Application of the Diffusion Model to Two-Choice Tasks for Adults Years Old

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1 Psychlgy and Aging Cpyright 007 by the American Psychlgical Assciatin 007, Vl., N., /07/$.00 DOI: 0.07/ Applicatin f the Diffusin Mdel t Tw-Chice Tasks fr Adults Years Old Rger Ratcliff Ohi State University Anjali Thapar Bryn Mawr Cllege Gail McKn Ohi State University The effects f aging n simple -chice decisin making was investigated with the diffusin mdel (R. Ratcliff, 978). Data fr 75- t 90-year-lds were cllected and cmpared with previus data frm 60- t 75-year-lds and cllege students fr 5 tasks: a signal detectin like task, letter and brightness discriminatin with masking, recgnitin memry, and leical decisin. The mdel fit the data well and therefre allws cmpnents f prcessing t be eamined as a functin f age. Cmpared with decisin-making prcesses in cllege students, decisin criteria and nndecisin cmpnents f prcessing increased with participants age. Hwever, the quality f the evidence n which decisins were based decreased with age nly fr letter and brightness discriminatin. Keywrds: aging, reactin time, cgnitive ability, diffusin mdel A central finding abut aging is that as peple age, their respnse times (RTs) increase. Als, there is smetimes a decrease in accuracy. Recently, Ratcliff, Thapar, and McKn (00, 00, 004); Ratcliff, Thapar, Gmez, and McKn (004); and Thapar, Ratcliff, and McKn (00) (hencefrth, RTM) eamined the effects f aging in several tw-chice tasks: tw signal detectin like tasks, a brightness discriminatin task with masked stimuli, a recgnitin memry task, a leical decisin task, and a letter discriminatin task with masked stimuli. We separated ut aging effects n cmpnent prcesses f the tasks by applying the diffusin mdel (Ratcliff, 978, 98, 985, 988, 00; Ratcliff & Ruder, 998, 000; Ratcliff & Smith, 004; Ratcliff, Van Zandt, & McKn, 999). We fund that 60- t 75-year-ld subjects adpted mre cnservative decisin criteria than did cllege-age subjects and als had slwer nndecisin cmpnents f prcessing (encding, respnse eecutin, memry access, leical access). Hwever, the quality f the stimulus evidence driving the decisin prcess was nt significantly wrse fr the lder subjects than fr the yung subjects ecept in masked letter discriminatin. The finding f lwer quality stimulus infrmatin fr masked letter discriminatin but nt fr masked brightness discriminatin is cnsistent with the psychphysical finding that deficits ccur with age fr high but nt fr lw spatial frequency stimuli (Spear, 99). Rger Ratcliff and Gail McKn, Department f Psychlgy, Ohi State University; Anjali Thapar, Department f Neural and Behaviral Sciences and Department f Psychlgy, Bryn Mawr Cllege. Preparatin f this article was supprted by Natinal Institute f Aging Grant R0-AG708 and Natinal Institute f Mental Health Grants R7- MH44640 and K05-MH089. Crrespndence cncerning this article shuld be addressed t Rger Ratcliff, Department f Psychlgy, Ohi State University, 85 Neil Avenue, Clumbus, OH ratcliff.@su.edu In the studies described in this article, applicatin f the diffusin mdel was etended t 75- t 90-year-lds. The questins addressed were whether the diffusin mdel culd fit the data frm the 75- t 90-year-lds as well as it had fit the data frm the yunger subjects and whether cmpnents f prcessing differ between 75- t 90-year-lds and 60- t 75-year-lds. Earlier research has fund substantial lss f cgnitive abilities fr 80- t 00-year-lds (Baltes, 998; Baltes & Smith, 00; Singer, Lindenberger, & Baltes, 00; Singer, Verhaeghen, Ghisletta, Lindenberger, & Baltes, 00). In ur studies, the 75- t 90-year-ld subjects were active and well functining, as evidenced by their willingness and ability t take part in ur eperiments, and they were matched t cllege students in terms f IQ and educatin. Methd In Eperiments 6, we used the same test lists, prcedures, and instructins as in the eperiments by RTM, and full descriptins can be fund in thse articles. All f the subjects in the eperiments reprted here (different subjects in each eperiment) and in RTM s eperiments met the fllwing inclusin criteria: a scre f 6 r abve n the Mini-Mental State Eaminatin (Flstein, Flstein, & McHugh, 975); a scre f 5 r less n the Center fr Epidemilgical Studies Depressin Scale (CES D; Radlff, 977); and n evidence f disturbances in cnsciusness, medical r neurlgical disease causing cgnitive impairment, histry f head injury with lss f cnsciusness, r current psychiatric disrder. All subjects cmpleted either the Picture Cmpletin and Vcabulary subtests r the Digit Symbl and Infrmatin subtests f the Wechsler Adult Intelligence Scale rd Editin (WAIS III; Wechsler, 997). All f these measures shwed that ur 75- t 90-year-ld subjects matched the ther tw grups (characteristics are shwn in Table ). Fr the Eperiments 6, there were 4, 5,, 5,, and 4 subjects, respectively. The same tw sites used fr earlier eperiments (Bryn Mawr Cllege and Nrthwestern University) prvided subjects, and the same eperimenters using the same apparatus tested subjects. 56

2 DIFFUSION MODEL AND CHOICE TASKS FOR OLDER ADULTS 57 Table Subject Characteristics Signal detectin Discriminatin Leical decisin Letter Brightness Recgnitin memry Pseudwrds Randm letters Measure M SD M SD M SD M SD M SD M SD Mean age Years educatin MMSE WAIS III Vcab/Inf WAIS III PC/Dig-Sym CES D Ttal Nte. Fr Eperiments 6, there were 4, 5,, 5,, and 4 subjects, respectively. MMSE Mini-Mental State Eaminatin; WAIS III Wechsler Adult Intelligence Scale rd editin (subjects were given either Vcabulary [Vcab] and Picture Cmpletin [PC] subtests r Infrmatin [Inf] and Digit-Symbl [Dig-Sym] subtests); CES D Center fr Epidemilgical Studies Depressin Scale. The eperimental tasks were chsen t span a range f pssible limitatins n cgnitive perfrmance. Eperiment used a signal detectin task: Subjects were asked t judge whether the distance between tw dts was large r small. The stimuli were clearly visible n a cmputer mnitr and were displayed until the subject respnded, s there were n perceptual r memry limits n perfrmance. In Eperiments and, in which, respectively, letter discriminatin and brightness discriminatin were tested, perceptual infrmatin abut the stimuli was limited thrugh masking. Eperiment 4 was a standard recgnitin memry task, and Eperiments 5 and 6 were standard leical decisin tasks. Fr Eperiment, we manipulated stimulus difficulty by varying the distances between the tw dts and, in Eperiments and, by varying