchnologiczny w Szczcini, Assssing th dgr of implmnting th main objctivs of th National Dvlopmntal Stratgy by provinc using corrspondnc analysis Poland and Ukrain in th Europan contxt. Rusłan Motoryn (UPUFiHM w Kijow, Iryna Motoryna, Ttiana Motoryna (Uniwrsytt Kijowski, A comparison of indicators of th us of houshold savings in Poland and Ukrain. Miczysław Kowrski (Wyższa Szkoła Zarządzania i Administracji w Zamościu, Studying conomic mood of ntrprnurs and consumrs at th rgional lvl basd on xampl of th Lublski provinc 3. Andrzj Młodak (Urząd Statystyczny w Poznaniu, Modrnization of conomic activity statistics on a pan-europan scal

217 6 Congrss 4. Magdalna Gabińska, Piotr Gołos, Alina Warlis (US w Białymstoku, Th valu of forst rsourcs in Poland th thortical aspct and mpirical rsarch 5. Karol Andrzjczak (Politchnika Poznańska, Changs and th growth limit of th indicator of th automobil markt saturation at th global lvl and in Poland 6. Dorota Kwiatkowska-Ciotucha, Urszula Załuska (UE w Wrocławiu, Assssing th us of ESF funding in diffrnt rgions of Poland in th currnt programming cycl Halth statistics. Agniszka Dyzmann-Sroka, Jrzy Moczko, Andrzj Roszak, Macij Trojanowski (Uniwrsytt Mdyczny im. K. Marcinkowskigo w Poznaniu, Mthods of incrasing data quality in malignant tumor rgistrs. Urszula Wojcichowska, Joanna Didkowska, (Cntrum Onkologii, Malignant tumors in Poland as a public halth problm. Modrn tools for masuring th phnomnon 3. Barbara Kołodzijczak, Magdalna Roszak (Uniwrsytt Mdyczny im. K. Marcinkowskigo w Poznaniu, Rapid -larning in biostatistics 4. Magdalna Roszak, Barbara Kołodzijczak (Uniwrsytt Mdyczny im. Karola Marcinkowskigo w Poznaniu, E-assssmnt of statistical knowldg of mdicin studnts 5. Anna Wirzbicka (Instytut Statystyki i Dmografii, Łódź, A taxonomic analysis of public halth in Poland in comparison with slctd Europan countris Statistics of sport and tourism. Jack Foks (Ministrstwo Sportu i Turystyki, Sport statistics in practic invitd papr. Barbara Librda (Uniwrsytt Warszawski, Łucja Tomaszwicz, Iwona Świrczwska (Uniwrsytt Łódzki, Problms of crating satllit accounts as xmplifid by sport satllit account for Poland 3. Iwona Bąk (Zachodniopomorski Uniwrsytt Tchnologiczny w Szczcini, A statistical analysis of tourist activity of snior citizns in Poland 4. Marcin Błażjowski (Wyższa Szkoła Bankowa w Toruniu, Applying modlling and prdiction algorithms to th tourism markt Classifications and standards. Włodzimirz Okrasa (Główny Urząd Statystyczny, Statystyka i socjologia: współzalżności rozwoju z pspktywy intrdyscyplinaryzacji badań społcznych. Aspkty mtodologiczn i instytucjonaln

