The Elements of Grophing Dotct

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1 Willim S. Clevelnd The Elements f Grphing Dtct Revised Editin AT&T Bell Lbrtries, Murry Hill, New.lersey

2 Published by Hbrt Press, Summit, New.lersey AT&T. All rights rcserved. Printcd in th Unitcd Sttcs tf'amcrtt' ISBN Cr.rH LrsnRny l- CNcnsss Cnrnr.ctc Cen NuH,tnps: PuBl-tsr Hn's CtelcrNG rn PuslrcnrrN Clevelnd, Willim 5., The elements f grphing dt / by Willim S. Clevelnd Revised editin. P.cm. Includes bibligrphicl rcferences nd index. 1. Grphic me.thds. 2. Mthemticl sttistics-grphic methds. I. Title. QA90.C '.5

3 Cntents Prefce Intrductin The Pwer f Grphicl Dt Disply The Chllenge f Grphicl Dt Disply 1.3 The Cntents f the Bk 76 Principles f Grph Cnstructin Terminlgy Cler Visin Cler Understnding Bnking t Scles Generl Strtegy 110 Grphicl Methds 1le 3.1 Lgrithms Residuls Distributins Dt Plts Pltting Symbls nd Curve TyP" Visul Reference Crids Less Time Series Sctterplt Mtrices Cplts f Scttered Dt Cplts f Surfces Brushing Clr Sttisticl Vritin 272

4 CrphiclPerceptin The Mdel Superpsed Curves Clr Encding Texture Symbls Visul Reference Grids Order n Dt Plts Bnking t 45" Crreltin Crphing Alng Cmmn Scle 4.10 Pp Chrts Bibligrphy 277 Figure Acknwledgements 2Bl Clphn 283 Index 285

5 Prefce This bk is but visulizing dt in science nd technlgy. It cntins grphicl methds nd principles tht re pwerful tls fr shwing the structure f dt. The mteril is relevnt fr dt nlysis, when the nlyst wnts t study dt, nd fr dt t'ttnlmunitlin, when the nlyst wnts t cmmunicte dt t thers. When grph is mde, quntittive nd ctegricl infrmtin is encded by disply methd. Then tl're infrmtin is visully decded. This visul perceptin is vitl link. N mtter hw clever the chicc f the infrmtin, nd n mtter hw technlgiclly impressive the encding, visuliztin fils if the decding fils. Smc disply methds led t efficient, ccurte decding, nd thers led tcr inefficient, inccurte decding. It is nly thrugh scientific study f visul perceptin tht infrmed judgments cn be mdc but disply methds. The disply methds f Eleme nts rest n fundtin f scientific enquiry. Except fr ne smll sectin, there is ntl'ring in this bk but cmputer grphics. The bsic ides, tl-re methds, nd the principles f the bk trnscend the cmputing cnvirnment used t implement them. While grphics technlgy is mving lng t rpid pce, the humn visul system hs remined the sme. The prerequisites fr understnding the bk re miniml- A few tpics require knwledge f the elementry cncepts f prbbility nd sttisticl science, but these tpics cn be skipped withut ffecting cmprehensin f the reminder f the bk. The bk Visulizing Dut is cmpnin vlume 126l- It fcuses n grphicl methds, the tpic f Chpter 3 f this bk; it presents fr mre methds thn cvered here nd is mre dvnced, requiring greter knwledge f sttistics. ButVisulizing Dut des nt delve int grphicl perceptin, nd tkes Elements s strting pint.

6 Prefcc Elements ws ment t be red frm the beginning nd t be enjyed. Hwever, it is pssible t red here nd there. Winding its wy thrugh the bk is summry f the mteril: the figures nd their legends. Reding this summry cn help reders direct themselves t specific items. The grphs in this bk re cmmunicting infrmtin but fscinting subjects, nd I hve nt hesitted t describe the subjects in sme detil when needed. In mny cses sme knwledge f the subject is required t understnd the purpse f grphicl nlysis r why grph is nt ding wht ws intended r wht new grphicl methd cn shw us but dt. I hpe the reder will shre with me the excitement f experiencing the incresed insight tht grphicl dt disply brings us but these subjects.