the time between presentatin f the stimulus and presentatin f the mask. In Eperiment, the stimuli were patches f piels, and we manipulated difficulty using bth stimulus duratin and brightness, with brightness ranging frm mstly white piels t mstly dark piels. Fr recgnitin memry, wrds n the study lists were high, lw, r very lw in frequency and were presented either nce r three times. Test wrds that had nt appeared in the study list were als high, lw, r very lw in frequency. The same high-, lw-, and very-lw-frequency wrds were used in the leical decisin eperiments. In Eperiment 5, the nnwrds were pseudwrds, and in Eperiment 6, they were randm letter strings. Fr Eperiments 4, n alternating blcks f trials, instructins stressed that respnses be either as accurate as pssible r as fast as pssible. Subjects were given feedback apprpriate t the instructins: In accuracy blcks, accuracy feedback was given n each trial, and in speed blcks, a t slw message was given after respnses that eceeded 700 ms in the signal detectin and brightness discriminatin eperiments, 650 ms in the letter discriminatin eperiments, and ms in the recgnitin memry eperiment. Fr Eperiments 5 and 6, subjects were instructed t respnd quickly and accurately. Results Respnse times shrter than 00 ms and lnger than 4,000 ms were eliminated frm the data (.8% f the data fr each eperiment). Figure shws the RTs and accuracy values averaged acrss all the independent variables in each eperiment fr the 75- t 90-year-lds reprted here and the cllege students and 60- t 75-year-lds reprted in the RTM articles. Fr the eperiments that included the speed r accuracy instructin manipulatin, cllege students were mre willing t trade accuracy fr speed than were lder subjects, as shwn by the larger differences fr cllege students wh received speed instructins Mean Crrect RT (ms) Accuracy cllege age years ld years ld accuracy cnditin speed cnditin A B C D E F A=signal detectin B=letter discriminatin C=brightness discriminatin D=recgnitin memry E=leical decisin (pseudwrds) F=leical decisin (randm letters) Figure. Plts f accuracy and mean respnse time (RT) averaged ver all subjects and all cnditins in the eperiments. In each plt, there are tw lines fr each grup f subjects fr the first fur eperiments. In the accuracy plt, the tp line crrespnds t the accuracy cnditin, and the bttm line crrespnds t the speed cnditin. Fr the RT plt, the tp line is fr the accuracy cnditin, and the bttm line fr the speed cnditin.

3 58 RATCLIFF, THAPAR, AND MCKOON cmpared with thse wh received accuracy instructins. With speed instructins, cllege students were always faster than 60- t 75-year-lds, wh were always faster than 75- t 90-year-lds. With accuracy instructins, 75- t 90-year-lds had RTs that were lnger than thse f 60- t 75-year-lds ecept in the signal detectin eperiment; hwever, sme f the differences were small and nt reliable. Fr 75- t 90-year-lds, the effect n RTs f speed instructins versus accuracy instructins varied acrss eperiments frm as little as 00 ms t as much as 00 ms. The RT effects were smaller fr cllege students and 60- t 75-year-lds. The effects f age n accuracy varied acrss tasks. Accuracy was rughly equivalent fr the three subject grups fr the signal detectin task; there were relatively small decrements as a functin f age in recgnitin memry; and accuracy was higher fr bth grups f lder subjects than fr cllege subjects in leical decisin. In the letter discriminatin task, in which the stimuli had high spatial frequency, cllege students were ver 0% mre accurate than either grup f lder subjects. In the brightness discriminatin task, in which the stimuli had lwer spatial frequency, cllege students and 60- t 75-year-lds shwed equivalent levels f accuracy, whereas the 75- t 90-year-lds shwed mre than a 0% drp. Quantile Prbability Functins Quantile prbability functins prvide a summary picture f the shapes f RT distributins, hw they vary acrss cnditins (i.e., levels f accuracy), and hw crrect RTs cmpare with errr RTs. The functins fr the 75- t 90-year-lds were cnstructed in the same way as they were fr the yunger subjects described in the RTM articles. The prbability f a respnse determines psitin n the -ais, and quantile RTs are pltted vertically n the y-ais. In Figures and, the.,.,.5 (median),.7, and.9 quantiles are pltted. Crrect respnses fall n the right-hand sides f the functins, and errr respnses n the left (the prbabilities f crrect respnses are usually greater than.5, and the prbabilities f errr respnses are usually lwer than.5). The quantiles fr crrect respnses fr the easiest (mst accurate) stimulus cnditins fall n the far right f the plts, and their errr quantiles n the far left. Fr mre difficult cnditins, the quantiles are nearer the center. The quantiles are rdered s that fr each vertical line (i.e., each stimulus difficulty cnditin), the lwest is the. quantile, the net lwest is the. quantile, and s n. The quantile prbability functins in the figures represent averages acrss subjects fr each eperimental cnditin. Fr Eperiment, the signal detectin eperiment, there were different RT quantiles (ms) RT quantiles (ms) Signal Detectin Letter Discriminatin Brightness Discriminatin speed speed speed errr crrect errr crrect errr crrect 00 accuracy errr crrect accuracy errr crrect 400 errr accuracy crrect Respnse prbability Respnse prbability Respnse prbability Figure. Quantile prbability plts fr the signal detectin, letter discriminatin, and brightness discriminatin eperiments. The Xs represent the data averaged acrss subjects, and the lines represent the theretical fits f the diffusin mdel. The quantile respnse times (RTs) in rder frm the bttm t the tp are the.,.,.5,.7, and.9 quantiles, and in each vertical line, the quantiles have t have this rder. Fr the brightness discriminatin eperiment in several cnditins, a mderate prprtin f subjects did nt have enugh respnses t allw cmputatin f quantiles, s n quantiles are presented fr these etreme errr cnditins. Fr signal detectin, the rder f the cnditins represents gruping presented in Ratcliff et al. (006). Fr letter discriminatin, the etreme pints represent stimulus duratins f 40, 0, 0, and 0 ms, respectively. Fr brightness discriminatin, the etreme pints represent mre etreme stimuli with.65 and.5 prprtin f white piels and lnger stimulus duratins (50 ms), whereas the cnditins in the center (accuracy near.5) represent mre difficult cnditins with.55 and.475 prprtin f white piels and shrter stimulus duratins (50 ms).

