Inverted-U and Inverted-J Effects in Self-Referenced Decisions

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1 Inverted-U and Inverted-J Effects n Self-Referenced Decsons Kenpe SHIINA (shnaatwaseda.jp) Department of Educatonal Psychology, Waseda Unversty, Tokyo, Japan Abstract Ratng one s own personalty trats s a common self-referental nformaton processng task. The current paper examned the mechansm underlyng ths sort of trat-ratng task by usng a PC cursor tracng technque (Shna, 211a, b). The target phenomenon of nterest was the nverted-u effect observed n trat ratngs. The PC cursor tracng technque analyzed response tmes, tangental veloctes, and rapd cursor movements (strokes). Results supported Klen s noton (Klen et al., 22) that self-referenced epsodc and semantc memores are used ndependently when makng these trat decsons. Keywords: Ratng decson; nverted-u effect; decsonal fluctuaton. Trat Ratngs and Inverted-U Effects Personalty trat ratng tasks are the typcal research paradgm n the feld of self-referental judgments and decsons, whch are an mportant topc for socal and neurocogntve scentsts (Leberman, 27) as well as psychometrcans. When makng trat ratngs wth Lkerttype scales, t was found that trat ratng needs more tme n the moderate than n the extremes of the scale. Response characterstcs of ths type can emerge n other dependent varables, and Mgnault, Marley, & Chaudhur (28) called them, the nverted-u response tme, error, and uncertanty effects, respectvely. The nverted-u effect has been observed n two major domans that use scale-lke response formats: personalty trat ratngs (Judd & Kulk, 198: Kuper, 1981; Mueller, Thompson, & Dugan, 1986; Akram, Hedlund, & Ekehammar, 27) and absolute dentfcaton judgments n psychophyscs (Stewart, Brown, & Chater, 25: Brown, Marley, Donkn, & Heathcote, 28). Two vews on of self-referental ratngs If you are asked to rate whether You talk a lot on a Lkert-type ratng scale, what s the mental computaton needed to do ths task? A socal cogntve scentst mght argue that f you are talkatve n all aspects of your lfe, then you wll consder yourself as talkatve based on your selfreflectons and the exogenous evaluatons made by your famly and frends. In ths case, talkatveness s a stable personalty trat and the proposton I talk a lot s drectly stored n your semantc memory, and thus the ratng judgment wll be quck and relable. In contrast, f you do not have ether of the followng propostons I talk a lot or I do not talk a lot n your memory, you should compute the truth of the proposton at the moment. You wll try to retreve epsodes concernng your talkatveness from your memory and may fnd that, for nstance, you are eloquent n publc but very quet at home. Ths creates an nternal conflct, whch leads to settlng on a mdpont ratng. The ratng judgment wll be slow and unstable. The combnaton of the above two dfferent modes of processes, that s, the quck retreval and slow delberaton processes, creates an nverted-u effect. A psychometrcan wll embrace a completely dfferent vew (Thurstone, 1959; Tourangeau, Rps, & Rasnsk, 2). She or he frst assumes a psychologcal contnuum of talkatveness and further assumes that people have a specfc poston on the contnuum. The self-ratng s consdered as a self-observaton on the contnuum. Although there do exst many sophstcated scalng models, t s reasonable to say that the most popular and oft-used method s stll Lkert-type scalng procedure wthn the framework of the classcal test theory. For the psychometrcan the ratng scale s a black-box and lttle attenton wll be pad to the nternal nformaton processng. Psychometrc vew wll predct that the ratng tmes are flat across ratng categores. A more elaborated vew may predct, however, that the hghest and lowest categores can have less chances of beng confused because they have only one neghbor category. In sum, both vews can predct the nverted-u patterns va completely dfferent assumptons and thus a method that can produce another type of nformaton s needed. Trajectory tracng