Attentional Limits on the Perception and Memory of Visual Information

Transcription

1 Jurnal f xperimental Psychlgy: Cpyright 1990 by the American Psychlgical Assciatin, Inc. Human Perceptin and Perfrmance /90/$ , Vl. 16, N. 2, Attentinal Limits n the Perceptin and Memry f Visual Infrmatin Jhn Palmer University f Washingtn Attentinal limits n perceptin and memry were measured by the decline in perfrmance with increasing numbers f bjects in a display. Multiple bjects were presented t Ss wh discriminated visual attributes. In a representative cnditin, 4 lines were briefly presented fllwed by a single line in 1 f the same lcatins. Ss were required t judge if the single line in the 2nd display was lnger r shrter than the line in the crrespnding lcatin f the 1 st display. The length difference threshld was calculated as a functin f the number f bjects. The difference threshlds dubled when the number f bjects was increased frm 1 t 4. This effect was generalized in several ways, and nnattentinal explanatins were ruled ut. Further analyses shwed that the attentinal prcesses must share infrmatin frm at least 4 bjects and can be described by a simple mdel. A classic prblem in the study f perceptin is determining hw much is perceived and remembered frm a brief presentatin. In early studies, this prblem was addressed by using the full reprt paradigm in which several letters were displayed and an bserver was asked t reprt their identity (e.g., Lappin, 1967; Lappin & llis, 1970; Wlfrd & Hllingswrth, 1974; fr a review f early wrk, see Wdwrth & Schlsberg, 1964). In mre recent studies, the prblem has been redefined t distinguish between different prcessing limitatins n perfrmance. Fr example, sme studies have measured limits due t perceptin and nt due t sensry prcesses such as lateral masking r respnse prcesses such as interference amng multiple respnses. Other studies have measured perfrmance fr visual infrmatin such as the size and shape f bjects rather than linguistic infrmatin such as the identity f letters. Here, I narrw the prblem further in tw ways. The first is t measure limits n perfrmance that explicitly depend n memry as well as perceptin. The secnd is t measure limits n perfrmance that are under attentinal cntrl. In shrt, the questin is hw des attentin limit perceptin and memry fr the visual infrmatin in a brief presentatin? Memry limits n perfrmance have been measured with the recgnitin paradigm (e.g., riksen & Lappin, 1967; Reicher, 1969). In a prttype recgnitin experiment, an initial display f several bjects is presented, fllwed by a secnd display with a single bject in ne f the same lcatins. The task is t cmpare the single bject with the I thank Cynthia Ames, Crlene Ankrum, Drrit Billman, David Brainard, Angela Brwn, Rbert Frick, Anthny Greenwald, arl Hunt, David Irwin, Barry Kantwitz, Beth Kerr, Dnald Lamine~ Geffrey Lftus, Misha Pavel, Allen Pirsn, Steve Yantis, Zelda Zabinsky, and annymus reviewers fr cmments n early versins f the manuscript. I als thank Ray Slettevld and Aura Hanna fr help cnducting the experiments. This wrk was supprted in part by Grant BRSG RR frm the Graduate Schl f the University f Washingtn. Crrespndence cncerning this article shuld be addressed t Jhn Palmer, Department f Psychlgy, NI-25, University f Washingtn, Seattle, Washingtn crrespnding bject in the first display. Limits n perfrmance are indicated by sesize effects: the declining recgnitin f the single bject with an increasing number f firsdisplay bjects. The paradigm intrduces a memry requirement because any firsdisplay bject may be tested; thus, all firstdisplay bjects must be remembered fr gd perfrmance. Such an explicit memry requirement is nt present in paradigms such as search and detectin. Attentinal limits n perfrmance have been measured by using tasks that cntrl nnattentinal prcesses such as lateral masking (e.g., Davis, Kramer, & Graham, 1983; Grindley & Twnsend, 1968). Here, attentin is defined by selectivity, that is, the ability t select ne surce f infrmatin rather than anther. If a prcess is under attentinal cntrl, then instructins t an bserver can be used t manipulate that prcess. By using this definitin f attentin, the sesize effect in recgnitin is attentinal if instructins specifying relevant subsets f a display have the same effect as presenting nly a subset f the display. In ther wrds, an instructin t ignre tw f fur stimuli in the display shuld have the same effect as physically remving tw stimuli frm the display. Here, the attentinal nature f the prcesses underlying the sesize effect will be evaluated by cmparing effects f set size manipulated by display with effects f set size manipulated by instructin. Current Mtivatins and Previus Research Rle f Memry The first gal f this study is t measure perfrmance limits due t memry as well as perceptin. The relative emphasis n memry is mtivated by an interest in the integratin f infrmatin acrss successive eye fixatins. Such integratin requires memry. Infrmatin frm early fixatins in a sequence must be remembered fr the secnd r s that separates them frm later fixatins. CnseqUently, memry limits what percepts can be built frm a sequence f fixatins. If memry is imperfect, then the integrated percept must als 332

2 ATTNTIONAL LIMITS 333 have thse imperfectins. Next, I review recgnitin and alternative paradigms as pssible mdels fr the memry requirements f integrating acrss fixatins. Cnsider nw previus recgnitin studies that measured sesize effects. riksen and Lappin (1967) measured sesize effects fr recgnizing nnsense frms. They briefly presented a sequence f tw r fur stimuli fllwed by a single stimulus. The bservers had t judge if the single stimulus was the same as r different frm ne f tw f the bjects in the initial display. The tw relevant stimuli were indicated by small visual markers. The percentage f crrect recgnitin declined as the set size increased frm tw t fur. This result was interpreted as indicating a limited capacity in either perceptin r memry. Reicher (1969) als measured the effect f set size in recgnitin. He briefly presented ne r mre letters t subjects and then tested memry fr ne f the letters by requiring a frced chice between tw pssible alternatives. Perfrmance declined even fr an increase in set size frm ne t tw letters. Rck, Halpern, and Claytn (1972) fund a similar effect fr recgnizing frms f increasing cmplexity. The frms were made up either f ne part r f tw parts in cmbinatin. Perfrmance declined as the number f parts was increased frm ne t tw. In all f these experiments, even small increases in set size reduced recgnitin perfrmance. Thus, when