4 DIFFUSION MODEL AND CHOICE TASKS FOR OLDER ADULTS 59 RT quantiles (ms) RT quantiles (ms) RT quantiles (ms) RT quantiles (ms) errr Recgnitin Memry speed 00 crrect errr crrect accuracy accuracy errr crrect errr crrect Prbability f an ld respnse Prbability f a new respnse Leical Decisin with Pseudwrd Nnwrds nnwrds wrds nnwrds 000 (errr) (crrect) (crrect) wrds (errr) Leical Decisin with Randm Letter String Nnwrds nnwrds (errr) wrds (crrect) Prbability f a wrd respnse Prbability f a nnwrd respnse wrds (errr) speed nnwrds (crrect) Figure. Quantile prbability plts fr the recgnitin memry and leical decisin eperiments. The Xs represent the data averaged acrss subjects, the Os represent theretical predictins, and the lines represent the best fits f the mdel t the data. Fr recgnitin memry fr the left-hand plts, the cnditins frm right t left represent V, L, H, V, L, H, NH, NL, and NV, where three presentatins, ne presentatin, N new wrds, V very-lw-frequency wrds, L lw-frequency wrds, and H high-frequency wrds. Fr the right-hand panel, the cnditins are in the reverse rder. Fr the leical decisin eperiments, wrd respnses fr the high-frequency wrds were mre accurate than thse fr the lw-frequency wrds, which were mre accurate than thse fr the very-lw-frequency wrds. RT respnse time. distances between the dts, gruped by similar RTs and accuracy (Ratcliff et al., 00) int fur cnditins in the figures. Fr Eperiment, there were fur pssible stimulus duratins between presentatin f a letter and presentatin f the mask. Fr Eperiment, there were 8 cnditins, defined by crssing three stimulus duratins with si different prprtins f white versus black piels. Fr these three eperiments, respnses fr the tw chices were apprimately symmetric fr bth accuracy and RTs. In ther wrds, in the signal detectin task, fr eample, the same accuracy and crrect and errr RTs were fund with respnses f large t a large stimulus as with respnses f small t the crrespnding small stimulus. Therefre, the crrect respnses fr the tw chices were gruped tgether as were the errr respnses, giving a single quantile prbability functin fr cnditins with speed instructins and a single functin fr cnditins with accuracy instructins. (Fr Eperiment, there were t few bservatins t plt quantiles fr errrs in the mst accurate cnditins; therefre, fr these cnditins, n quantiles are displayed.)

5 60 RATCLIFF, THAPAR, AND MCKOON Fr Eperiments 4, 5, and 6 (recgnitin memry and leical decisin tasks), accuracy and RTs were nt symmetric fr the tw chices, s there were tw quantile prbability functins fr each eperiment: fr recgnitin memry, ne fr ld respnses and ne fr new respnses, and fr leical decisin, ne fr wrd and ne fr nnwrd respnses. Fr Eperiment 4, there were si cnditins fr studied wrds (presented nce r three times crssed with three levels f frequency) and three cnditins fr wrds that had nt been studied (three levels f frequency). Fr Eperiments 5 (pseudwrds as nnwrds) and 6 (randm letter strings as nnwrds), there were three cnditins fr wrds, defined by three levels f wrd frequency. Overall, with bth speed and accuracy instructins, the. quantile RTs fr crrect respnses changed by less than 00 ms acrss levels f accuracy, whereas the.9 quantile RTs changed by as much as several hundred ms. In general, errr respnses were slwer than crrect respnses, and, as with crrect respnses, changes in median errr RTs acrss cnditins were mainly reflected in the RT distributins spreading rather than shifting (changing by as much as,000 ms in the.9 quantiles in leical decisin). The patterns fr the 75- t 90-year-lds qualitatively match thse fr the tw yunger grups described in the RTM articles. Cmparing the 75- t 90-year-lds reprted here with the 60- t 75-year-lds in the earlier eperiments, we fund that accuracy was lwer fr 75- t 90-year-lds nly in brightness discriminatin, whereas RTs were lnger in all cnditins ecept with accuracy instructins in Eperiment. The questin fr the diffusin mdel is what cmpnents f prcessing are respnsible fr these effects. Interpreting the Data Thrugh the Diffusin Mdel Our gal with the diffusin mdel is t eplain the cgnitive prcesses invlved in making simple tw-chice decisins. The mdel separates the quality f evidence entering a decisin frm the decisin criteria and frm ther, nndecisin prcesses such as stimulus encding and respnse eecutin. Decisins are made by a prcess in which infrmatin accumulates ver time frm a starting pint z tward ne f tw respnse criteria, r bundaries, a and 0. When a bundary is reached, a respnse is initiated. The rate f accumulatin f infrmatin is called the drift rate (v), and it is determined by the quality f the infrmatin etracted frm the stimulus in perceptual tasks and by the quality f the match between the test item and memry in memry and leical decisin tasks. The nndecisin cmpnents f prcessing such as encding and respnse eecutin are cmbined int ne cmpnent with mean T er. Within-trial variability (nise) in the accumulatin f infrmatin frm the starting pint tward the bundaries results in prcesses with the same mean drift rate terminating at different times (prducing RT distributins) and smetimes at the wrng bundary (prducing errrs). It is assumed that cmpnents f prcessing vary frm trial t trial. Acrss-trial variability in drift rate (nrmally distributed with SD ) and starting pint (unifrmly distributed with range s z ), in cnjunctin with bundary psitins and drift rates, determines the relative speed f crrect respnses versus errr respnses. It is als assumed that the nndecisin cmpnent varies acrss trials, unifrmly distributed with range s t. Fr further details f the mdel, see the RTM articles and Ratcliff and Tuerlinck (00). The main manipulatins in the eperiments were stimulus difficulty and, in Eperiments 4, speed instructins versus accuracy instructins. We manipulated difficulty with distance between the dts in the signal detectin task, stimulus duratin in the letter discriminatin task, brightness and stimulus duratin in the brightness discriminatin task, number f repetitins and wrd frequency in recgnitin memry, and wrd frequency in leical decisin. Differences in difficulty are