The current study attempted to understand the nverted-u effects by employng the technque of PC cursor trajectory tracng (Fgure1), n vew of the recent upsurge n cursor trajectory analyss that can capture cogntve components of decsons (for revews, see Song & Nakayama, 29; Freeman, Dale, & Farmer, 211). By analyzng cursor trajectores n PC based ratngs, t was expected that the method could provde drect evdence showng that the nverted-u effect s a jont effect of extreme trat ratngs that are memorybased and made wthout conflct, and moderate trat ratngs that are modulated by nternal conflct resoluton. A total of 16 ratng tasks (Table 1), 1 of whch pertaned to personalty trats and thus to self-referenced decsons, were analyzed and contrasted Fgure 1: The form used n Task 13 n Table 1, along wth an example of trajectory, whch traveled from Start button to Category 5. The start button was erased after the ntal clck. 2919

2 The Data Overvew The ratng data are a complaton of the author s past studes over a 5-year perod (Shna, 28, 211a, 211b, 212). The data were gathered from 568 partcpants and the same expermental procedure and PCs were used. Tasks -1 were admnstered to the pool of 14 subjects. The other tasks were admnstered to dfferent pools of partcpants. Ths was done because as many as 16 tasks (Table 1) were compared at the same tme n the current study to detect the nverted-u, nverted-j, and other patterns. Procedure The form shown n Fgure 1 was used to record trajectores, fnal ratng judgments, and response tmes. There were 5 ordered categores wth ether a set of numercal labels from 1 to 5 as shown n Fgure 1 or wth a set of verbal labels no, don t know, and yes n the poston of categores 1, 3, and 5, respectvely. There were no labels at the postons of 2 and 4. The ratng experment was subject-paced. As soon as the subject clcked the Start button supermposed at the center of the form, the button was erased and a problem appeared n the dsplay box n the center of the form. Partcpants were asked to clck a correct or most sutable category button as quckly as possble. The cursor trajectory and the tme between the ntal and last clcks were regstered. Then Start button reappeared to proceed to the next tral by callng up the next problem. An expermental sesson ncluded several of the tasks n Table 1 and thus the number of trals for each subject was around 1. The expermental program was wrtten n VBA for Mcrosoft Excel and the experment was run on Excel. Tasks Sxteen tasks were used across dfferent cogntve and self-referenced domans (Table 1). The frst task (Task ) was a Benchmark task n whch one of the numbers from 1 to 5 was randomly presented and subjects were asked to clck the correspondng button on the form. A prevous study (Shna, 28) showed that the trajectores n ths task show typcal goal-drected (smple reachng) movements and thus ths task served as a baselne that nvolved a mnmum of cogntve workload. Tasks 1-12 were nternally-guded tasks wth no correct answers: Tasks 1-1 were standard psychologcal scales that were the major target of the present study and Tasks were cogntve tasks that evoke deep cogntve processng but were not drectly related to the self. Tasks were externally-guded tasks wth correct answers. In Task 13, the stmul were smple math expressons that ncluded addton and subtracton of three dgts (e.g., 3-2+1). The partcpants clcked the correct number as quckly as possble. Task 14 was a dvson task n whch partcpants dvded one prme number by another number (e.g., 17/13) and rounded the answer off to the nearest nteger to clck the category button. Task 15 conssted of dffcult geography quzzes that demand delberaton. All the tasks were presented n Japanese. The psychologcal scales were Japanese versons. Partcpants The number of partcpants for each task s shown n Table 1. All partcpants were Waseda Unversty undergraduates. Table 1: Summary of 16 Tasks Items N ) Benchmark ) Self esteem (Rosenberg) ) Maxmzaton (Schwartz) ) Regret (Schwartz) ) Bg 5 Extraverson ) Bg 5 Neurotcsm ) Bg 5 Conscentousness ) Bg 5 Agreeableness ) Bg 5 Openness to Experence ) Indetermnacy ) Socal desrablty (Marlowe-Crowne) ) Lfe style (e.g., We can be happy wthout money) ) Opnon (e.g., Japan has rather a brght future) ) Addton and subtracton (e.g., 3-2+1, ) ) Dvson (e.g., 17/13.) )Geography (France s larger than Japan n land area) Note Category label was used. Otherwse No- Don t know-yes label was used. Response Tme Analyss: Inverted-J RT Effect Fgure 2 dsplays the mean response tmes as a functon of the fnal category clcked for the 16 tasks. We can fnd that 13 curves have and 3 curves do not have an nverted- U shape. Interestngly, many of the nverted-u patterns were from nternally-guded (no correct answer) tasks (Tasks 1 12). The 3 curves that were not nverted-u shaped were from Benchmark, Addton and subtracton, and Geography tasks. Emergence of nverted-j patterns It was further observed that n the 12 curves out of the 13 nverted-u curves, YES responses (category 5 responses) were faster than NO responses (category 1 responses). These response patterns produced nverted-j rather than nverted-u shapes and the excepton was Task 14 (Dvson), whch was an externally-guded task. In Fgure 2, panels (a) and (b) show nverted-j patterns wth dfferent maxma. All the nverted-j patterns were from nternally-guded (no correct answer) tasks (Tasks 1-12) ncludng all the selfdescrptve psychologcal scales (Tasks 1-1). The emergence of the nverted-j pattern n selfreferenced ratngs s not new but has never been clamed explctly. We can see clear nverted-j-shaped patterns n Mueller et al (1986, Fgure 1, for trat adjectves) and Akram et al (27, Fgure 1, for Bg 5 trats) as well, although many of the prevous studes do not nclude graphs that show ths relatonshp between ratng categores and a dependent varable. The reason why the prevous studes dd not hghlght the nverted-j shapes would be that they dealt wth relatvely few trats and descrptons and could not dscover the statstcal regularty across trats. Inverted-J patterns wll be the target of the present study, although more data s needed to conclude the generalty of nverted-j patterns n self-referenced or nternally-guded ratngs. 292

3 MEAN TIME (S) Benchmark Self esteem Maxmzaton Regret Extraverson Neurotcsm Conscentousne ss Agreeableness Openness to experence Indetermnacy Socal desrablty Lfe style Opnon Addton Dvson Geography (a) (b) (c) Fgure 2: Mean RTs as a functon of the fnal category chosen. (a) Inverted-J wth maxmum at Category 2, (b) Inverted-J wth maxmum at Category 3, and (c) No nverted-j. A possble explanaton of nverted-j patterns Klen, Cosmdes, Tooby, & Chance (22) argue that judgments about the self use two ndependent memores: an epsodc store, whch represents specfc events and behavors nvolvng the self, and a semantc store, whch ncludes summares of the personalty trats abstracted from a set of partcular events. Klen et al. further argue that the two memory systems are ndependently represented and used. Wthn ths framework, the nverted-j effect can be schematcally explaned as follows: Yes responses are the fastest because drect retreval from semantc memory s at work. Don t know responses are the slowest because, to arrve at ths category, partcpants should frst compute the degree of consstency to the trat by usng epsodc stores and then fal to attan hgh or low consstency. Fnally, No responses are ntermedate because both drect stores and computaton usng epsodc stores are at work. An mmedate crtcsm to ths nterpretaton s that f the affrmatve proposton I have Trat X can be drectly stored n semantc memory, there s no logcal reason to exclude the possblty that a fuzzy proposton, I have Trat X moderately, can be stored n the semantc memory as well. The trajectory analyss now comes n. Trajectory-Analyss 1: Averaged Velocty Shape We defne a trajectory as a tme-ndexed 2-dmensonal vector: ( x( t), y( t)), t RT ). We frst dvde the RT by 256 to defne a step sze n tme doman, and then estmated the locaton of ( x, y),, 