memry was explicitly required, perfrmance was always limited by set size. In cntrast t recgnitin, ther paradigms minimize the effects f memry. Perhaps the mst cmmn is visual search (e.g., riksen & Spencer, 1969; stes & Taylr, 1966), wherein the bserver must decide whether a prespecified target bject is present in sme display. Althugh search smetimes shws sesize effects, there exist cnditins in which set size has little r n effect (e.g., geth, Jnides, & Wall, 1972; Schneider & Shiffrin, 1977; Sperling, Budiansky, Spivak, & Jhnsn, 1971; Teichner & Krebs, 1974; Treisman & Gelade, 1980). This may be due t the minimum memry requirements f search. The need fr memry is minimized because nly the ccurrence f a target must be remembered in the search task. Mrever, there is evidence that search des indeed bypass memry. The distractrs in search are rarely remembered, particularly in the situatins that prduce small sesize effects (Brand, 1971; Gleitman & Jnides, 1976). Other paradigms that minimize memry requirements als shw sme cnditins in which set size has little effect. Detectin resembles search, with the exceptins that nly a single bject is presented and set size refers t the number f pssible presentatin lcatins (e.g., Davis et al., 1983). Partial reprt resembles full reprt but with the reprt f nly a subset f the display (e.g., Speding, 1960). In summary, search, detectin, and partial reprt minimize memry requirements and demnstrate cnditins in which set size has little effect. Memry requirements may be the critical distinguishing feature between these tasks and recgnitin. Thus, the recgnitin paradigm is the preferred chice t measure perfrmance that depends n memry as well as perceptin. Rle f Attentin The secnd gal f the present study is t measure perfrmance limits due t prcesses that are under attentinal cntrl. Scene perceptin is limited by bth attentinal and nnattentinal prcesses. Fr example, peripheral viewing (e.g., Aulhrn & Harms, 1972) and lateral masking (e.g., Kahneman, 1968) are almst certainly nnattentinal, whereas cntrlling the directin f gaze r selecting items t rehearse are inherently attentinal. The intent f this article is t separately measure the rle f the attentinal prcesses that act n brief presentatins. Nnattentinal prcesses are cntrlled t btain a pure measure fattentinal effects. As nted earlier, attentinal prcesses are defined here by selectivity; that is, a prcess is under attentinal cntrl if ne surce f infrmatin can be selected ver anther. This distinctin between selective and nnselective prcesses is similar t Bradbent's (1958) distinctin between central and sensry prcesses. In the recgnitin paradigm, selectivity is indicated by a cmparisn between different kinds f sesize effects: Remval f half f a display shuld have the same effect as instructins that cue the relevant half f a display. Display and instructin manipulatins are expected t prduce the same effect if attentinal prcesses underlie the display effect as well as the instructin effect. This selectivity criterin has been tested several times in different paradigms and has been satisfied in sme instances (e.g., Davis et al., 1983; Grindiey & Twnsend, 1968) but nt in thers (e.g., riksen & Lappin, 1967; riksen & Rhrbaugh, 1970). When the criterin was nt satisfied, the instructin t ignre part f the display had an intermediate effect that was nt as large as remving that part f the display. In these cases, it seems likely that nnattentinal prcesses cntributed t the sesize effects. Fr example, riksen and Rhrbaugh fund that the criterin failed with clsely spaced stimuli but was nearly met with widely spaced stimuli, suggesting that perfrmance was als limited by nnattentinal sensry prcessing such as lateral masking. In this study, I designed the displays t minimize limitatins due t such nnattentinal prcessing. Althugh selectivity is certainly a necessary criterin fr an attentinal prcess, sme authrs argue fr an additinal criteria f limited-capacity prcessing. In particular, many authrs distinguish perfrmance limits that are due t perceptin and memry frm perfrmance limits that are due t decisin. The need fr this distinctin arises because decisin prcesses can mediate sesize effects in search and detectin tasks (e.g., Graham, Kramer, & Yager, 1987; Kinchla, 1974; Shaw, 1982; Sperling & Dsher, 1986; Swets, 1984; and Tanner, 1955, as described in Swets, 1984). These tasks have been analyzed as having tw stages: perceptual and memry prcesses fr each stimulus and a decisin prcess in which infrmatin is integrated frm all f the stimuli. Interestingly, even if the perceptual and memry prcesses shw n effect f set size, the decisin prcess prduces an effect f set size. The effect is due t multiple stimuli creating mre surces f nise that cntribute t the decisin prcess. The additinal nise makes a higher respnse criterin necessary t maintain a given false alarm rate. Thus, an effect f set size ccurs even if there is n effect f set size n the prcessing befre the decisin stage. Several methds have been prpsed t distinguish such a decisin effect frm attentin effects befre decisin. Shaw (1980, 1982, 1983) derived the maximum setsize effect that can be prduced by the decisin prcess and

3 334 JOHN PALMR shwed that it is exceeded fr sme stimuli but nt fr thers. Sperling and Dsher (1986) used a cncurrent task that has separate respnses fr each cmpnent stimulus and thus makes the decisin stage f each cmpnent independent f set size. In this study, I used a sampling prcedure t make the decisin prcess independent f set size (e.g., Reicher, 1969; Sperling, 1960). The Partial Discriminatin Paradigm The present experiments measured discriminatin f the attributes f briefly presented stimuli. The prttype task was line length discriminatin, and is illustrated by the schematic sequence f stimuli shwn in Figure I. The displays appeared in rder frm the tp t the bttm f the figure. First, a fixatin display was presented; secnd, a study stimulus was presented, cnsisting f ne t fur lines arranged arund fixatin; and third, a test stimulus was presented, cnsisting f a single line in the same lcatin as ne f the study lines. ach presentatin was brief, and the interval between study and test was 2 s. The bserver judged if the test line was lnger r shrter than the study line in the crrespnding psitin. This prcedure is referred t as partial discriminatin, and the number f stimuli in the study display is the set size. This prcedure differs frm previus studies f size discriminatin (e.g., Burbeck, 1987; Fechner, 1860/1966; On, 1967; Palmer, 1986; Pllck & Chapanis, 1952; Westheimer & McKee, 1977) in measuring perceptin f multiple-bject displays instead f single-bject displays. The partial discriminatin paradigm was designed t measure the attentinal limits n the perceptin and memry fr visual infrmatin. It is a memry as well as a perceptual task because the bserver must remember all f the study stimuli Time Fixatin Display /\ (~(~ Alternative Study Stimuli \ / (~ Test Cmmn Stimulus Figure 1. A schematic illustratin f the display sequence f fixatin, study, and test. (The study displays vary in set size but nly ne stimulus is tested.) until the test stimulus appears. It is likely t depend n attentinal prcesses because the sensry, respnse, and decisin prcesses are nt affected by set size. It measures visual infrmatin because the judgment is f a visual characteristic that is nt easily categrized. ach f these pints is cnfirmed in cntrl experiments. The experiments were rganized int three grups: (a) initial experiments demnstrating a sesize effect in line length discriminatin, (b) experiments generalizing these effects t several stimulus attributes and a range f memry cnditins, and (c) experiments shwing equivalence between display sesize manipulatins and attentin instructin manipulatins. General Methd Subjects. Subjects fr each experiment were selected frm a pl f 15 trained, 20- t 40-year-ld bservers. Mst were graduate students, each was paid $5 per hur (except Observer 1, the authr), and all had a nrmal r crrected-t-nrmal acuity. The bservers were identified by a set f nncntiguus numbers that were the same as thse used in a related study (Palmer, 1988). Apparatus. The displays were cntrlled by a Hewlett Packard mdel 9817 cmputer and were presented n a 14-in. cathde-ray tube (Hewlett Packard mdel 35122A). The tube has a P31 phsphr, a 60-Hz raster refresh, and a 512 x 390 pixel reslutin. The displays were viewed frm 78 cm thrugh a 15-cm aperture reductin screen that was 15 cm in frnt f the display. This cmbinatin resulted in a viewing area f abut 14* f arc in diameter. The cathde-ray tube was indirectly illuminated t prduce a backgrund luminance f 3 cd/m 2. The surrunding reductin screen was a similar gray with a luminance f 2 cd/m 2. The displayed lines had an intensity equivalent t a luminance f 100 cd/m 2. (This equivalence was measured frm a hmgeneus display f the lines.) These well-lit cnditins eliminated any visible phsphr persistence. Stimuli. In mst experiments, the stimuli were hrizntal lines with lengths near a standard f 60 arc min. The length was mdified in steps f 2 arc rain. As shwn in the middle panels f Figure 1, up t fur lines were arranged n an imaginary circle 180 arc rain frm a central fixatin pint. The centers f the lines were always placed n the circle at 1, 4, 7, and l0 'clck. The stimulus sequence is als illustrated in Figure 1. The fixatin display was presented fr 2,000 ms fllwed by a 500-ms interval; the study display was presented fr 100 ms fllwed by a 2,000-ms delay interval; the test display was presented fr 100 ms. The length f the test line was always 60 arc rain. Of the lines in the study display, ne served as a cmparisn and the thers were distractrs. The length f the cmparisn line was determined by an adaptive prcedure restricted t a range f plus r minus apprximately tw times the estimated difference threshld. Fr example, if the difference threshld was estimated t be 6 arc rain fr the 60 arc min standard, then cmparisn lines were between arc min. The length f each distractr line was chsen frm the same range. Fr all set sizes, the t-be-tested line was presented equally as ften in ne f the fur pssible psitins. Fr example, in set size l the line can ccur in any f the fur lcatins. As a result, the prbability f testing any ne lcatin was always.25 and the psitinal uncertainty f the t-be-tested line was cnstant fr the different set sizes. On the ther hand, nce the study is shwn, the cnditinal prbability f the test lcatin des vary with set size. Fr example, when set size equals 1, then the test line always ccurs at the same lcatin as the single study line. Sesize effects were measured withut this cnfund in the eye mvement artifact cntrl discussed with xperiment 1.

4 ATTNTIONAL LIMITS 335 Prcedure. The bservers made a tw-alternative frced chice discriminatin f line length. After the test display, they pressed ne key if they thught the test line was shrter than the crrespnding study line, and anther key if they thught it was lnger. There was n time pressure, and respnse accuracy feedback was prvided by tnes. An adaptive prcedure was used t select study stimuli frm fur t six lengths that were near difference threshld. The prcedure reduced the size f the length difference by ne step after three crrect respnses and increased the size f the length difference by ne step after ne incrrect respnse. This 3:1 rule cncentrates measurements at a value that prduces a.79 prbability f a crrect respnse (Levitt, 1971). A psychmetric functin was frmed by calculating the prprtin f"lnger" respnses as a functin f the cmparisn length. The bserved functin was fit t a cumulative nrmal by Prbit analysis (Finney, 1971), and the difference threshld was defined as half the difference between the stimulus that prduced 25% lnger respnses and the stimulus that prduced 75% lnger respnses. In additin, the pint f subjective equality was defined as the stimulus that resulted in 50% lnger respnses. This estimate is reprted in terms f the cnstant errr, that is, the estimated pint f subjective equality fr the study line minus the actual length f the study line. Fr bth f these estimates, standard errrs were calculated frm all f the data t prvide the leasbiased estimates. Fr statistical cmparisns between cnditins, estimates were calculated fr individual blcks f trials and variability was calculated frm replicatins ver blcks t prvide the mst cnservative variability estimates. Trials were presented in blcks f 32 t 48 trials; a sessin cnsisted f 8-10 blcks. Only ne sessin was cnducted per day. ach bserver participated in at least five sessins f general practice befre any f the reprted data were cllected. In additin, befre each experiment, bservers participated in ne r mre sessins f specific practice in that experiment. This resulted in at least 1,800 trials f practice per bserver. xperiment 1 The first experiment used a line length discriminatin task as described earlier. It prvided the first measurement f a sesize effect in the partial discriminatin task. In additin, a number f cntrls cnfirmed that the sesize effect was nt due t sensry factrs and that categrizatin strategies were minimized. Methd Set