mdeled by differences in drift rate. Speed accuracy tradeffs are mdeled by changes in the distance between the bundaries in the decisin prcess wider bundaries require mre infrmatin befre a decisin can be made, and this leads t mre accurate and slwer respnses. The assumptins that nly drift rate can change with difficulty and that nly bundary separatin can change between speed and accuracy instructins prduce a highly cnstrained mdel, ne that wuld be falsified by many pssible deviatins f the data frm predicted values (Ratcliff, 00). Because f the results f the RTM studies, we epected respnse bundaries and T er t increase with age in all si eperiments. Fr the signal detectin task, there were n perceptual r memry limits n the infrmatin available t the subjects; therefre, accrding t Ratcliff et al. (00), drift rates shuld nt vary with age. Fr the ther tasks, the RTM studies fund that drift rates were lwer fr 60- t 75-year-lds than fr cllege students nly in masked letter discriminatin, but fr 75- t 90-year-lds, lwer drift rates might als be epected in masked brightness discriminatin and recgnitin memry. We fit the diffusin mdel t the data using a standard minimizatin rutine (Ratcliff & Tuerlinck, 00). Each subject s data were fit individually, and the resulting parameter values were averaged acrss subjects (Tables and ). Standard errrs in the parameter values can be fund by dividing the standard deviatins by the square rt f the number f subjects fr each eperiment. T perfrm significance tests fr differences in parameter values between the 75- t 90-year-ld subjects tested here and the 60- t 75-year-ld subjects frm the RTM articles, we cmbined the standard errrs frm the tw grups t prduce a pled standard errr; this pled standard errr dubled was used as the critical value. The mdel was als fitted independently t the data averaged acrss subjects: Accuracy values and each quantile RTs were averaged acrss subjects fr each cnditin. These fits prvided the lines in Figures and. Grup data have ften been used in fitting mdels, and the assumptin (usually implicit) is that the parameter values fr fits t the grup data will be the same as averages frm fits fr the individual subjects. This was true fr ur eperiments. Parameter values btained frm the fits t the grup data and average parameter values acrss individuals were within standard errrs f each ther fr all parameters with nly tw eceptins: Fr brightness discriminatin, the differences were the result f a relatively lw number f errrs in high accuracy cnditins, and fr the leical decisin eperiment with randm letter strings, the differences ccurred because sme cnditins had very high accuracy and cnsequently very lw numbers f errrs. Gdness f fit. Figures and shw that the mdel des a gd jb f capturing changes in crrect and errr RT distributins and accuracy values, with nly drift rate changing acrss cnditins f stimulus difficulty. Fr the eperiments in which tw

6 DIFFUSION MODEL AND CHOICE TASKS FOR OLDER ADULTS 6 Table Means and Standard Deviatins in Parameter Values Acrss Subjects fr Fits f the Diffusin Mdel t the Eperiments Eperiment a s a a T er s z s t p z s z a yr cllege df Mean Signal detectin Letter discriminatin Brightness discriminatin Recgnitin memry Leical decisin a 04 a 77 (psued) Leical decisin a 7 a 77 (randm) Signal detectin (60 75 yr) Signal detectin (cllege) Standard deviatin Signal detectin Letter discriminatin Brightness discriminatin Recgnitin memry Leical decisin (pseud) Leical decisin (randm) Nte. The last tw clumns shw the average chi-square values frm the cllege student and 60- t 75-year-ld grups frm the Ratcliff, Thapar, and McKn (00, 00, 004); Ratcliff, Thapar, Gmez, and McKn (004); and Thapar, Ratcliff and McKn (00) studies. The last tw clumns f means (fr the signal detectin eperiment with cllege and 60- t 75-year-ld subjects) are fits t the data sets frm Ratcliff, Thapar, and McKn (00) in which mre up-t-date prgrams were used in fitting all the ther eperiments and in which a parameter representing variability in T er (s t ) and a parameter representing the prprtin f cntaminant RTs ( p ) were used. a s bundary separatin fr speed cnditin; a a bundary separatin fr accuracy cnditin; T er nndecisin cmpnent f respnse time; standard deviatin in drift acrss trials; s z range f the distributin f starting pint (z); s t range f the distributin f nndecisin times; p prprtin f cntaminants; z s starting pint fr speed cnditin; z a starting pint fr accuracy cnditin. a Values are frm data cllapsed int supersubjects s that the chi-square values are inflated relative t the values fr the 75- t 90-year-ld subjects. variables were manipulated (presentatin duratin and brightness in brightness discriminatin; wrd frequency and repetitins in recgnitin memry), the RT quantiles lie n the same functins. This is cnsistent with the assumptin that bth variables affect a single cmmn cmpnent f prcessing, drift rate. The mdel als captures the effects f speed and accuracy instructins, with nly bundary separatin changing. The nly systematic misses are in the.9 quantile RTs with accuracy instructins in brightness discriminatin and recgnitin memry (with smaller misses in signal detectin and letter discriminatin) and in the. quantile RTs fr brightness discriminatin and recgnitin memry. First, the.9 quantile RTs may miss because subjects did nt allw prcesses t run t cmpletin (RTs are lng, e.g.,.5 s), thereby reducing their.9 quantile RTs relative t predictins. Secnd, it may be that accuracy instructins slw prcessing fr cmpnents ther than the decisin prcess, leading t a larger value f T er. A mdest increase in T er (e.g., 0 0 ms, see Rinkenauer, Osman, Ulrich, Müller-Gethmann, & Mattes, 004) wuld prduce a slight increase in the predicted. quantile RTs (e.g., 0 0 ms), which wuld allw the mdel t better match the data in the brightness discriminatin and recgnitin memry eperiments. This wuld require a smaller value f bundary separatin (a) t prduce the best fits, which wuld reduce the predicted.9 quantile RTs t better match the data. The change in T er and a wuld nt significantly affect the values f the ther parameters f the mdel