255 by lnear nterpolaton n order to standardze the trajectores. Tangental velocty of a trajectory at tme s defned as: TV ( x ) RT / ( y x 1 y ) Traveled Dstance tme step Tangental velocty s the speed of the trajectory, whch reflects task characterstcs. See Shna (28, 211a, b) for more detals. Average tangental velocty The average tangental velocty curves as a functon of tme and a fnal ratng category clcked were computed (Fgure 3. Due to space lmtaton, not all relevant fgures could be presented). For example, Fgure 3a depcts the 5 average tangental velocty curves n Benchmark Task correspondng to the ratng categores fnally clcked. The numbers n the parentheses are mean RTs. In ths task, a cursor movement should be a type of smple reachng movement wth an ntal ballstc phase and a second correctve control phase. Ballstc movements are quck and bellshaped, and mply that there s dssocaton between motor and cogntve components, because ballstc movements are under feed-forward control and thus ther ntal velocty and drecton should be determned before the ntaton of the movement (Ellott, Helsen, & Chua, 21). In contrast, non-ballstc movements reflect the examnee s decsonal conflct and vacllaton. Therefore, a ballstc movement can be used as a marker to ndcate no-hestaton. Because the curves n Fgure 3a show an ntal large bell-shaped ballstc movement (a peak on the left) followed by small correctve movements (small vbratons on the rght), we can defne that a bell-shaped curve whose top speed s over 2 dot/s s a ballstc movement. Wth reference to ths rule, we can judge that the tangental veloctes of the trajectores amng at categores 1 and 5 tended to be ballstc and the curves toward the mddle categores were non-ballstc. More specfcally, we can judge that there s no smple reachng movement n Dvson and Indetermnacy Tasks, and the trajectores amng at categores 1 and 5 n Extraverson Task (Fgure 3b) are ballstc. Further, we can observe n Fgures 3c and 3d that all the curves moved slowly n the ntal perod, whch s apparently related to readng or calculaton. Ths analyss mght appear somewhat tautologcal because there s no wonder f a quckly movng cursor reaches ts destnaton faster. Ths crtcsm would be vald f the cursor movements were always optmal and economcal, but trajectores wth unwasted moton were very rare. Because a ballstc movement s quck and reflects nohestaton, ths analyss gves a crude explanaton of the nverted-u RT effect but cannot predct the nverted-j effect. A fner analyss wll be presented n the next secton. 2921

4 VELOCITY (dot/s) category 1 (1.33s) category 2 (1.21s) category 3 (1.23s) category 4 (1.23s) category 5 (1.36s) Fgure 3a: Average tangental veloctes n Benchmark Task. VELOCITY (dot/s) category 1 (2.35s) category 2 (3.5s) category 3 (2.57s) category 4 (2.36s) category 5 (2.17s) Fgure 3b: Average tangental veloctes n Bg 5 Extraverson Task. VELOCITY (dot/s) category 1 (3.78s) category 2 (4.7s) category 3 (3.75s) category 4 (3.62s) category 5 (3.52s) Fgure 3c: Average tangental veloctes n Indetermnacy Task. VELOCITY (dot/s) category 1 (3.47s) category 2 (5.8s) category 3 (4.79s) category 4 (3.81s) category 5 (3.82s) Fgure 3d: Average tangental veloctes n Dvson Task. Trajectory-Analyss 2: Velocty Varablty Havng notced that an analyss of average curves alone s nsuffcent to explan the nverted-j effect, we conducted another analyss focusng on varablty of veloctes. Let X =average of tangental veloctes at tme s = standard devaton of tangental veloctes at tme. CV s / X =varaton of an average velocty curve at tme (Pearson s Coeffcent of Varaton). Because larger quanttes tend to have larger varatons, the ndex measures trajectory-varablty takng account of magntudes of averages. If CV s are averaged over all tme ponts, we obtan 8 (16 Tasks X 5 Categores) estmates of trajectory varabltes correspondng to all the ponts n Fgure 2. The trajectory varablty ndces reflect nternal ndetermnacy of partcpants. Usng the CV ndex, a quadratc model: RT =.65 (Number of letters of a