sizes f ne, tw, and fur were presented in separate blcks. Fifteen bservers participated in fur sessins with the three sesize cnditins, yielding 384 trials per cnditin per bserver. Tw bservers (Observers 3 and 5) had slightly different display cnditins (12, 3, 6, and 9 'clck display rientatin and a wider range f distractr lengths) and participated in nly tw sessins; Observer 7 had slightly mre trials per cnditin (576). The general methds were therwise fllwed. Results The bld line in Figure 2 is the mean length difference threshld pltted as a functin f set size. The difference in threshld between set sizes 4 and 1 was lg arc rain, t(14) , p <.001, In ther wrds, the threshld increased by a factr f 2. In additin, the difference between threshlds fr set sizes 2 and 1 was lg arc rain, v - 100"..c: 10- c- a r- c--._1 t. Mean f 15 Observers... Selected Single Observers I I I I Set Size Figure 2. xperiment 1: The bld curve is the mean length difference threshlds as a functin f set size; the dtted curves are the threshlds fr selected individual bservers; and all errr bars are the standard errr f the mean t~ ~ e- - t(14) = 7, p <.001. This is a change f a factr f just under 1.4. Thus, the sesize effect was reliable even fr the change frm set size 1 t 2. In Figure 2, lg threshld is pltted as a functin f linear set size and shws a rughly linear trend; hwever, a similar linear trend wuld be evident if the figure had a linear rdinate. The lgarithmic rdinate was adapted t maintain rughly cnstant standard errrs f the threshld estimates. Sme f the data frm individual bservers are als shwn in Figure 2 by the dtted lines that are labeled by bserver number. These bservers had the lwest and highest threshlds r had the smallest (0.12 lg arc min) r largest (0.59 lg arc min) effect f set size. All f the individual bserver data are shwn in Figure 3 in a scatterplt f the difference threshld fr set size 4 and the difference threshld fr set size 1. ach bserver's result is marked by an identifying number. Fr each bserver, the threshlds fr set size 4 are reliably (p <.05) larger than fr set size 1, fr example, Observer 1, t(11) = 12, p < This effect can be seen in the scatterplt by the psitin f each pint being well abve the diagnal line that marks equal perfrmance in the set size 1 and 4 cnditins. A similar cmparisn between set sizes 1 and 2 was reliable fr 10 ut f 15 bservers. Increasing set size als increased variability between bservers, with a between-subjects standard deviatin f lg arc min fr set size 1 and lg arc min fr set size 4. In Individual t tests were based n 12 blcks f data, three frm each sessin f- r~ i.- 1

5 336 JOHN PALMR Scatterplt f Length Threshlds (arc min) 100 O LL N O "O O - ffl r- F- [~ I I I I i, I I! I I I Threshld fr Set Size One Figure 3. xperiment 1: A scatterplt f the length difference threshlds frm each bserver fr tw cnditins, the set size 4 cnditin against the set size 1 cnditin. (ach pint is dented by the bserver's identifying number.) summary, the difference threshld increased with set size fr every bserver. There was sme evidence that set size als affected the cnstant errr (fr a discussin f cnstant errr, see Green & Swets, 1966; Jrdan & Uhlarik, 1985; Wdwrth, 1938). Fr set sizes 1-4, the mean cnstant errr in linear units changed frm arc min t -0.7 _+ 0.9 arc min. This effect is as if the subjective length f the study lines decreased fr the larger set size. The difference f arc min was reliable verall, t(14) = 2.3, p <.05, but was nt reliable fr individual bservers. The use f feedback in xperiment 1 was intended t eliminate cnstant errr and therefre makes the residual cnstant errr difficult t interpret. Furthermre, the cnstant errr effect was nt clearly replicated in further experiments and thus is nt pursued. In summary, xperiment 1 demnstrated a sesize effect fr the partial discriminatin task. The threshld dubled when the set size was increased frm 1 t 4. In the fllwing cntrl measurements, I rule ut several sensry explanatins f this effect and prvide data n categrizatin strategies. Cntrls Pssible eye mvement artifact. An eye mvement artifact remained a pssibility in xperiment 1. An bserver might mve his r her eyes in anticipatin f the test stimulus. This strategy is particularly helpful fr displays f set size 1 because the test stimulus culd be viewed fveally instead f 180 arc min peripherally. Pilt studies indicated that such an effect might be as large as 0.10 lg arc min. Similarly, eye mvements might help set size 2 when the stimuli are n the same side f the display. On the ther hand, eye mvements culd nt have much effect when the stimuli were n ppsite sides f the display in set sizes 2 and 4. The sesize effect fr trials with ppsite side stimuli was determined fr all bservers except Observers 3 and 5, wh had incmplete data recrds.

6 ATTNTIONAL LIMITS 337 The mean difference threshld fr the ppsite-side, set size 2 cnditin was ; the mean difference threshld fr the set size 4 cnditin was 1.03 ± The difference between these cnditins yields a sesize effect f lg arc min, t(12) = 8, p <.001. Thus, the difference between set sizes 2 and 4 was still fund when there was little pssibility f useful eye mvements. A cntrl experiment was cnducted t establish that eye mvements were nt respnsible fr the difference between set sizes 1 and 2. The experiment was similar t xperiment 1, except that it included nly set sizes I and 2 and it changed the display f the test stimulus. Specifically, the test line was always presented at fixatin and a dt was presented at ne f the study lcatins t indicate which line was t be cmpared with the test line. Thus, the test was always at fixatin regardless f set size. Five bservers participated in three sessins with tw sesize cnditins, yielding 480 trials per bserver per cnditin. The mean difference between difference threshlds fr set sizes 1 and 2 was lg arc min, t(4) = 3.7, p <.025. This difference was individually reliable (p <.05) fr 2 f the 5 bservers and marginally reliable fr ne f the thers. Thus, the sesize effect is replicated when there can be n eye mvement artifact. Cnfiguratin effects. Increasing set size intrduced the pssibility f effects f stimulus cnfiguratins. Fr example, if tw lines were lined up side by side, then it wuld be easy t cmpare their lengths by an alignment cue (On, 1967). Of cncern in xperiment 1 was the pssibility f an illusinary change in the perceptin f ne stimulus due t the additin f extra stimuli (e.g., the parallel line illusin, Jrdan & Uhlarik, 1985; and illusry cnjunctins, Treisman & Schmidt, 1982). In such situatins, the features f ne