and therefre wuld nt change any cnclusins. The chi-square values averaged ver individual subjects are shwn in Table. Acrss all the eperiments, the chi-square values fr the 75- t 90-year-lds are similar t thse fr the cllege students and 60- t 75-year-lds in RTM s eperiments. The similarity f the chi-square values shws that the mdel fits the data well acrss all three age grups (see Ratcliff, Thapar, Gmez, & McKn, 004, p. 85, fr discussin f the pwer f the chi-square test). Differences in parameter values with age. Table 4 summarizes z tests fr parameter values fr the 75- t 90-year-lds cmpared with thse f RTM s 60- t 75-year-lds and RTM s 60- t 75-year-lds cmpared with cllege students with pled standard deviatins as nted abve (significance level.05). The three parameters identified in the RTM articles as mst likely t be invlved in slwing f lder relative t yunger adults are bundary separatin, the nndecisin cmpnent f prcessing, and drift rate. As Figure 4 and Table 4 shw, bundary

7 6 RATCLIFF, THAPAR, AND MCKOON Table Means and Standard Deviatins in Drift Rates and Drift Criteria fr Fits f the Diffusin Mdel t the Eperiments Eperiment v v v v 4 v 5 v 6 v 7 v 8 v 9 v cr v cr46 v cr79 Mean Signal detectin Letter discriminatin Brightness discriminatin Recgnitin memry Leical decisin (psued) Leical decisin (randm) Signal detectin (60 75) Signal detectin (cllege) Standard deviatin Signal detectin Letter discriminatin Brightness discriminatin Recgnitin memry Leical decisin (psued) Leical decisin (randm) Nte. Fr signal detectin, drift rates (v) represent gruping presented in the tet. Fr letter discriminatin, v v 4 represent stimulus duratins f 40, 0, 0, and 0 ms respectively. Fr brightness discriminatin, the first three, secnd three, and third three drift rates are fr 50-, 00-, and 50-ms stimulus duratins, respectively. Within each grup f three drift rates, the first has.5 and.65 piel cnditins cmbined, the secnd,.45 and.575 cmbined, and the third,.475 and.55 cmbined. v crij represents the drift criterin fr cnditins i and j. Fr recgnitin memry, the first three drift rates are fr items presented three times, the net three fr items presented nce, and the last three fr new items. Within each grup f three, the first drift rate is fr very-lw-frequency wrds, the secnd fr lw-frequency wrds, and the third fr high-frequency wrds. Fr leical decisin, the first drift rate is fr high-frequency wrds, the secnd fr lw-frequency wrds, the third fr very-lw-frequency wrds, and the furth fr nnwrds. The last tw clumns f means (fr the signal detectin eperiment with cllege and 60- t 75-year-ld subjects) are fits t the data sets frm Ratcliff, Thapar, and McKn (00) in which mre up-t-date prgrams were used in fitting all the ther eperiments and in which a parameter representing variability in the nndecisin cmpnent f respnse time (range f the distributin f nndecisin times) and a parameter representing the prprtin f cntaminant respnse times were used. separatins were larger fr 75- t 90-year-lds than fr 60- t 75-year-lds with speed instructins in the signal detectin and brightness discriminatin eperiments and with accuracy instructins in the brightness discriminatin and recgnitin memry eperiments. In RTM s eperiments, 60- t 75-year-lds had larger bundary separatins than did cllege students fr all the tasks ecept brightness discriminatin. Bundary separatin is assumed t be under subjects cntrl, s it might be epected that differences with age wuld nt be cnsistent acrss eperiments; instead, bundary settings wuld depend n hw subjects differentially interpreted instructins. Hwever, this was nt the finding: The separatins were cnsistently smaller fr cllege students relative t 75- t 90-year-lds in all the eperiments, indicating a general trend f increasing bundary separatin with age. The nndecisin cmpnent f prcessing was slwer fr 75- t 90-year-lds than fr 60- t 75-year-lds nly in signal detectin, recgnitin memry, and leical decisin with randm letter strings. In RTM s eperiments, the nndecisin cmpnent was slwer fr 60- t 75-year-lds than fr cllege students in all the tasks. The mst striking result is that fr three f the tasks signal detectin, recgnitin memry, and leical decisin drift rates did nt significantly decrease with age. This indicates that the quality f infrmatin entering the decisin prcess did nt decline with age. Fr letter discriminatin, drift rates decreased frm cllege students t 60- t 75-year-lds but n further fr 75- and 90-year-lds. Fr brightness discriminatin, drift rates were the same fr cllege students and 60- and 75-year-lds and decreased frm 60- and 75-year-lds t 75- and 90-year-lds. Brightness discriminatin was the nly task fr which drift rates were lwer fr 75- and 90-year-lds than fr 60- and 75-year-lds. These last tw results were replicated in Ratcliff, Thapar, and McKn (in press) with small grups f subjects. The estimates f variability parameters have prprtinally larger standard deviatins than d the estimates f ther parameters (Ratcliff & Tuerlinck, 00), s differences amng them must be much larger t be significant. Overall, in Eperiments 6 and in the RTM studies, there was a tendency fr larger variabilities in drift rate, starting pint, and the nndecisin cmpnent f prcessing fr the 75- and 90-year-lds than fr the yunger The riginal fits f the signal detectin eperiment (Ratcliff et al., 00) did nt use mre recent fitting prgrams that include variability in the nndecisin cmpnent f prcessing (s t ) and the pssibility f cntaminant (e.g., utlier) respnse times ( p ). In additin, the data presented here had slightly different biases in the zer pint f drift acrss subjects, s a drift criterin parameter that represents this difference was added. These changes increased the number f degrees f freedm frm 78 t 59 (because large respnses t large stimuli and small respnses t small stimuli were fit separately, but the data and fits were displayed cmbined as in Ratcliff et al., 00). The nly majr effect n parameter values was an increase in the value f T er because the inclusin f variability allwed shrter values f the quantiles t be accmmdated (the new minimum was T er s t /).