queston) (category number) -.72 (category number) ^ CV could produce the 12 nverted-j curves for nternally guded tasks (Fgure 2) very well (R 2 =.94, F (4, 55) =21.79, p<.1, Fgure 4). In ths formula, the number of letters comprsng a queston determnes the overall level of response tmes, the quadratc part generates nverted-u shapes, and the CV part transforms U to J meanng that the CV s for Category 5 were small and for the mddle categores were large. A natural nterpretaton of ths result s that the trajectores toward the mddle categores were shudderng and thus ncreased the response tmes. If the assumpton that trajectory-varablty (CV) reflects nternal conflct s vald, we can nfer a causal chan: nternal fluctuaton -> trajectory perturbaton ->longer response tmes -> nverted-u (-J) effect. The result and nterpretaton seem to be reasonable, but we do not know why CV s for the mddle categores were large and for Category 5 were small. The next analyss addresses ths queston. Trajectory-Analyss 3: Stroke Analyss Shna (211b) reported that a cursor trajectory often ncludes pulse-lke movements (Fgure 5) called strokes and over 5% of velocty curves were sngle peaked n the Benchmark Task whereas the rate was much lower n other tasks. Therefore, another nterpretaton for average veloctes n Fgure 3 s that they are a fuson of pulses (strokes) reflectng pulse frequences. Smlarly, another nterpretaton of CV values s that they are measurng nstablty (tme heterogenety) of dscrete events at tme. Because ballstc sngle-stroke velocty curves mply no nternal hestaton whereas multple stroke veloctes mply nternal conflct, the proporton of sngle peaked trajectores was calculated for each category n each task (Fgure 6, Shna, 211b). The fgure looks dsordered but a clear J emerged by averagng the curves. The results strongly supports the vew that less nternal conflct 2922

5 6.5 PREDICTED MEAN TIME (S) Self esteem Maxmzaton Regret Extraverson Neurotcsm Conscentousness Agreeableness Openness to experence Indetermnacy Socal desrablty Lfe style Opnon PROPORTION OF SINGLE PEAKED TRAJECTRIES Self esteem Maxmzaton Regret Extraverson Neurotcsm Conscentousness Agreeableness Openness to experence Indetermnacy Socal desrablty Lfe style Opnon AVERAGE 1 Fgure 4: A quadratc model that mmcs nverted-j curves n Fgure a) sngle stroke b) double stroke c) trple stroke d) drft Fgure 5: Examples of raw velocty curves found n Dvson Task (Shna 211b). The pulses are called strokes. The abscssa s tme and the ordnate s tangental velocty. Fgure 6: Proporton of sngle-peaked trajectores as a functon of ratng category. Average curve (Large red square) shows a clear J-pattern. ncreases sngle peaked ballstc movements, and ballstc movements nduce shorter RTs, whch yeld the nverted-j curves. Summary and Dscusson 1) The nverted-j RT effect occurred as a functon of tasks, especally when tasks were nternally guded. 2) The tangental velocty analyss suggested that ballstc movements are a plausble source of nverted-j effects. 3) The trajectory-varablty analyss showed that the trajectory varablty ndex (CV) could produce a reasonable quadratc regresson model (Fgure 4) that mmcs the nverted-j patterns n Fgure 2. 4) The stroke analyss revealed that sngle peaked trajectores, whch can be nterpreted as a marker of nonhestaton, are a source of quck responses and the nverted-j effect. 5) It s plausble that partcpants conflct causes nternal fluctuatons, whch then manfests multple-strokes and trajectory vbratons that lead to the nverted-u effect. 6) The ultmate reason for the nverted-j effect s unknown. A possble explanaton s presented n the followng secton. It has been suggested that extreme ratngs are memory dependent whereas the mddle ratngs are process- 2923