stimulus are assimilated by r cnfused with thse f anther stimulus. Fr example, a lng line might make the ther lines appear lnger than they really are. Because different line cmbinatins cause different illusins, a difference threshld culd be inflated by averaging these illusry effects. Furthermre, the amunt f averaging wuld have increased with larger set sizes. Thus, length illusins might have mediated the sesize effect. T check fr these illusins, the set size 2 cnditin f xperiment 1 was reanalyzed fr all but Observers 3 and 5, wh had incmplete data recrds. This cnditin yielded the simplest cmparisn because ne line was tested and nly ne ther line prvided a cntext line that might induce an illusin. The first analysis addressed the relative length f the cntext line: Cntext lines smaller than the test line were cntrasted with cntext lines that were larger than the test line. The cntext line's length did nt affect difference threshlds (difference = lg arc rain) r cnstant errrs (linear difference = arc min). The secnd analysis was f the effect f hetergeneus cntext lines: Cntext lines similar in size t the test line (55-65 arc min) were cmpared with cntext lines that were dissimilar in size (50-56 and arc min). There was n detectable effect f hetergeneus cntext lines (difference between threshlds = 0.01 ± 0.03 lg arc min, cnstant errr linear difference = -0.5 ± 0.4 arc min). A further examinatin f the set size 4 cnditin and the ther experiments in this article als shwed n cnsistent illusin phenmena. Thus, illusry phenmena were unlikely t have mediated the sesize effect. Anther different pssible effect f cnfiguratin cue has t d with the use f a single line in the test display. Suppse cnfiguratin cues are critical fr judging the length f lines in a multiple-line displays. Then a test with a single line such as that used in xperiment l has the effect f remving thse cues when there were multiple lines in the study display. This differentially impairs perfrmance in the larger sesize cnditins because cnfiguratin cues are destryed fr the larger set sizes and d nt exist t be destryed fr set size 1. The pssibility f such an effect was tested by cmparing the display sequence used in xperiment l with a sequence that used a test display that included all f the study lines. The test displays als included a new central arrw that pinted t the line that was t be judged. The experiment had tw cnditins: a cntrl cnditin, which had a single line in the test display t replicate the previus experiments, and an experimental cnditin, which had all fur lines f the study display repeated in the test display. Fr bth cnditins, study displays were identical t the set size 4 study displays f xperiment I. Tw bservers participated in three sessins, resulting in 480 trials per cnditin per bserver. There was n reliable effect f adding the lines t the test displays n the difference threshlds. The threshlds fr the cntrl and experimental cnditins were lg arc rain and lg arc min fr Observer 3 (difference = _ 0.05), t(14) = 0.6, p >.l, and were 0.57 ± 0.04 lg arc min and 0.56 ± 0.02 lg arc min fr Observer 7 (difference = 0.01 ± 0.05), t(14) = 0.2, p >.l. Thus, remving cnfiguratin cues did nt mediate the sesize effect. Categrizatin strategy. Several bservers reprted a strategy that may accunt fr sme f the individual variatin in this experiment. These bservers used the fact that the test stimulus was always 60 arc min in length and made an abslute judgment f the lines in the study display by cmparing each line with a memry standard. Sme bservers (particularly Observer 7) pursued this pssibility and intentinally judged each line in the study display as "shrter" r "lnger" than their memry standard. Cnsequently, they had t remember nly these judgments rather than the lengths f the lines. Infrmally, this strategy seemed successful in reducing the magnitude f the sesize effects. This raises the pssibility that these experiments understated the sesize effects that wuld be btained if this categrizatin strategy was prevented. T evaluate the effectiveness f the categrizatin strategy, a cntrl experiment was cnducted with cnditins that made it mre difficult t use. Tw versins f the set size 4 cnditin were cnstructed. One was exactly as in xperiment 1, in which there was little uncertainty abut the test length. The secnd intrduced uncertainty by intermixing trials with standards f lengths 48, 60, and 72 arc min. Tw bservers participated in five sessins, yielding 960 trials f the lwuncertainty cnditin and 320 trials fr each f the three standards in the high-uncertainty cnditin. T make a fair cmparisn, the fllwing results are nly fr the 60-arc-min standard in bth cnditins. First, Observer 7, wh reprted using the categrizatin strategy, perfrmed wrse in the high-

7 338 JOHN PALMR uncertainty cnditin (0.87 _ 0.05 lg arc min) than in the lw-uncertainty cnditin ( lg arc min), a difference f lg arc min, t(4) = 2.8, p <.05. Secnd, Observer 10, wh reprted nt using the categrizatin strategy, perfrmed indistinguishably in the high-uncertainty ( lg arc rain) and the lw-uncertainty cnditins ( lg arc rain), an unreliable difference f lg arc min. Thus, it appears that the categrizatin strategy may have been used by sme but nt all bservers and the magnitude f the sesize effect may thus have been underestimated fr sme bservers. Discussin The length difference threshld fr a line increases with an increase in the number f lines in the display. This increase was reliable fr a change frm ne t tw lines and increased prprtinally fr fur lines. Analyses and a cntrl experiment shwed that the sesize effect was nt mediated by eye mvements at test r by illusins amng the multiple lines. Other cntrls indicated that sme bservers may have used a categrizatin strategy that reduced the magnitude f their sesize effects. The ccurrence f such a strategy makes it mre difficult t interpret the size f the btained effects, but it des nt in any way weaken the evidence fr a sesize effect. In cnclusin, these results prvide a first answer t the questin psed in the intrductin: Perceptin and memry fr line length is reduced by increasing set size. xperiment 2 xperiment 1 presented the sesize effects in terms f difference threshlds. Such threshlds are gd summaries nly if all cnditins prduce psychmetric functins f a cnsistent shape. In difference threshld experiments, psychmetric functins have the same shape if they can be described by ff [(x - p)t], where ~k is a fixed functin f x and the nly thing that varies frm cnditin t cnditin are the parameters p (pint f subjective equality) and t (threshld). Only if the