8 DIFFUSION MODEL AND CHOICE TASKS FOR OLDER ADULTS 6 Table 4 Effects f Subject Grups n Parameters f the Diffusin Mdel Parameter difference 60 t 75-year-ld vs. cllege-age subjects 75 t 90-year-ld vs. 60 t 75-year-ld subjects Eperiment a s T er v a s T er v Signal detectin higher lnger ns higher lnger ns Letter discriminatin (masked) higher lnger lwer ns ns ns Brightness discriminatin (masked) ns lnger ns higher ns lwer Recgnitin memry higher lnger ns ns lnger ns Leical decisin pseudwrds higher lnger ns ns ns ns Leical decisin randm letter strings higher lnger ns ns lnger ns Nte. Fr the leical decisin eperiment, there is ne value fr a, and fr the ther fur eperiments, the value f a fr the speed (s) cnditin is used. a bundary separatin; T er nndecisin cmpnent f respnse time; v drift rate bundary separatin speed cnditin: a s A B C D 0.0 bundary separatin accuracy cnditin:a a nndecisin cmpnent 0.60 mean: T er SD in drift acrss 0. trials: η A B C D E F A=signal detectin B=letter discriminatin C=brightness discriminatin D=recgnitin memry E=leical decisin (pseudwrds) F=leical decisin (randm letters) =cllege age subjects =60-75 year ld subjects =75-90 year ld subjects range in starting 0.08 pint acrss trials: s z range in nndecisin cmpnent 0.5 acrss trials:s t drift rate: v A B C D E F Figure 4. Plts f the parameter values frm the diffusin mdel as a functin f eperiments (A F) and f subject grups. The results frm the cllege-age subjects and the 60- t 75-year-ld subjects are frm Ratcliff, Thapar, and McKn (00, 00, 004); Ratcliff, Thapar, Gmez, and McKn (004); and Thapar, Ratcliff and McKn (00). The drift rate is the average ver all cnditins in the eperiments. grups (Table ). Hwever, a few differences were significant: first, the differences in between cllege students and 60- t 75-year-lds fr letter discriminatin and recgnitin memry, and between 60- t 75-year-lds and 75- t 90-year-lds fr brightness discriminatin; secnd, the differences in s z between cllege students and 60- t 75-year-lds fr leical decisin with randm letter strings and between 60- t 75-year-lds and 75- t 90-yearlds fr brightness discriminatin; and third, the differences in s t between cllege students and 60- t 75-year-lds fr signal detectin and between 60- t 75-year-lds and 75- t 90-year-lds fr brightness discriminatin and recgnitin memry. Crrelatins. Relatinships amng the dependent variables (accuracy, crrect RTs, and errr RTs) and the main parameters f the mdel (drift rate, bundary separatin, and the nndecisin cmpnent) averaged ver all the eperiments are shwn in Table 5. Fr thse eperiments with speed r accuracy instructins, we calculated crrelatins nly fr cnditins with speed instructins because the data were mre stable and the bundary separatin parameters mre cnsistent acrss subjects than fr cnditins with accuracy instructins. Fr the dependent variables, means were calculated acrss all the cnditins f an eperiment. The crrelatins were remarkably similar acrss the si eperiments reprted here and acrss RTM s eperiments. Fr eample, the crrelatins between crrect mean RTs and a were.85,.89,.75,.86,.89, and.57, and the crrelatins between accuracy and drift rate were.67,.79,.94,.80,.57, and.5 fr Eperiments 6, Table 5 Average Crrelatins Acrss Eperiments fr the Main Features f the Data and the Parameter Values Variable ERT Pr CRT a s T er Pr. CRT.80 a.0 a s.74 a.0.80 a T er a drift.0 a.69 a a Nte. The critical value f the crrelatin cefficient fr crrelatins averaged ver si eperiments is.. Fr the recgnitin memry and leical decisin eperiments, all the drift rates fr new items and nnwrds were negative, s their abslute values were used. ERT errr RT; Pr prbability f the respnse (accuracy); CRT crrect RT; a s bundary separatin fr the speed cnditin; T er nndecisin cmpnent f prcessing; SD in drift acrss trials. Respnse times are averaged ver cnditins. a Values had the same sign fr each eperiment.

