Computer Administering of the Psychological Investigations: Set-Relational Representation

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1 Open Journal of Appled Senes do: /ojapps Publshed Onlne June 2012 ( Coputer Adnsterng of the Psyhologal Investgatons: Set-Relatonal Representaton Krasr Yordzhev 1 Ivelna Peneva 2 1 Faulty of Matheats and Natural Senes South-West Unversty Blagoevgrad Bulgara 2 Departent of Psyhology Faulty of Phlosophy South-West Unversty Blagoevgrad Bulgara Eal: {yordzhev velna_peneva}@swu.bg Reeved Marh ; revsed Aprl ; aepted May ABSTRACT Coputer adnsterng of a psyhologal nvestgaton s the oputer representaton of the entre proedure of psyhologal assessents test onstruton test pleentaton results evaluaton storage and antenane of the developed database ts statstal proessng analyss and nterpretaton. A atheatal desrpton of psyhologal assessent wth the ad of personalty tests s dsussed n ths artle. The set theory and the relatonal algebra are used n ths desrpton. A relatonal odel of data needed to desgn a oputer syste for autoaton of ertan psyhologal assessents s gven. Soe fnte sets and relaton on the whh are neessary for reatng a personalty psyhologal test are desrbed. The desrbed odel ould be used to develop real software for oputer adnsterng of any psyhologal test and there s full autoaton of the whole proess: test onstruton test pleentaton result evaluaton storage of the developed database statstal pleentaton analyss and nterpretaton. A software projet for oputer adnsterng personalty psyhologal tests s suggested. Keywords: Coputer Adnsterng; Coputer Testng; Coputer Psyho Dagnost; Matheatal Modelng; Set Theory; Relatonal Algebra; Databases 1. Introduton Psyhologal assessent wll be alled any psyhologyal testng ade wth the help of a prelnary prepared test a lst of questons or stateents that the assessed person or group of people has to answer or to gve ther opnon for. The separate parts of the test are alled tes. We wll all oputerzed psyhologal assessent any psyhologal testng where one or several phases of the testng are ade wth the use of a oputer. Coputer adnsterng of psyhologal tests s the oputer representaton of the entre proedure of psyhologal assessents test onstruton test pleentaton results evaluaton storage and antenane of the developed database ts statstal proessng analyss and nterpretaton. Personalty questonnares are those psyhologal tests whh are purposed for desrpton and evaluaton of the haratersts of ogntve (behavoral) eotonal and otvaton sphere the nterpersonal relatons and atttudes of an ndvdual [1]. It s typal for the Personalty questonnares (n ontrast to Aheveent tests or Intellgene tests) that the tes are questons or stateents for whh answers the respondent has to report ertan nforaton onernng hself hs experene and relatons. The forat of the answers to tes s also spef ost often they are desrbed wth the help of а fnte set of prelnary known answers or stateents whh we wll ark by Ans. In our exanatons we wll aentuate anly on fnte sets of possble responds to eah te of the test. For exaple Ans = { Yes No } Ans = { True False } Ans = { I lke t I don t lke t } Ans = { Often Soetes Never } Ans = { True I don t know False } Ans = { Agree I not sure Dsagree }. Ites wth ratng sales are also used n prate but we wll exane just ratng sales that represent defnte and onsequently dsrete set of real nubers. For ore detals about bas ters n personalty psyhologal testng see for exaple n [23]. There are dfferent ways to struture proess and store data n a software produt. Data and data lnks are abstraton of fats and relatons fro the real world [4]. Very often ths abstraton s rather oplex and requres a speal atheatal odel for ts desrpton a data odel. The use of one or other odel eans that n ertan nforaton syste are hosen dfferent prnples for data struturng or data operaton. The ost wdespread data odel nowadays s the relatonal odel suggested for the frst te by E. F. Codd at the begn- Copyrght 2012 SRes.