functins are f cnstant shape will the lg threshld differences between cnditins nt depend n the respnse level that defines the threshld. Interestingly, sme attentinal hyptheses predict that the shape f the psychmetric functins des change fr larger set sizes. Fr example, if a larger set size causes guessing n a higher prprtin f trials, the the maximum pssible perfrmance is decreased and the shape f the psychmetric functin must change (see the Type 1 mixture mdel f Shaw, 1980; fr a review, see Swets, 1984). In particular, these theries predict that deviatins frm a cnstant shape psychmetric functin will be mst evident fr values f stimulus change that prduce near-perfect discriminatin. Cnfirmatin that the psychmetric functins are the same shape will be imprtant t the discussin f alternative hyptheses at the end f this article. In summary, this experiment has three gals: replicate xperiment 1; shw that the psychmetric functin is the same shape ver its usual range; and investigate its shape fr extreme values. Methd Psychmetric functins were measured with a slight variatin f xperiment I. The methd f cnstant stimulus was used t better estimate the functin's shape. The cmparisn lengths were scaled lgarithmically and spaced at intervals f apprximately ne-third, ne, and three times the threshld. This last value is mre extreme than is typically used in threshld experiments, and perfrmance is expected t apprach perfect discriminatin fr this cmparisn length. The data were fit t a functin /(x) that was a cumulative nrmal, with the mean interpreted as the pint f subjective equality and the standard deviatin inversely prprtinal t the threshld. Tw bservers participated in fur sessins f each set size, yielding 256 trials per cmparisn stimulus. Results Figure 4 shws the psychmetric functins fr the tw setsize cnditins and fr Observers 11 and 13 in fur separate panels. In each graph, the axes are the prbability f respnding that the cmparisn stimulus was larger as a functin f the size f the cmparisn stimulus. The pints represent data and the lines represent the besfit cumulative nrmal functins (Finney, 1971; Green & Swets, 1966). Three pints are evident. First, this experiment replicated the sesize effect. In the figure, the sesize effect is reflected in the reduced slpe f the psychmetric functin fr the set size 4 cnditin cmpared with the set size 1 cnditin. Such a slpe change prduces a crrespnding change in the difference threshld. Fr example, Observer I l had a difference threshld f arc min fr set size 1 and arc min fr set size 4. This was an increase f lg arc min, t(3) = 4, p <.05; this replicates xperiment 1. Secnd, the cumulative nrmal functin was a gd fit fr the central fur cmparisn stimuli in bth cnditins, fr example, Observer 13: x2(2, N = 256) , p >. 1, fr set size 1 and x2(2, N = 256) = 1.9, p >. 1, fr set size 4. These central values are typical f the range used in all ther experiments in this article. Thus, the shape f the psychmetric functin can be mdeled as a cumulative nrmal fr the central fur pints. Third, the extreme stimulus values prduced respnses that were less extreme than predicted. In ther wrds, the largest cmparisn stimulus did nt prduce the predicted >.99 prbability lnger respnse and the smallest cmparisn stimulus did nt prduce the predicted <.0t prbability lnger respnse. Instead, respnse prbabilities were n mre extreme than abut.98 r.02. Such a result is cmpatible with abut 4% f the respnses being guesses. This can be quantified anther way by shwing that the cumulative nrmal functin did nt fit the entire data set, fr example, Observer 13: x2(4, N = 256) = 916, p <.001, fr set size 1 and x2(4, N= 256.) = 118, p <.001, fr set size 4. These last results are analyzed further at the end f this article. Discussin xperiment 2 established hw the psychmetric functin was affected by set size. The shape f the psychmetric functin was similar fr the different sesize cnditins. It

8 ATTNTIONAL LIMITS 339 N =m 0 l O.--I = 2 a Observer 11 Observer 13 data thery r 1.0 f 0.8 i ~ 0.2 data f th.....,.. = Length Change (arc min) ,.., Length Change (arc min) 0 O ~ A data f N n- ~ I -~ 0.4 n- 0.6, ~ (I.4. ~ (I.2. O. = v., Length Change (arc min) i , = - - = - - i Length Change (arc min) Figure 4. xperiment 2: Psychmetric functins fr Observers 11 and 13 and fr set sizes 1 and 4 in fur separate panels. (Pints represent the data and the lines represent the besfit cumulative nrmal functins fr the central fur data pints.) was well fit by a cumulative nrmal ver mst f its range with deviatins nly when perfrmance apprached 98% crrect. ven then, the deviatins were similar fr bth setsize cnditins. The cnstant shape f the psychmetric functin ver its central range supprts the use f threshlds as a summary f perfrmance ver that range. Furthermre, this means that large set sizes d nt necessarily mean pr perfrmance. One can always find a stimulus change large enugh t get near-perfect discriminatin fr a set size f fur. xperiment 3 The next experiment investigated a brader range f stimulus characteristics and their assciated judgments. xperiment 3 included tw ther judgments f a line segment (vertical psitin and rientatin) and ne judgment f utline rectangles (shape). Fr all f these judgments, there is a literature fr single stimulus displays but nt fr multiple stimulus displays (e.g., psitin--attneave, 1955; Legge & Campbell, 1981; rientatin--buma & Andriessen, 1968; Matin & Drivas, 1979; Westheimer, 1982; shape--menzer & Thurmnd, 1970; Weintraub, 1971). Methd Sesize effects were measured fr each f the three judgments with set sizes f 1, 2, and 4. This resulted in a ttal f nine cnditins. Sessins with different judgments were run sequentially. Tw bservers participated in fur sessins, resulting in 576 trials per cnditin per bserver. The differences in stimuli and prcedure fr each judgment are described in the fllwing sectins. Otherwise, the methds f this experiment were identical t xperiment 1. Vertical psitin. Fr the vertical psitin judgment, the study displays cnsisted f ne, tw, r fur hrizntal lines that were 60 arc rain lng and arranged arund fixatin as shwn in the left side f Figure 5. The psitin f each line was defined in relatin t the