9 64 RATCLIFF, THAPAR, AND MCKOON respectively. (The lwer crrelatins fr leical decisin with randm letters as nnwrds in Eperiment 6 might be due t etreme values f drift rate that result in a lwer range f drift rates acrss subjects.) Given the general similarity, the table reprts the crrelatins averaged acrss eperiments. We cmputed a significance value,., frm the crrelatins in Table 5. The value was btained under the assumptin that bth the data and the parameter values cme frm nrmal distributins fr each eperiment. The. value was btained frm repeated cmparisns carried ut in Mnte Carl simulatins fr each parameter and data statistic. There are seven data statistics and parameter values (see Table 5), and each was used in si cmparisns. The significance value was the value f the 500th largest f 0,000 simulatins (the 5% pint). Differences mderately larger than. are likely significant ( likely because the data and distributins f parameter values might deviate frm nrmality). Crrelatins with abslute values greater than. and the same sign fr each eperiment (asterisked values in Table 5) are certainly significant. The main results (Table 5) are that mean RTs fr bth crrect and errr respnses strngly crrelate with bundary separatin and that accuracy strngly crrelates with drift rate. The ther results are as fllws: The standard deviatin in drift rate acrss trials is crrelated with drift rate. Crrect and errr RTs are crrelated with each ther and are weakly negatively crrelated with drift rate. Neither accuracy and mean RT nr bundary separatin and drift rate are crrelated. The nndecisin cmpnent f prcessing is nt strngly crrelated with any f the ther quantities. The results bradly replicate thse f RTM. The verall level f RT (bth crrect and errr RTs) is determined by the bundary separatin that subjects adpted. Mre cnservative subjects respnded mre slwly, less cnservative subjects mre quickly. RT is at mst weakly determined by drift rate: The quality f the infrmatin n which decisins were based was nly slightly better fr faster subjects than fr slwer subjects. Overall accuracy is mainly determined by drift rate: Subjects with higher drift rates perfrmed mre accurately than subjects with lwer drift rates. Accuracy is nt a functin f bundary separatin: Mre cnservative subjects were nt mre accurate than less cnservative subjects. It is imprtant t stress that these crrelatins cncern individual differences in verall levels f perfrmance averaged acrss all the cnditins with speed instructins in each eperiment. Even thugh verall accuracy and RT are nt crrelated acrss subjects, it is the case that within a subject, changes in drift rate, fr eample, have strng and reliable effects n bth accuracy and RT (Figures and ). General Discussin Fr tw-chice decisin tasks, the diffusin mdel allws cmpnents f prcessing t be etracted frm RT and accuracy data. In this article, applicatin f the mdel was etended frm the cllege age and 60- t 75-year-ld subjects f earlier eperiments (RTM) t 75- t 90-year-lds. The mdel fit the data well, apart frm sme mdest misses in the. and.9 quantiles f RT distributins in sme cnditins fr sme eperiments. The mdel is highly cnstrained, especially in the behavir f RT distributins. This was prven by Ratcliff (00). Several fake data sets that were plausible but never bserved empirically were generated; fr eample, fr ne set, RT distributins had nrmal distributins instead f the right-skewed distributins that are bserved empirically. Fr anther set, RT distributins shifted as task difficulty increased instead f spreading. The mdel was fit t all the fake data sets, and in each case, the mdel failed t fit significantly. The mst salient result f the eperiments reprted here is that the quality f the infrmatin entering the decisin prcess, drift rate, was as high fr the 75- t 90-year-lds as fr the 60- t 75-year-lds in five ut f the si eperiments and as high as fr the cllege students in fur ut f the si. Drift rates differed between the 75- t 90-year-lds and the 60- t 75-year-lds nly fr brightness discriminatin. Drift rates differed between bth the 60- t 75-year ld and 75- t 90-year-ld grups and the cllege students fr letter discriminatin. The signal detectin task ffers a useful cntrl fr the ther eperiments. It shws that drift rates d nt decline as participants age in a task with little cgnitive r memry lad and with n limit n the availability f perceptual infrmatin. In masked letter discriminatin, in which the stimuli have high spatial frequencies, drift rates decreased between the cllege students and the 60- t 75-year-lds (RTM) but nt between the 60- t 75-year-lds and the 75- t 90-year-lds. Fr masked brightness discriminatin, in which the stimuli have lw spatial frequencies, drift rates did nt significantly decrease between the cllege students and the 60- t 75-year-lds, but they did decrease between the 60- t 75-yearlds and the 75- t 90-year-lds. Drift rates fr recgnitin memry did nt significantly decline acrss the three grups f subjects (RTM s studies and Eperiment 4). Previusly, the cnclusin in the literature has been that aging has little effect n recgnitin memry (Balta, Dlan, & Duchek, 000; Bwles & Pn, 98; Craik, 994; Craik & Jennings, 99; Craik & McDwd, 987; Erber, 974; Grdn & Clark, 974; Kausler, 994; Neath, 998; Naveh-Benjamin, 000; Rabinwitz, 984; Schnfield & Rbertsn, 966). Hwever, this cnclusin has been based nly n accuracy measures. In Eperiment 4 and in RTM s eperiments, lder adults were much slwer than cllege students. This presents a puzzle: Slwing fr lder adults has ften been interpreted as a deficit such that, fr eample, cgnitive peratins are nt fully cmpleted in the available time r the prducts f earlier peratins are nt fully available fr later peratins (e.g., Salthuse, 996). The diffusin mdel recnciles the RT and accuracy data: Older adults are as accurate as cllege students because the quality f their infrmatin frm memry is as gd as that f the students. Older adults are slwer because they set their respnse bundaries mre cnservatively. Drift rates fr leical decisin als shwed n significant differences amng the three age grups, suggesting that vcabulary des nt change with age. Less accurate perfrmance by cllege students results frm their less cnservative decisin criteria (Ratcliff, Thapar, Gmez, & McKn, 004, and Eperiments 5 and 6). In mst tasks, the 60- t 75-year-lds set mre cnservative decisin criteria than cllege students (RTM) and the 75- t 90-year-lds set mre cnservative criteria in all si eperiments reprted here. Hwever, the 75- t 90-year-lds were mre cnservative than the 60- t 75-year-lds nly fr sme f the eper-