2 K. YORDZHEV I. PENEVA 111 nng of the 1970s of the last entury and desrbed n a set of artles one of the earlest s [5]. For ths artle E. F. Codd won a prestgous A. Turng award of the Aeran Assoaton for Coputng Mahnery n Let the faly of sets D D D D 1 2 whh we wll all doans be gven. Let s exane the Cartesan produt: W D D D 1 2 n 1 2 n k k k x x x x D D D k 1 2 n (It s possble for soe s and t D W D.) Eah subset s t s alled n-аrу relaton on D. Fro a pratal pont of vew the fnte relatons are of nterest.e. all possble fnte subsets of W and therefore n the present pee of wrtng relaton wll ean fnte relaton (besdes the opposte s expltly ephaszed) no atter t s supposed that the sets D 1 2 ould possbly be nfnte (for exaple nfnte sets of real nubers). Let s ark wth R the set of all n-ary relatons fored by n n 1 2 (not defntely dfferent) sets (doans) fro the faly D. Let R and let r r1 r2 r n be the -th eleent of. r s alled the -th reord of the relaton. In ths ase s an eleent ndex not an exponent. The oponent r j of r s alled value of the j-th attrbute n the -th reord of. The values of the j-th attrbutes of all reords of ake the j-th feld of. Fro the defnton of the ter feld follows that the eleents of j-th feld an reeve values fro one sole doan D j D. In the set R of all relatons n D n ertan rustanes t s possble to defne varous operatons unon nterseton subtraton opleent projeton oposton ndexng sortng et. Relatonshps respondng to ertan ondtons are possble between the separate attrbutes. Thus R together wth the ntrodued operatons and relatonshps between attrbutes turns nto algebra alled relatonal algebra. Relatonal algebra s n the base of relatonal data odel. The database anageent systes whh have the relatonal odel n ther bases are also alled relatonal databases. Bas knowledge n the feld of the theory of relatonal algebras an be obtaned n [6]. Eah relaton R ould be vsually presented lke a retangular table n whh the -th row s the -th reord and the j-th olun s the j-th feld of. Ths orrespondene s one-to-one.e. the so bult table opletely deternes the relaton presented by t. Due to that reason and to help eah user easly understand the an notons of relatonal algebra n the ost of software anuals for relatonal database they talk about and operate ostly wth the noton table as a synony of the noton relaton n the faly of doans [4] never nd that fro a pratal pont of vew there ould be a greater nuber of table types and not every table ould present onrete relaton.e. not every type of table ould be used n a software for relatonal database. For exaple the alendar s a retangular table whh annot be dentfed wth the above defned ter relaton. 2. Sets of Values and Relaton on The Whh Are Neessary for Creatng a Personalty Psyhologal Test To reate a Personalty psyhologal test usng the help of a oputer t s neessary to defne and spefy the followng sets: 1) The set Qst s opound of questons or stateents presented for answer or opnon to the tested ndvdual or group of people fro the researh psyhologst. The eleents of Qst are the tes of the test. The presentng order of the tes has a sgnfant eanng for the psyhologst as the sequene of the dsussed tes has nfluene to answers and therefore s portant for drawng the fnal onluson and test results nterpretaton. In ths relaton arses the need of next set: 2) Set Z 1 2 where Qst s the ardnal nuber of the eleents of set Qst. Eah eleent of the set Z s a unque nuber of te n the set Qst. 3) There s a bjetve appng Qst Z between the sets Z and Qst and the author of the psyhologal test for eah qqst has to defne very arefully the age k q of the eleent q n the appng. In ths ase k s a nuber of the te q and deternes the order of tes presentaton to the tested ndvdual. As t was above ephaszed deternng the nuber of eah te s portant for the fnal onluson and all that s n the opetene of the psyhologst author of the test. In addton the nuber ust be n the nterval 1 of natural nubers. In ths sense n a database anageent syste needed for oputer Personalty psyhologal test (Tests generator) developent when deletng an te or nsertng a new one between two exstng tes an autoat tes renuberng has to be provded. In ths sense the feld Z s qute dfferent fro the auto nreent feld envsaged n a nuber of database anageent systes whh serves a prary key. For felds of that type the above entoned operatons dvson and te nserton are not followed by renuberng even ore t s not allowed to ake hanges n the prary key value. 4) A fnte set Ans of possble answers to the tes (see seton 1). Copyrght 2012 SRes.