9 340 JOHN PALMR Scale Drawings fr Different Study Stimuli Vertical Orientatin Shape Psitin Figure 5. A scale drawing f the study displays used in xperiment 3. (The panels are fr the vertical psitin, rientatin, and shape discriminatin tasks.) fur standard psitins that were used in xperiment 1. Namely, the standard psitin placed the center f each line n an imaginary circle 180 arc rain frm fixatin at an angle frm fixatin crrespnding t 1, 4, 7, r 10 'clck. T vary vertical psitin, each line was displaced upward r dwnward by a maximum f 42 arc rain frm the standard psitin. The test display was identical t that used in xperiment 1 (see Figure 1) and the single line was always at ne f the standard psitins. The bserver's task was t discriminate if the test line appeared abve r belw the psitin f the crrespnding study line. Observers reprted using the relative psitin between the fixatin pint and the lines as the main cue. Difference threshlds were calculated in terms f the vertical psitin change in arc minutes. Orientatin. Fr the rientatin judgment, the standard displays f line segments were mdified by changing the rientatin f the lines in the study display by up t a maximum f 6*. An example is shwn in the middle f Figure 5. The test display always cnsisted f the standard stimulus, a hrizntal line. With these displays, bservers judged the directin f rientatin change frm study t test. Owing t limited display reslutin, small rientatin changes were apprximated by placing the endpints at the crrect lcatins and drawing shrt hrizntal line segments with vertical steps between them. The smallest pssible rientatin change was 1.9"; this was with a single pixel "rise" f 2 arc rain fr the "run" f 60 arc min. Discriminatin threshlds were calculated in terms f the rise in arc minutes t make the units similar t previus experiments. Fr these stimuli, the cnversin rule is 1 arc rain f rise fr apprximately 1" f rientatin change. Shape. Fr the shape judgment, the bservers were required t judge the shape f utline rectangles. The rectangles were elngated either vertically r hrizntally frm a 60-arc-rain square as shwn in the right panel f Figure 5. In the study display, each rectangle was mdified frm a square by reducing ne dimensin (e.g., height) and increasing the ther dimensin (e.g., width) by an equal amunt up t a maximum f 10 arc rain. The test display was always the standard, a 60-arc-rain square. Observers judged the directin f elngatin change frm study t test. Discriminatin threshlds were calculated in are minutes f elngatin. In summary, sesize effects were measured fr three judgments. Difference threshlds were calculated fr each in terms f the arc min change in the apprpriate dimensin. Results Vertical psitin. In the left panel f Figure 6, difference threshlds are pltted as a functin f set size fr Observers 3 and 7. The difference threshlds are scaled lgarithmically with a vertical axis f 2 lg units (as used in all figures in this article). Set size affects vertical psitin difference threshld. Frm set size 1 t 4, the mean difference threshld increases by 0.39 lg arc min: Observer lg arc min, t(l 1) = 7.0, p <.001; Observer _ 0.04 lg arc min, t(l 1) = 9.4, p <.001. This is a 2.5-fld increase in difference threshld. The mean increase frm ne t tw items was 0.16 lg arc min, which was als reliable in bth bservers: Observer lg arc rain, t(l 1) = 3, p <.01; Observer _ 0.04 lg arc min, t(11) = 6, p <.001. Orientatin. In the middle panel f Figure 6, difference threshlds are pltted as a functin f set size by using units f the vertical rise in arc rain. These rientatin difference threshlds als increased with set size. Fr Observer 3, the increase was 0.8 lg arc min; fr Observer 7, the set size 1 difference threshld culd nt be estimated due t nearperfect discriminatin perfrmance with the smallest available rientatin change. The upper bund n the difference threshld is indicated in the figure. Cnsequently, the sesize effect n the difference threshld was n smaller than 0.2 lg arc min. Near-ceiling perfrmance als prevented parametric statistical tests f these effects. Nnetheless, fr each bserver, each blck f set size 4 yielded wrse perfrmance than the paired blck f set size 1, which is reliable (p <.05) by a sign test. Shape. In the fight panel f Figure 6, elngatin difference threshlds are pltted as a functin f set size. Again, set size has an effect. The difference between set sizes 1 and 4 was 0.89 _ lg arc min fr Observer 3 and lg arc rain fr Observer 7, t(l l) = 1 l, p <.00 l, and t(l l) = 5, p <.001, respectively. The difference between set sizes 2 and 1 was als reliable: Observer _ lg arc min, t(l 1) = 5, p <.001; Observer _ lg arc min, t(l l) = 4, p <.005. Discussin xperiment 3 extended the findings f xperiment l t three ther judgments. It seems likely that experiments f this type culd be extended t any cntinuusly varying visual characteristic. Fr example, ne culd find difference threshlds as a functin f set size fr the hue, cntrast, and depth f an bject. On the ther hand, it is nt bvius what the best way is t generalize this experiment t stimuli such as letters that have categrical definitins. xperiment 4 xperiment 4 was designed t demnstrate the cnsistency f sesize effects acrss a range f retentin intervals (cf. Laming & ScheiwiUer, 1985). It was similar t xperiment 1 with the exceptin that the delay between study and test displays was either 0.5 r 8 s instead f the 2 s used previusly. Use f briefer delays was nt desirable because f apparent mtin artifacts (Palmer, 1986). Such brief delays were inves-

10 ATTNTIONAL LIMITS 341 Results fr Different Study Stimulus Vertical Orientatin Shape Psitin 100~ Observers 10: Observers A 100 ~ Observers ~ , -, (1. Set Size "~ 1 t"- g e Set Size Z ~ 1 -, -,-,-, ~ 10 " (n Set Size Figure 6. Threshlds fr the three tasks used in xperiment 3. (In the left panel, vertical psitin difference threshlds are shwn as a functin f set size fr 2 bservers. In the middle panel, rientatin difference threshlds are shwn as a functin f set size fr 2 bservers. In the fight panel, shape difference threshlds are shwn as a functin f set size fr 2 bservers.) tigated in Palmer (1988) by using a cuing paradigm similar t partial reprt. Methd The methds were thse f xperiment 1, with the fllwing exceptins. Fur cnditins were defined by cmbining tw delays (0.5 s and 8 s) with tw set sizes (2 and 4). These fur cnditins were presented in a mixed-list fashin. Tw bservers participated in fur sessins, yielding 256 trials per bserver per cnditin. Results Length difference threshlds are shwn in Figure 7. Results fr Observer 11 are in the left panel and thse fr Observer 13 are in the fight panel. The slid line indicates the 0.5-s delay cnditins and the dtted line indicates the 8-s delay cnditins. The mean sesize effect was 0.37 lg arc min and was reliable fr bth bservers: Observer lg arc min, F(I, 13) = 63, p <.001; Observer lg arc rain, F(I, 13) = 8, p <.05. Delay had a mean effect f 0.21 lg arc rain: Observer _ 0.05 lg arc min, F(1, 