6 dependent and these qualtatvely dfferent mechansms create the nverted-j effect. The emergence of the nverted-j effect s by no means surprsng for memory researchers, whereas the effect s very dffcult to explan for psychometrcans. Therefore, the mplcaton of the present results for psychometrcs s that numbers arsng from ratng decsons are qualtatvely dfferent. What s the nverted-j effect? Why should the response patterns be nverted-j shaped n self-descrpton judgments? A smple explanaton would be as follows: when a stmulus statement s ether very consstent or very nconsstent wth the self-descrpton n memory, ratng decsons becomes easer and qucker than when the statement s nether consstent nor nconsstent. Ths nterpretaton s rather faulty, however, because f the stmulus statement s I talk a lot and you have the proposton I am average n talkatveness drectly n memory, you should be able to check a moderate ratng category equally quckly. To valdate the consstencybased nterpretaton, therefore, we should ether prove that very few ntermedate propostons are stored n memory or present drect evdence that moderate ratngs tend to be nterrupted by decsonal conflct. The contrbuton of the present study s that t provded the behavoral evdence that trajectores toward mddle categores are fluctuatng and those toward extreme categores are stable, producng the nverted-u effect. Strctly speakng, the above explanaton s vald only for the nverted-u effect but not for the nverted-j effect, because, f the probablty that I do not have Trat X s stored n memory s approxmately the same as the probablty that I have Trat X s stored n memory, the above explanaton cannot account for the nverted-j effect. Therefore, a supplementary assumpton that there are more affrmatve propostons than negatve propostons n memory mght be needed. For example, f you are a teacher, then you are not a farmer, a fsher, or a carpenter, and so on. Negatve propostons would be too numerous to be stored n memory and you need not (and should not) store such an endless lst n your memory. Of course, t s undenable that not a few negatve propostons are stored n semantc memory: the pont s that the number of propostons that correctly descrbe you should be far fewer than the number of propostons that wrongly descrbe you. The nverted-j effect may be a Yes-effect arsng from nformaton parsmony and asymmetry n memory. The Yes-effects would have a strong connecton to the acquescence effect (Krosnck, 1999) and SNARC effect (Dehaene, 211), although more research s needed to fully address ths matter. References Akram, N., Hedlund, L., & Ekehammar, B. (27). Personalty scale response latences as self-schema ndcators: The nverted-u effect revsted. Personalty and Indvdual Dfferences, 43, Brown, S. D., Marley, A. A. J., Donkn, C., & Heathcote, A. (28). An ntegrated model of choces and response tmes n absolute dentfcaton. 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Annual Revew of Psychology, 58, Mgnault, A., Marley, A. A. J., and Chaudhur, A. (28). Inverted-U effects generalze to the judgment of subjectve propertes of faces. Percepton & Psychophyscs, 7, Mueller, J. H., Thompson, W. B., & Dugan, K. (1986). Trat dstnctveness and accessblty n the self-schema. Personalty and Socal Psychology Bulletn, 12, Shna, K. (28). Vacllaton and hestaton n category ratng: Evdence from PC cursor trajectores. Proceedngs of the 3th Annual Conference of the Cogntve Scence Socety (pp ). Shna, K. (211a). Trajectory-varablty and nverted-u effects n ratng decsons. European Perspectves on Cogntve Scence: Proceedngs of the European Conference on Cogntve Scence. Shna, K. (211b). Tracng the process of ratng decsons through cursor movements. Proceedngs of the 33rd Annual Conference of the Cogntve Scence Socety Shna, K. (212). A cursor-tracng paradgm for ratng decsons: Another wndow on mnd? Paper read at SJDM Meetng. Song, J. H., & Nakayama, K. (29). Hdden cogntve states revealed n choce reachng tasks. Trends n Cogntve Scences, 13, Stewart, N., Brown, G. D. A., & Chater, N. (25). Absolute dentfcaton by relatve judgment. Psychologcal Revew, 112, Thurstone, L.L. (1959). The measurement of values. Unversty of Chcago Press. Tourangeau, R., Rps, L. J., & Rasnsk, K. (2). The psychology of survey response. Cambrdge: Cambrdge Unversty Press 2924