7 The Elements f GrPhing Dt Dd \M[[[[qnn S. Gfleveflnd

8 , 100 _ E f z 6 (t) C l Yer - z Yer GRAPHICAL METHODS AND prlnclples. The visuriztin f dt requires bsic principles nd methds. Bth pners f this grph shw the yerry sunspt numbers trm 1749 t A dispry methd, bnking t 45", hs been used t chse the shpe, r spect rti, f the bttm pnel. The methd llws us t perceive n rmprtnt prperty f the sunspts tht is nt reveled in the tp pnel - the sunspts nse mre rpidly thn they fll.

9 I Intrductrcn Dt disply is criticl t dt nlysis. Grphs llw us t explre dt t see verll ptterns nd t see detiled behvir; n ther pprch cn cmpete in reveling the structure f dt s thrughly. itphs llw us t view cmplex mthemticl mdels fitted t dt, nd they llw us t ssess the vlidity f such mdels' But relizing the ptentil f dt visuliztin requires methds nd bsic principles. Figure 1.1 illustrtes this. The tp pnel grphs the yerly sunspt numbers frn7749 t The dminnt frecluency cmpnent f vritin in the dt is the cycles witl'r perids f but 11 yers. The existence f the cycles is clerly reveled, but n imprtnt prperty f them is nt. And this prperty is criticl t understnding ihe vritin in the cycles, which in turn is criticl t develpins; theries f slr physics tht explin the rigin f the sunspts. The prblem is the shpe, r spect rti, f the g;rph, squre. The dt re grphed gin in tne bttm pnel; methd clled bnking t015, which will be intrduced in chpter 2, is used t determine tl're spect rti, nd the result is nrrw rectngle. Nw the grph revels the imprtnt prperty. The cycles typiclly rise mre rpidly thn they fll; this tehvir is mst prnunced fr the cycles with high peks, is less prnunced fr thse with medium peks, nd disppers fr thse cycles with the very lwest Peks. This bk is but methds nd bsic principles tht help the dt nlyst t relize the ptentil f visuliztin. The next three chpters f the bk divide the mteril int principles f grph cnstructin, grphicl methds, nd grphicl perceptin. In this chpter, sectin 1.1 tpp. -ll demnstrtes the pwer f visuliztin, sectin 1.2 (pp. 9-1'5), demnstrtes hw esy it is fr the grphing f dt g wrng, nd sectin 1.3 (pp ) briefly describes the cntent f the next three chpters.

10 Intrductin I.l The Pwer f Grphicl Dt Disply Figure 1.2 illustrtes the pwer f visuriztin t revel cmplex ptterns in dt. The tp left pnel is grph f mnthly urr"rug" tmspheric crbn dixide cncentrtins mesured i the Mun L bservtry in Hwii[9,77]. These dt wke up the wrld. Chrles Keeling pineered their cllectin nd fstered thlm midst the dversity f nture t the tp f vlcn nd the cntrversy f mn clser t se level. The cntrversy rged first in science nd then lter in plitics [108]. Erlier dt hd hinted tht tmspheric c2 ws rising due t mn-mde emissins, but Keeling's dit prved the cse, signling the dnger f glbl climte chnge. The remining pnels _ f Figure r.2 shw numericl decmpsitin clf the dt int fur frequency cmpnents f vritin whse sum is equl t the C2 cncentrtins. The decmpsitin ws crried ut by sttisticl prcedure, STL t211. On the five verticl scles f the figure, the number f units per cm vries. The heights f the brs n the right sides f the pnels prvide visuliztin f the reltive scling; th! heights represent eclul chnges in prts per millin n the five verticl scles. The cmpnent grphed in the upper right pnel is trencl cmpnent tht describes the persistent lng-term increse in the level f the cncentrtins. This rise, if cntinuedunbted, will eventully cuse tmspheric tempertures t rise, the plr ice cps t melt, the cstl res f the crrtinents t fld, nd the climtes f different regins f the erth t chnge rdiclly [52,80,108]. And the grph shws tht the rte f increse f C2 is itself incresing thrugh time. The cmpnent grphed in the third pnel frm the bttm is sesnl cmpnent: yerly cycle in the cncentrtins due t the wxing nd wning f flige in the Nrthern Hemisphere. when flige grws in the spring, plnt tissue bsrbs c2 irm trre tmsphere, depsiting sme f the crbn in the sil, nd tmspheric cncentrtins decline. when the flige decreses t the end f the summer, CO2 returns t the tmsphere, nd the tmspheric cncentrtins increse. The grph shws tht the mplitudes f these sesnl scilltins hve incresed slightly thrugh time.