3 112 K. YORDZHEV I. PENEVA 5) A set Ctg of psyhologal ategores (Personalty haratersts) whh are subjet of analyss and evaluaton onernng the assessed ndvdual or group of people wth the ad of the tes fro the set Qst and the onrete answer that s hosen. It s not oblgatory for eah te to be related to gven psyhologal ategory. 6) We are exanng the fnte faly of subsets of Qst T T Qst Ctg wth the eleent qqst whh belongs to the subset T f and only f the te q has a relaton to the ategory Ctg n the orrespondent psyhologal assessent. Obvously T Qst and f qqst and q T Ctg Ctg (2) then the te q wll not effet the entre test and wll drop out. 7) Let Ans a 1 a 2 ak. For every a Ans we put together the set of nubers S.e. we exane the followng faly of sets of nubers S a Ans 12 k We are buldng the Cartesan produt of the sets S 1 2 k : Sl S a Ans 1 2 s s s s S 12 k k Ans k Eah eleent s S a Ans fro a pratal pont of vew represents an assessent nueral value of the psyhologal ategores fro the set Ctg on ondton that the assessed person ould possbly respond to a rando te wth an answer or a stateent a Ans. Qute often these assessent values are 1 or 0. For exaple f Ans 2 and we assue that the assessent value for eah postve answer s equal to 1 and for eah negatve answer s 0 then we an easly alulate the total nuber of postve answers. 8) Let s rend that a bnary relaton f A B s alled funton f for eah x A there s no ore than one y B so that x y f. The fat that f AB s a funton s presented also lke that f : A B and nstead of x y f we wrte y f x. For eah psyhologal ategory Ctg s defned one funton f : Qst Sl wth the ad of whh the psyhologst evaluates the assessed person regardng the ategory Ctg. Suh funton s alled a sale for the psyhologal ategory Ctg. It s a oon prate the nae of the sale to be exatly the sae as the nae of the psyhologal ategory. The set of funtons f Ctg oposed by all sales for the exaned psyhologal ategores s alled a sale of the Personalty psyhologal test. What s the assessent of the dfferent tes regardng the orrespondent answers.e. how the funtons are defned f : Qst Sl Ctg and what s the nfluene of ths to the suary assessent of the test pleentaton an be estated after wde psyhologyal and statstal nvestgatons [1-37]. 9) Relaton Bnd q f q Ctg q Qst Ctg Qst Sl where Ctg Qst and Sl are sets whh are defned orrespondngly n subsetons 5) 1) and 7) and the relaton f Ctg s a funton defned n 8) (sale of psyhologal ategory ). Every reord n DBNae_ Bnd ontans the nuber of the sores we an take when the person does the orrespondng answer a Ans aordng the sale f q for ategory Ctg and te q Qst. 10) Let Ctg and let n f q (5) where qqst x1 x2 xk n x1 x2 xk In other words s the nu assessent value (nu sore) whh ould possbly be obtaned n a rando testng related to the ategory Ctg and dependng on the orrespondent sale f : Qst Sl. Analogously we spefy the axu assessent value where M ax f q (6) qqst x1 x2 xk ax x1 x2 xk Obvously M. We exane the fnte sequene of nubers b b b b M 0 1 l 1 l. As we denote l we ephasze the fat that the nuber of the ebers n the row depends on the ategory Ctg. We are separatng the nterval M to the subntervals b b 0 1 b1 b 2 b2 b 3 b b l1 l. Let s ark wth D the set of all ntervals of that type 1 b b 0 1 and b 1 b 23 l orrespondng to the ategory Ctg. The nuber l and eah of the ntervals 1 2 l should be a result of profound psyhologal nvestgatons. Let denote by D D Ctg the set of all ntervals of nubers whh ould be useful for ertan personalty psyhologal test. Copyrght 2012 SRes.