218 STATISTICS IN TRANSITION-nw sris, March 0 7. Srgiy Grasymnko (Uniwrsytt Kijowski Olna Chupryna, (Narodowy Uniwrsytt Karazina w Chakowi, Optimizing an invntory of indicators for th comparativ assssmnt of socio-conomic ntitis 3. Grzgorz Krzykowski, Marcin Kalinowski, Data slction as a ky lmnt in statistical survys in th contxt of financial markts 4. Piotr Krasucki (Instytut Spraw Publicznych, Władysław Wisław Łagodziński, An intgratd systm of statistical data on halthcar th ssntial minimum 5. Artur Mikulc, Alksandra Kupis - Fijałkowska, (Uniwrsytt Łódzki, An mpirical analysis of Mojna and Wishart's fficincy critrion in clustr analysis 6. Mariusz Kraj, (GUS, A structur and dvlopmnt plan of a statistical ducation and rsarch cntr of th Cntral Statistical Offic in Jachranka Statistical infrnc. Mirosław Krzyśko, Łukasz Waszak (Uniwrsytt im. Adama Mickiwicza w Poznaniu Krnl canonical corrlation analysis. Grzgorz Kończak (UE Katowic, Statistical infrnc for multivariat data in multiway contingncy tabls 3. Joanna Kisilińska (SGGW Warszawa, Using th bootstrap mthod to produc prcis stimats of man and varianc 4. Ewa Mllr (US Poznań, Small ara stimation for slctd variabls of th labour markt 5. Łukasz Wawrowski (US Poznań, Povrty analysis at th NUTS 4 lvl in th provinc of Wilkopolska using small ara statistics mthodology Economic and social dvlopmnt analysis. Elżbita Stańczyk (Urząd Statystyczny w Wrocławiu, Dolnośląski Ośrodk Badań Rgionalnych, Occupational qualifications of th unmployd on th basis of rsarch by CSO. Intrvoivodship Comparativ Analysis. Józf Hozr, Marta Hozr-Koćmil (Uniwrsytt Szczcinski, Quantum satis for companis in Poland in 0 3. Janusz Korncki, Piotr Cmla (Urząd Statystyczny w Łodzi, Stratgic dilmmas of supporting micro businss dvlopmnt in Poland 4. Rafał Nowakowski (Urząd Statystyczny w Wrocławiu, Local govrnmnt lctions basd on th xampl of capital citis of th Dolnośląski, Małopolski and Wilkopolski rgions 0 yars of xprinc 5. Jack Białk (Uniwrsytt Łódzki, A spcial cas of a crtain gnral formula of th pric indx

219 8 Congrss Postr sssion. Bata Bal-Domańska (Uniwrsytt Ekonomiczny w Wrocławiu, WGRiT w Jlnij Górz Convrgnc procsss modlling th Europan rgional spac. Macij Bręswicz (UE w Poznaniu, Intrnt data sourcs in th light of th national cnsus basd on th xampl of th ral stat markt in Poznan 3. Anna Błaczkowska (Wyższa Szkoła Bankowa w Wrocławiu, Alicja Grzśkowiak (Uniwrsytt Ekonomiczny w Wrocławiu, Dmographic and conomic conditions of th procss of junior high school ducation in th rgions of Dolny Śląsk and Opolszczyzna in th yars Hanna Dudk, Joanna Landmssr (Katdra Ekonomtrii i Statystyki SGGW w Warszawi Wag satisfaction and rlativ dprivation 5. Konrad Furmańczyk, Stanisław Jaworski ( Dtcting changs in a sris of indpndnt obsrvations 6. Alicja Ganczark-Gamrot (Samodzilny Zakład Dmografii i Statystyki Ekonomicznj UE w Katowicach, Multivariat FIGARCH modls for risk assssmnt on th Polish lctricity markt 7. Hanna Gruchociak (UE w Poznaniu, Dlimitacja lokalnych rynków pracy w Polsc 8. Marta Małcka (Katdra Mtod Statystycznych, Uniwrsytt Łódzki, Assssing th varianc of Valu at Risk (VaR stimators 9. Magdalna Okupniak (UE w Poznaniu, Applying intra- and intrblock analysis in conomic statistics 0. Elżbita Paszko, Anna Maria Jurk (Katdra Mtod Statystycznych, Uniwrsyttu Łódzkigo Application of TQM - Total Quality Managmnt - in th procss of improving taching mthods. Agniszka Pobłocka (Uniwrsytt Gdański, Polski rynk ubzpiczń w latach Wojcich Roszka (UE w Poznaniu, Applying mass imputation mthods to intgrat databass from various sourcs 3. Danuta Rozpędowska-Matraszk (Instytut Ekonomii Stosowanj PWSZ w Skirniwicach Assssing th fficincy of halthcar in Poland an analysis basd on groups of similar NUTS 4 units (poviats 4. Elżbita Sobczak (Uniwrsytt Ekonomiczny w Wrocławiu Workforc by th intnsity of R&D activity in EU countris spacstructural analysis 5. Agniszka Stanimir (Uniwrsytt Ekonomiczny w Wrocławiu, Diffrnt tchniqus of prsnting non-mtric variabls 6. Marta Styrc (Instytut Statystyki i Dmografii, Szkoła Główna Handlowa, Factors affcting th stability of first marriags in Poland 7. Marta Styrc (Instytut Statystyki i Dmografii, Szkoła Główna Handlowa, Th ducational gradint of divorc in Poland