11 The Elements f Grphing Dt E - g N 335 "633s Yer Yer (g c On (d 0.) L n7 (u : U.U 0.7 d 0.7 -tu c E E Yer 1.2 THE POWER OF GRAPHICAL DATA DISPLAY. Visuliztin prvides insightht cnnt be pprecited by ny ther pprch t lerning frm dt. n this grph, the tp left pnel displys mnthly verge COz cncentrtins frm Mun L, Hwii. The remining pnels shw frequency cmpnents f vritin in the dt. The heights f the five brs n the right sides f the pnels prtry the sme chnges in ppm n the five verticl scles.

12 Intrductin An scilltry cmpnent, grphed in the secnd pnel frm the bttm, is mde up mstly f vritin with perids in bnd centered ner three yers. This vritin is sscited with chnges in the suthern scilltin index, mesure f the difference in tmspheric pressure between Ester Islnd in the Suth Pcific nd Drwin, Austrli. chnges in the index re ls sscited with chnges in climte. Fr exmple, when the index drps shrply, the trde winds re reduced nd the temperture f the equtril Pcific increses. This wrming, which hs imprtnt cnsequences fr suth Americ, ften ccurs rund Christms time nd is clled El Nin - the child [23]. The cmpnent shwn in the bttm pnel hs n pprent, strng, time pttern nd behves, fr the mst prt, like rndm nise. Figure. 1.2 cnveys lrge munt f infrmtin but the CO2 cncentrtins. We hve been ble t summrize verll behvir nd t see detiled infrmtin. As the eminent sttisticin W. Edwrds Deming wuld hve put it [45], "the grph retins the infrmtin in the dt." Mny techniques f dt nlysis hve dt reductin s their first step. Fr exmple, clssicl sttisticl prcedures, widely used in science nd technlgy, fll in this ctegry. The first step is t tke ll f the dt nd reduce them t few sttistics such s mens, stndrd devitins, crreltin cefficients, vrince cmpnents, nd t-tests. Then, inferences re bsed n this very limited cllectin f vlues. using nly numericl reductin methds in dt nlyses is fr t limiting. we cnnt expect smll number f numericl vlues t cnsistently cnvey the welth f infrmtin tht exists ir-r dt. Numericl reductin methds d nt retin the ir-rfrmtin in the dt. Cntined within the dt f ny investigtin is infrmtin tht cn yield cnclusins t questins nt even riginlly sked. Tht is, there cn be surprises in the dt. The prgress f science depends hevily n frmulting hyptheses nd prbing them by dt cllectin. Drwin, in letter t Henry Fwcett in 1861, writes [54]: "Hw dd it is tht nyne shuld nt see tht ll bservtin must be fr r ginst sme view if it is t be f ny service." But nlyses f dt shcluld nt nrrwly fcus n just thse hyptheses tht led t cllectin. This inhibits finding surprises in the dt. T regulrly miss surprises by filing t prbe thrughly with visuliztin tls is terribly inefficient