4 K. YORDZHEV I. PENEVA ) For eah of the ntervals D Ctg defned n 10) we reate text t 1 2 l orrespondng to the text gven by a professonal psyhologst about the psyhologal ondton of the assessed person regardng the psyhologal ategory C tg n ase that the total suary (the su of all onrete evaluaton for the orrespondng te for the pleentng test aordng to the sale f ) belongs to the nterval. Thus for eah Ctg we obtan the sets of texts T t 1 2 l 12) Let Ctg. By the thngs we have entoned above t follows that there exsts funton g : D T Let G t gt 12 l (7) s the orrespondng bnary relaton of ths funton. The funton g : D T s alled nterpretaton of the test onernng the psyhologal ategory Ctg. We denote by T T Ctg the set of all nterpretatons whh an be gven of the psyhologal exaner after the pleentaton of a gven personalty psyhologal test. 13) Then we defne the relaton Ntp g Ctg D Ctg D T (8) where D and D are the sets of nuber ntervals we have already looked at 10) and g Ctg and T are orrespondngly the funtons and the set of nterpretatons defned n 12). The sense of eah reord n Ntp s as follows: For eah psyhologal ategory C tg when the test s pleented f the assessed person obtan r nuber of ponts (obtaned assessent value for the ategory) then we hek n whh nterval of nubers D Ctg r s stuated and we gve the expert nterpretaton of the test aordngly wth the ategory Ctg and the funton g : D T defned n 12). 3. A Software Projet for Coputer Adnsterng Personalty Psyhologal Tests Beause of all that s wrtten above we onsder that t s approprate a oputer syste for adnsterng personalty psyhologal tests to ontan three bas and several ontrbutve relatvely ndependent odules. How do these separate odules work s shown on a dagra n Fgure 1. 1) Module Generator. Ths odule wll reate fles ontanng sets and relatons desrbed n seton 2 for a onrete personalty psyhologal test. At the oent we do not take an aount of the data for orrespondng to the onrete database anageent syste (Orale Database dbase Paradox FoxPro MS Aess SQL et.). Conrete realzaton of the odule generator s desrbed n [8]. 2) One or several ontrbutve odules. They serve for addtonal forng of a onrete oputer test - reatng startng wndow enter a prelnary nstruton desrpton of deograph feld (f t s neessary) and others. The deograph feld s a set of dfferent data haraterzng the exaned person as what s hs/her sex age eduaton work settleent et. 3) Module Exeutor. Ths s a oputer progra whh reads the data fro fles and akes a onrete oputer testng. Fro psyhologal pont of vew t s desrable the nterfae of ths progra to be as sple as possble. It s enough n the an wndow to appear the text of the seral te of the set Qst. The order they appear s aordng to the bjetve appng between the eleents of the set Qst and the set Z 1 2 Qst n asendng order of the eleents n Z desrbed n subseton 3). By request just before the progra fnshes workng appears a wndow nterpretaton n whh are desrbed the onlusons obtaned fro analyzng the data of the onrete testng aordng to the relaton Ntp desrbed n subseton 13). The data wll be reorded n a fle beause we wll need t for the ong odules of the syste for oputer adnsterng of psyhologal tests. 4) Modules for statst proessng. They serve for autoated statst proessng of the data whh s obtaned when the odule exeutor s used any tes testng any persons. We an use unversal progras for statst proess whh are often used n prate suh as SPSS STATISTICA MatLab Maple MS Exel and others. Certanly as we have n nd the spef features of the data obtaned n a result of a oputer psyhologal testng we onsder that t s advsable to reate spef software for the onrete statst proessng whh has to read and proess the data obtaned when the odule exeutor works. Ths wll lead to axu autoaton of the psyhologal exanatons. Generator Contrbutve Modules Exeutor Modules for statst proessng Fgure 1. A oputer syste for adnsterng personalty psyhologal tests. Copyrght 2012 SRes.

5 114 K. YORDZHEV I. PENEVA 4. Conluson The desrbed atheatal odel s a useful task for unversty studes n databases ourse. On the other hand dsussed n the work notes wll stulate the psyhologsts to ake wder use of oputer ethods n ther work. Ths odel ould be used to develop real software for oputer adnsterng of any psyhologal test and there s full autoaton of the whole proess: test onstruton test pleentaton result evaluaton storage of the developed database statstal pleentaton analyss and nterpretaton. REFERENCES [1] E. Sdorenko Methods for Matheatal Proessng n Psyhology Reh Sankt Petersburg [2] A. Anastas and S. Urbna Psyhologal Testng Prente-Hall Englewood Clffs [3] S. A. Mller Developental Researh Methods 2nd Edton Prente-Hall Englewood Clffs [4] M. J. Hernandez Database Desgn for Mere Mortals 2nd Edton Addson Wesley Boston [5] E. F. Codd A Relatonal Model of Data for Large Shared Data Banks Counaton of the Assoaton for Coputng Mahnery Vol. 13 No pp do: / [6] D. Maer The Theory of Relatonal Databases Coputer Sene Press New York [7] A. Nasledov Matheatal Methods for Psyhologal Assessents Analyss and Data Interpretaton Reh Sankt Petersburg [8] K. Yordzhev I. Peneva and B. Krleva-Shvarova A Relatonal Model of Personalty Psyhologal Tests Proeedngs of the 3rd Internatonal Conferene of Faulty of Matheats & Natural Sene (FMNS2009) Blagoevgrad 3-7 June 2009 pp Copyrght 2012 SRes.