10 DIFFUSION MODEL AND CHOICE TASKS FOR OLDER ADULTS 65 iments. Our interpretatin f these results is that lder subjects tend t adpt mre cnservative criteria, but that this is variable acrss individuals and their understanding f speed and accuracy instructins. Such variability is t be epected if criteria settings are under the cntrl f subjects (as they must be because speed accuracy instructins have large effects n RT). In the eperiments reprted here and in the RTM articles, with fully functinal lder adults matched n relevant characteristics, it is likely that the 75- t 90-year-lds and the 60- t 75-year-lds were similar enugh that differences in criteria smetimes ccurred and smetimes did nt. The same interpretatin applies t the nndecisin cmpnent f prcessing. Whereas the 60- t 75-year-lds were almst always slwer in this cmpnent than the cllege students, the 75- t 90-year-lds were nly smetimes slwer than the 60- t 75-yearlds. Again, there may be less difference between fully functining and matched 75- t 90-year-lds and 60- t 75-year-lds than the age difference might suggest. In all f the studies in this article and in the RTM articles, if the RT data were cnsidered in islatin frm the accuracy data, the suggestin wuld be that aging has a relatively large effect n cgnitive prcesses. On the ther hand, if the accuracy data were cnsidered alne, the suggestin wuld be that aging has a relatively small effect. In the diffusin mdel framewrk, the RT and accuracy data are jintly interpreted: The large differences in RTs arise frm differences in nndecisin cmpnents f prcessing and criteria settings. Accuracy is similar acrss the age grups (in all but the letter and brightness discriminatin eperiments) because drift rates are similar. Previus research with fully functining 80- t 00-year-lds has indicated a substantial decline in cgnitive abilities relative t 60- t 75-year-lds. Baltes and clleagues (Baltes, 998; Baltes & Smith, 00; Singer, Lindenberger, & Baltes, 00; Singer, Verhaeghen, et al., 00) reprted significant declines in memry, language fluency, general knwledge, and especially perceptual speed. Our results are cnsistent with the findings n perceptual speed: 75- t 90-year-lds were always slwer than 60- t 75- year lds, wh were always slwer than cllege students (with ne minr eceptin in ne cnditin). Hwever, we fund high levels f accuracy fr bth ur lder grups in recgnitin memry, leical decisin, and signal detectin. One reasn perfrmance was better fr ur ldest subjects than fr Baltes and clleagues subjects might be that urs were yunger, with a mean age f abut 80 and an upper limit f 90. Anther reasn might be that the cmpnents f prcessing in ur simple tw-chice tasks are relatively preserved fr 75- t 90-year-lds. We believe that prcesses like thse in ur tasks are representative f the building blcks that make up higher level prcesses, and we hypthesize that they are the last cgnitive prcesses t shw decrements with advanced age. As the theretical analyses f the diffusin mdel are brught t varius tasks, the quality f the infrmatin etracted frm stimuli is decupled frm criterin effects and frm nndecisin cmpnents f prcessing. Instead f a mnlithic accunt f prcessing speed in terms f nly mean crrect RTs, we have instead an accunt based n all aspects f the data. The quality f infrmatin etracted frm stimuli can be separated frm subject-adjustable decisin criteria. The data and analyses frm the studies reprted here add t a grwing bdy f supprt fr the diffusin mdel in particular and quantitative mdeling appraches in general. References Balta, D. A., Dlan, P. O., & Duchek, J. M. (000). Memry changes in healthy lder adults. In E. Tulving & F. I. M. Craik (Eds.), The Ofrd handbk f memry (pp ). New Yrk: Ofrd University Press. Baltes, M. M. (998). The psychlgy f the ldest-ld: The furth age. Current Opinin in Psychiatry,, Baltes, P. B., & Smith, J. (00). New frntiers in the future f aging: Frm successful aging f the yung ld t the dilemmas f the furth age. Gerntlgy, 49, 5. Bwles, N. L., & Pn, L. W. (98). An analysis f the effect f aging n recgnitin memry. Jurnal f Gerntlgy, 7, 9. Craik, F. I. M. (994). Memry changes in nrmal aging. Current Directins in Psychlgical Science,, Craik, F. I. M., & Jennings, J. (99). Human memry. In F. I. M. Craik & T. A. Salthuse (Eds.), The handbk f aging and cgnitin (pp. 5 0). Hillsdale, NJ: Erlbaum. Craik, F. I. M., & McDwd, J. M. (987). Recall, recgnitin, and aging. Jurnal f Eperimental Psychlgy: Learning, Memry, and Cgnitin,, Erber, J. T. (974). Age differences in recgnitin memry. Jurnal f Gerntlgy, 9, Flstein, M. F., Flstein, S. E., & McHugh, P. R. (975). Mini-Mental State: A practical methd fr grading the cgnitive state f patients fr the clinician. Jurnal f Psychiatric Research,, Grdn, S. K., & Clark, W. C. (974). Adult age differences in wrd and nnsense syllable recgnitin memry and respnse criterin. Jurnal f Gerntlgy, 9, Kausler, D. H. (994). Learning and memry in nrmal aging. San Dieg, CA: Academic Press. Naveh-Benjamin, M. (000). Adult age differences in memry perfrmance: Tests f an assciative deficit hypthesis. Jurnal f Eperimental Psychlgy: Learning, Memry, and Cgnitin, 6, Neath, I. (998). Develpmental changes in memry. In Human memry: An intrductin t research, data, and thery (pp ). Pacific Grve, CA: Brks/Cle. Rabinwitz, J. C. (984). Aging and recgnitin failure. Jurnal f Gerntlgy, 9, Radlff, L. S. (977). The CES D Scale: A self-reprt depressin scale fr research in the general ppulatin. Applied Psychlgical Measurement,, Ratcliff, R. (978). A thery f memry retrieval. Psychlgical Review, 85, Ratcliff, R. (98). A thery f rder relatins in perceptual matching. Psychlgical Review, 88, Ratcliff, R. (985). Theretical interpretatins f speed and accuracy f psitive and negative respnses. Psychlgical Review, 9, 5. Ratcliff, R. (988). Cntinuus versus discrete infrmatin prcessing: Mdeling the accumulatin f partial infrmatin. Psychlgical Review, 95, Ratcliff, R. (00). A diffusin mdel accunt f reactin time and accuracy in a tw-chice brightness discriminatin task: Fitting real data and failing t fit fake but plausible data. Psychnmic Bulletin and Review, 9, Ratcliff, R., & Ruder, J. F. (998). Mdeling respnse times fr twchice decisins. Psychlgical Science, 9, Ratcliff, R., & Ruder, J. F. (000). A diffusin mdel accunt f masking in tw-chice letter identificatin. Jurnal f Eperimental Psychlgy: Human Perceptin and Perfrmance, 6, Ratcliff, R., & Smith, P. L. (004). A cmparisn f sequential sampling mdels fr tw-chice reactin time, Psychlgical Review,, 67. Ratcliff, R., Thapar, A., Gmez, P., & McKn, G. (004). A diffusin