13 The Elements f Grphing Dt becuse the cst f intensive dt nlysis is typiclly very smll cmpred with the cst f dt cllectin. A grph f CO2 cncentrtins similr t tht f Figure 1.2 prduced surprise discvery. Fr lng time it ws thught tht the mplitude f the sesnl cmpnent ws stble nd nt chnging thrugh time, but eventully three grups - ne t cslr in Austrlil1.02l, secnd t scripps Institutin f cengrphy in the United sttes [3], nd third t AT&T Bell Lbrtries in the United Sttes t30l - independently discvered the smll, but persistent chnge in the Mun L sesnl cycles. Fr the Bell Lbs grup, the discvery ws serendipitus. The gl f the nlysis hd been t study the reltinship between CO2 nd the Suthern Oscilltin index. The first step in the nlysis ws t decmpse the CO2 cncentrtins s in Fip;ure 1.2 t get the scilltry cmpnent s it culd be crrelted with the inclex. Frtuntely, the grup grphed ll f the cmpnents, nd the grph shwed clerly the persistent chnp;e in the mplitude f the sesnl cmpnent. This surprise ws s excitins; tht the grup switched its missin t the sesnl behvir f CO2 nd bndned the riginl missin. N ne yet hs gd understnding f wht is cusing the chnge. It might be hrbinger f chnges in the erth's climte r it might be simply prt f the nturl vritin in COz. t.2 The Chllenge f Grphicl Dt Disply Visuliztin is surprisingly difficult. Even the mst simple mtters cn esily g wrng. This will be illustrted by three exmples where seemingly strightfrwrd grphicl tsks rn int truble.

14 10 Intrductin Ae rs I C nc e ntrti ns Figure 1.3 is grphicl methd clled q-q plt which will be discussed in detil in Chpter 3; the figure shws the grph s it riginlly ppered in St:ient'e reprt [31]. As with lmst ll f the reprduced grphs in this bk, the size f the grph is the sme s tht f the surce. The disply cmpres Sundy nd wrkdy cncentrtins f ersls, r prticles in the ir. First, the grph hs cnstructin errr: the 0.0 lbel n the hrizntl scle shuld be 0.6. Unfrtuntely, the errr mkes it pper tht the left crner is the rigin; mny reders prbbly wndered why the line y - :u;, which is drwn n the grph, des nt g thrugh the rigin. A secnd prblem is tht the scles n the grph re prly chsen; cmprisn f the sundy nd w.rkdy vlues wuld hve been enhnced by mking the hrizntl nd verticl scles the sme. scle issues such i these re discussed in Chpter 2. Finlly, the disply f the dt misses n pprtunity t see the behvir f the dt mre thrughly. n this single pnel it is nt esy t cmpre the verticl distnces f the pints frm tlre line y : i1;; the slutin is grphicl methd clled thetukcy men-diffcrenc plt, which will be intrduced in Chpter 3. A c rri\ trzbcrh ( ruds I 1.3 THE CHALLENGE OF GRAPH CAL DATA DtSpLAy. This grph cmpres Sundy nd wrkdy cncentrtins f ersls. The line shwn is,!t - t:. The grph hs prblems. There is cnstructin errr: the 0.0 lbel n the hrizntl scle is wrng nd shuld be 0.6. The hrizntl nd verticl scles shuld be the sme but re nt. Furthermre, it is hrd t judge the devitins f the pints frm the line,rr - rr;. O-Ring Dt n Jnury 27,7986, the dy befre the lst flight f the spce shuttle Chllenger, grup f engineers met t study n lrm tht hd been rised. The frecst f temperture t lunch time the fllwing dy ws 31".- There ws suggestin tht the lw temperture might ffect the perfrmnce f the -rings tht seled the jints f the rik"t mtrs.

15 The Elements rl'grphing Dctt 71 T ssess the issue, the engineers studied grph f the dt shwn in Figure 1.4. Ech dt pint ws frm shuttle flight in which the O-rings hd experienced therml distress. The hrizntl scle is O-ring temperture, nd the verticl scle is the number f O-rings experiencing distress. The grph reveled n effect f temperture n the number f stress prblems, nd Mrtn Thikel, the rcket mnufcturer, cmmunicted t NASA the cnclusin tht the "temperture dt [re] nt cnclusive n predicting primry O-ring blwby" [43]. The next dy Chllenger tk ff, the O-rings filed, nd the shuttle explded, killing the seven peple n brd. Q c q) ' c b 0) _ E l z 1.4 STATISTICAL REASONING. These dt were grphed by spce shuttle engineers the evening befre the Chllenger ccident determine the dependence f O-ring filure n temderture. Dt fr n filures ws nt grphed in the mistken belief tht it ws irrelevnt t the issue f dependence. The engineers cncluded frm the grph tht there is n dependence Clculted Jint Temperture ('F) The cnclusin f the Jnury 27 nlysis ws incrrect, in prt, becuse the nlysis f the dt by the grph in Figure 1.4 ws fulty. It mitted dt fr flights in which n O-rings experienced therml distress. Figure 1.5 shws grph with ll dt included. Nw pttern emerges. The Rgers Cmmissin, grup tht intensively studied the Chllenger missin fterwrd, cncluded tht the engineers hd mitted the n-stress dt in the mistken belief tht they wuld cntribute n infrmtin t the therml-stress questin [43].

16 l2 Intrductin c) ^.; c O C' l z p!! 1.5 STATISTICAL REASONING. The cmplete set f O-ring dt is nw grphed, including the bservtins with n filures. A dependence f filure n tempertu re is reveled Clculted Jint Temperture ("F) Thc grphicl nlysis.f the O-ring dt filed, nt becuse f the disply methd used, s with the ersl dt, but rther becuse f pr chice f the sttisticl infrmtin selected fr the grph. This rse becuse f flw in the sttisticl resning tht underly thc grph. The flw vilted bsic sttisticl principle: in the nlysis f filure dt, the vlues f cusl vrible when n filures ccur re s relevnt t the nlysis s the vlues when filures ccur. Sttisticl thinking is vitl t dt disply. A number f sttisticl principles re discussed in Chpters 2 nd 3. Brin Msscs und Bdy Msses faniml Spet'ies Figure 1.6 is grph frm Crl Sgn's intriguing bk, The Drgns rf'eden [107]. The grph shws the brin msses nd bdy msses, bth n lg scle, f cllectin f niml species. we cn see tht lg brin mss nd lg bdy mss re crrelted, but this ws nt the min resn fr mking the grph.

17 The Elements rf Grphing Dt 1 L-) 0,000 5,000 l, I rrn $s 'i rn. E s.0 'e & r t)llllrirt l-lt'1>hrrt ' Mtterr'nu..!.r,,,,1'l;1i,11,,'. H.r. lrbilis /.l,r",,,,,,ru,,r,,, (lrcile Austrlpithecus - rer. [.t,"' I chinpv.ct. ;{y1,1f Brc; ilirrrrrr^ Bht>rt -.'/. Surrnithid - [)ipldctts Or,ri.h. Vmpire bt (]ldtish Mle r Ilurnrningbird Alligtr r (lrw Opssum r (lelcnlh. Rt ' Eel /' Stegsrtrttr I l0 100 Bdy rnss in kilgrrns 1.6 THE CHALLENGE OF GRAPHICAL DATA DISPLAY. This grph shws brin nd bdy msses f niml species. The intent ws fr viewers t judge n intelligence mesure, but the judgments require visul pertin tht is t difficult. Wht Sgn wnted t describe ws n intelligence scle tht l'rs been investigted extensively by Hrry J. Jerisn [651. Sgn writes tht this mesure f intelligence is "the rti f the mss f the brin t the ttl mss f the rgnism." Lter he dds, referring the reder t the grph, "f ll the rgnisms shwn, the best with the lrgest brin mss fcrr its bdy weight is creture clled Hmrt spicns. Next in such rnking re dlphins." The first prblem is tht Sgn hs mde mistke in describing the intelligence mesure; it is nt the rti f brin t bdy mss but rtl'rer is (brin mss)/(bdy mss.)2/3. If we study grup f relted species, such s ll mmmls, brin mss tends t increse s functic'rn f bdy mss. The generl pttern f the dt is resnbly well described by the equtin brin mss : r: (bdy mss)2/3.

18 74 Intrductin Since the densities f different species d nt vry rdiclly, we my think f the msses s being surrgte mesures fr vlume, nd vlume t the 2/3 pwer behves like surfce re. Thus the empiricl reltinship sys tht brin mss depends n the surfce re f the bdy; Stephen Jy Guld cnjectures tht this is s becuse bdy surfces serve s end pints fr s mny nerve chnnels [52]. Nw suppse given species hs greter brin mss thn ther species with the sme bdy mss; wht this mens is tht ( brin mss)/(bdy mssl2/3 is greter. we might expect tht the big-brined species wuld be mre intelligent since it hs n excess f brin cpcity given its bdy surfce. This ide leds t mesurin6; intelligence by this rti. Let us nw return t Figure 1.6 nd cnsider the grphicl prblem, which is serius ne. Hw d we judge the intelligence mesure frm the grph? Suppse tw species hve the sme intelligence mesure; then bth hve the sme vlue f (brin mss) (bdy mss)2/3 Thus lg(brin mss) :2l3lg(bdy mss) * lg (r.) fr bth species. This mens tht in Figure 1.6, the tw eqully intelligent species lie n line with slpe 2/3. suppse ne species hs greter vlue f r thn nther; then the smrter ne lies n line with slpe2/3 tht is t the nrthwest f the line n which the less intelligent ne lies. In ther wrds, t judge the intelligence mesure frm Figure 1.6 we must mentlly superpse set f prllel lines with slpe2/3. (If we ttempt t judge Sgn's mistken rtis, we must superpse lines with slpe 1.) This visul pertin is simply t hrd. Figure 1.6 cn be gretly imprved, t lest fr the purpse f shwing the intelligence mesure, by grphing the mesure directly n lg scle, s is dne in the dt plt f Figure 1.7. Nw we cn see strikingly mny things nt s pprent frm Figure 1.6. Hppily, mdern mn is t the tp. Dlphins re next; interestingly, they re hed f ur ncestr Hm hbilis.

19 The Elements rl Grphing Dt 15 The prblems with Figure 1.6 d nt stp here. Five f the lbels re wrng. The fllwing re the crrectins: "surrnithid" shuld be "wlf," "wlf" shuld be "surrnithid," "hummingbird" shuld be "gldfish," "gldfish" shuld be "mle," nd "mle" shuld be "hummingbird." The crrect lbels yield the stisfying result tht hummingbird is smller thn mle. It shuld be emphsized tht fr sme purpses, crrected versin f Figure 1.6 is useful grph. Fr exmple, it shws the vlues f the brin nd bdy msses nd gives us infrmtin but their reltinship. The pint is tht it des pr jb f shwing the intelligence mesure Mdern Mn Dlphin Hm hbilis Grcile Austrlpithecus Chimpnzee Bbn Crw Vmpire Bt Wtf Grill Elephnt Hummingbird Ltn Rt Mle Opssum Blue Whle Surrnithid Gldlish Ostrich Alligtr Tyrnnsurus rex Celcnth Eel Slegsurus Brchisurus Dipldcus ''' O ' ' Lg, Brin Weight - 2/sLg ', Bdy Weight 1.7 DOT PLOT. The intelligence mesure is shwn directly by dt plt. (Bth msses re expressed in grms fr this cmputtin.) The vlues f the mesure cn be judged fr mre redily thn in Figure 1.6. Fr exmple, we cn see mdern mn is t the tp, even hed f ur very clever fellw mmmls, the dlphins. Incrrect lbels n Figure 1.6 hve been crrected here.

20 T6 Intrductin I.3 The Cntents f the Bk Chpter 2: Principles f Grph Cnstruc:tin Figure 1.8 grphs n estimte f verge temperture in the Nrthern Hemisphere fllwing nucler wr invlving 10,000 megtns f nucler wepns. The dt re frm Science rticle, "Nucler Winter: Glbl Cnsequences f Multiple Nucler Explsins," by Turc, Tn, Ackermn, Pllck, nd Sgn [125]. The tempertures re cmputed frm series f physicl mdels tht describe script fr the nucler wr, fr the cretin f prticles, fr rditin prductin, nd fr cnvectin. Figure 1.8 shws tht the predicted temperture drps t bcrut -25"C nd then slwly increses twrd the current verge mbient temperture in the Nrthern Hemisphere, which is shwn by the hrizntl line n the grph. In Figure 1.8 there re fur scle lines tht frm rectngle, the tick mrks re utside f the rectngle, the size f the rectngle is set s tht n vlues f the dt re grphed n tp f it, nd there re tick mrks n ll fur sides f the grph. Principles f grph cnstructin such s these re the tpic f Chpter 2. The fcus is n the bsic elements: tick mrks, scles, cptins, pltting symbls, reference lines, keys, nd lbels. These detils f grph cnstructin re criticl cntrlling fctrs whse prper use cn gretly increse the ccurcy f the infrmtin tht we visully decde frm displys f dt. O f, 6 6n (D c ( r _20 (g Eqn t"' l.B CHAPTER 2. On this grph there re fur scle lines tht frm rectngle, the tick mrks re utside f the rectngle, the size f the rectngle is set s tht n vlues f the dt re grphed n tp f it. nd there re tick mrks n ll fur sides f the grph. Chpter 2 is but principles f grph cnstructin such s these. Time After Detntin (dys)

21 The Elements rf Grphing Dtn 77 Chpter 3: Grphicl Methds Figure 1.9 is dt plt, grphicl methd tht ws invented t disply mesurements with lbels 123,261. The lrge dts cnvey the vlues nd the dtted lines enble us t visully cnnect ech vlue with its lbel. The dt plt hs severl different frms depending n the nture f the dt nd the structure f the lbels. The dt in Figure 1.9 re the number f spekers fr 21 f the wrld's lnguges [98J. Only lnguges spken by t lest 50 millin peple re shwn. The dt re grphed n lg bse 2 scle, s mving frm left t right, vlues duble frm ne tick mrk t the next. Lg Number f Spekers (lg, millins) 6789 Mndrin (Chin) English Hindustni (Pkistn, Indi) Russin (Gret Russin Only) Spnish Arbic Bengli (Bngldesh, Indi) Prtuguese Mly - Indnesin Jpnese Germn French Punjbi (lndi, Pkistn) Kren Itlin Telugu (lndi) Tmil (lndi, Sri Lnk) Mrthi (lndi) Cntnese (Chin) Wu (Chin) Jvnese '...4 ''....4 ''''''. ',,,.. ' Number f Spekers (millins) 1.9 CHAPTER 3. The figure shws grphicl methd clled dt plt, which cn be used t shw dt where ech vlue hs lbel. The dt re the number f sekers fr the wrld's 21 mst spken lnguges. The dt re grphed n lg bse 2 scle, s vlues duble in mving left t right frm ne tick mrk t the next.

22 18 Intrdur:tin Figure 1.10 is grph f zne ginst wind speed fr 111 dys in New Yrk City frm My 1 t September 30 f 7973 [13). The grph shws tht zne tends t decrese s wind speed increses due t the incresed ventiltin f ir pllutin tht higher wind speeds bring. Hwever, becuse the pttern is embedded in lt f nise, it is difficult t see mre precise spects f the pttern, fr exmple, whether there is liner r nnliner decrese. In Figure 1.11 smth curve hs been dded t the grph f zne nd wind speed. The curve ws cmputed by methd clled lclly w,eighted regressin, ften bbrevited t lw,ess, r less [22,26,281. Less prvides grphicl summry tht helps ur ssessment f the dependence; nw we cn see tht the dependence f zne n wind speed is nnliner. One imprtnt prperty f less is tht it is quite flexible nd cn d gd jb f fllwing very wide vriety f ptterns. Chpter 3 is but grphicl methds such s the dt plt, less, nd grphing n lg bse 2 scle. Sme f the grphs re methds by virtue f the design f the visul vehicle used t cnvey the dt; the dt plt is n exmple. Other methds use the stndrd Crtesin grph s the visul vehicle, but re methds by virtue f the cluntittive infrmtin tht is shwn n the grph; grphing less curve is n exmple f such methd.

23 The Elements f Grphing Dt g _ 100 q) c N 50 O^ I "^r u g q - fj^ ^u- ^6-".-6U ^ -"38t$33g'u.:nu" w R v 1.10 CHAPTER 3. An ir pllutnt, zne, is grphed ginst wind speed. Frm the grph we cn see tht zne tends t decrese s wind speed increses, but judging whether the ttern is liner r nnliner is difficult Wind Speed (mph) A 1 I q) c N 50 eṛ - OO g CHAPTER 3. Less, methd fr smthing dt, is used t cmpute curve summrizing the dependence f zne n wind seed. With the curve superpsed, we cn nw see tht the dependence f zne n wind speed is nnliner. Chpter 3 is but grphicl methds such s less, dt plts, nd grphing n lg bse 2 scle Wind Speed (mph)

24 20 Intrductin Chpter 4: Grphicl Perc:eptin When grph is cnstructed, quntittive nd ctegricl infrmtinis e*ded, chiefly thrugh psitin, size, symbls, nd clr. when we study the grph, the infrmtin is visully clet'detl. A grphicl methd is successful nly if the decding prcess is effective. Infrmed decisins but hw t encde dt cn be chieved nly thrugh n understnding f the visul decding prcess, which is clled,u, t'u 1t 11 i 1' 1 pt' n' pt i t tn. A disply methd tht leds t inefficient visul decding cn prevent imprtnt spects f dt frm being detected r cn led tcr distrtins in the perceptin f infrmtin. ne exmple ws discussed erlier in Sectin t.1 (pp. 6-9); the fster rise thn fll f the sunspt numbers culd nt be perceived in the ip pnel f Figure 1.1. Figurc 1.12 shws nther exmple. The tp pnel grphs the vlues f imprts nd exprts between Englnd nd the Est Irrdies. Tl-re dt were first displyed in1786by willim Plyfir t1041. T visully decde tlre imprt dt we cn mke judgmerrts f psitins lng the verticl scle; the sme is truc f exprts. Anther imprtnt set f quntittive vlues encded n this grph is the munts by which imprts exceed exprts. T visully decde these vlues we must judge the verticl distnccs between the tw curves. But we perfclrm this visul pertin inccurtely; ur visul system tends b judge minimum distnces between tw curves rther thn verticl distnces. Fr exmple, frm the tp pnel f Figure f.i2 imprts minus exprts pper nt t chnge by much during; the perid just fter 1760 when bth series re rpiclly incresing. This is incrrect. Imprts minus exprts re grphed directly in the bttm pnel f Figure 1.12 s tht the vlues cn be visully decded by judgments f psitin lng cmmn scle, nd n.w we cn see there is rpid rise nd fll just fter 7760.

25 The Elements fgrphing Dt ^A F= Pd =+ (u6 ) -O) =- xc X LU X: LUH = z!d E CHAPTER 4. The tp Pnel is grph f exprts nd imprts between the Est Indies nd Englnd. The dt re frm grph published by Willim Plyfir in lt is difficult visully decde imprts minus exprts, which re encded by the verticl distnces between the curves. lmprts minus exprts re grphed directly in the bttm nel. nd nw we cn see tht their behvir just fter 1760 is quite different frm wht we visully decde in the tp pnel. Chpter 4 dels with issues f grphicl perceptin such s this. Yer The nly rute t n understnding f disply methds is ri5;rus study f grphicl perceptin. Chpter 4 is but such rigrus study. First, mdel fr grphicl perceptin is presented tht prvides frmewrk fr investigtins f grphicl perceptin. Then tl-re mdel is used t investigte number f disply methds intrduced in erlier chpters. This prvides bth justifictin f the methds nd guidnce fr crrying ut ther investigtins. The rigrus study cntrsts with the pprch f mny pst discussins f disply methds, where, in medievl-science fshin, pure pinin dmintes with n fcts t prvide guidnce.

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