13) = 9, p <.05; Observer _ 0.12 lg arc min, F(1, 13) = 5, p <.05. The data were apprximately additive fr lg threshlds but were nt reliable enugh t clsely evaluate the degree f interactin. In summary, the sesize effect is fund fr a range f retentin intervals. general t a variety f respnse levels, stimulus attributes, and retentin intervals. In the next three experiments, I examine if the sesize effect is due t attentin. xperiment 5 Sesize manipulatins cnfund tw things: Mre stimuli are presented t the bserver and mre stimuli are relevant t the task. Cnsequently, the sesize effect may be sensry in nature wing t additinal stimuli in the display, r it may be attentinal in nature wing t the additin f relevant stimuli. Sensry hyptheses assert that a single line is mre difficult t perceive in the cntext f additinal lines. Fr example, adjacent lines might cause masking (Andriessen & Discussin Set Size Set Size Figure 7. xperiment 4: Length difference threshlds are shwn as xperiments 2, 3, and 4 establish the generality f xperi- a functin f set size fr tw delays. (The separate panels shw results ment 1. The sesize effect in partial discriminatin was fr Observers II and 13.) A C " I- t 100: ~- lo Observer 11 Observer : Delay (s) c Delay (s) "- 8.0 ""P 8.~ / " a 1 =,,,

11 342 JOHN PALMR Buma, 1976; Kahneman, 1968), r they might cause illusins (Cren & Girgus, 1978). In xperiment 5, these hyptheses were tested by hlding the number f relevant lines cnstant while manipulating the number f displayed lines. Tw r fur lines were displayed and a cue indicated tw lines that were relevant t the test. The test was always f ne f the relevant lines. The display set size f fur was cmpared with a display set size f tw in which nly the tw relevant stimuli were presented. Sensry hyptheses predicted an effect f display set size despite hlding the relevant set size cnstant. In previus tests f this srt, it is nt uncmmn t find evidence fr a sensry cntributin tward sesize effects (e.g., riksen & Lappin, 1967). In summary, the displayed set size was manipulated independently f the relevant set size. Methd The displayed set size was tw r fur, as shwn by the alternate study stimuli in Figure 8. Shwn n the left is an example f displaying a set size f tw. The lines were always n ppsite sides f the fixatin pint and appeared at either the 1 and 7 &dck psitins (vertical pair) r at the 4 and 10 'clck psitins (hrizntal pair). Shwn n the fight is an example f displaying a set size f fur. With all fur stimuli present, ne f the ppsite-side pairs was precued with a small cue fine at fixatin fr 1,000 ms befre the study display. If the cue was vertical, then the test wuld be f the nearvertical pair (1 and 7 'clck); if the cue was hrizntal, then the test wuld be f the near-hrizntal pair (4 and 10 'clck). Thus, the relevant set size was always tw. Six bservers participated in three sessins, resulting in 480 trials per cnditin per bserver. In ther ways, this experiment was identical t xperiment 1. Results The effect f display set size is shwn in Figure 9. The bld curve indicates the mean difference threshld fr each display set size and the dtted curves indicate threshlds fr selected individual bservers. The difference in threshld between displaying fur and tw lines was lg arc min. This was nt reliably different than zer (t = 0.6, p >. 1) and was much smaller than the 0.22 lg arc min effect fund fr the cmparable sesize effect in xperiment I. Mre precisely, ne can rule ut a display sesize effect f mre than 0.06 lg arc min. Thus, there is n evidence fr any sensry effect, and the wrst pssible case limits sensry hyptheses t accunting fr a quarter f the sesize effect. This result makes it unlikely that any sensry hypthesis can accunt fr the sesize effects fund in this article. xperiment 6 xperiment 5 ruled ut sensry explanatins fr the setsize effect. The next step is t find direct evidence fr an attentinal hypthesis f the sesize effect. One way t d this is t shw similar effects fr attentinal instructins as thse fr set size. Specifically, manipulating the relevant set f stimuli by instructin shuld have the same effect as Time ~~) Identical Attentin Cues ~ ~Alternate Study Stimuli Cmmn Test Stimulus Figure 8. A schematic illustratin f the display sequence used in xperiment 5. (Display set size was either tw r fur and a cue always indicated tw lines as relevant.) "" v - t/) I- (1) - (1) C) a)._l I- Mean f 6 Observers Selected 13 Single Observers T 4...,..t.J""f i I i I Displayed Set Size t/) - t.) N a.,-i Figure 9. xperiment 5: The bld curve is the mean length difference threshlds as a functin f the displayed set size; the dtted curves are the threshlds fr selected individual bservers; and the relevant set size is always tw.

12 ATTNTIONAL LIMITS 343 manipulating set size, as in xperiment 1. T test this predictin, xperiment 6 manipulated the relevant set size while hlding cnstant the displayed set size. Methd The study display always cnsisted f fur lines (Figure 10). Hwever, cues indicated a relevant set size f either tw r fur. The cues were presented at the beginning f each trial, as was dne in xperiment 5. A relevant set size f tw was defined by a line cue that indicated a pair f stimuli, as in xperiment 5. Fr example, as shwn in the left f Figure 10, a vertical cue line at fixatin indicated a test at either the 1 'clck r 7 'clck psitin. A similar hrizntal line was used n alternate trials t cue the ther lines. In cntrast, as shwn n the right, a relevant set size f fur was indicated by a neutral cue that cnveyed n infrmatin abut which line f the fur was t be tested. The neutral cue was a cmbinatin f tw ther cue lines that made up a "plus" sign. Cues were presented 1 s befre the study display, as in xperiment 5. ight bservers participated in three sessins t yield 480 trials per bserver per cnditin. Results The effect f relevant set size is shwn in Figure 11. The bld curve is the mean length difference threshld pltted as a functin f the number f relevant stimuli. Increasing the number f relevant stimuli increased the difference threshld by _ 0.05 lg arc min, t(7) = 3.6, p <.005. The magnitude f this effect was similar t the 0.22 lg arc min difference fund between set sizes 2 and 4 in xperiment 1. Figure 11 als shws sme f the individual bserver data Time Fixatin Display Alternative Attentin Cues Identical Study Stimuli Cmmn Test Stimulus Figure 10. A schematic illustratin f the display sequence used in xperiment 6. (A cue indicated whether a relevant set size was either tw r fur; a displayed set size was always fur.) "" v -.- /) 100" - 10 I- 0~ t21 e--._1 -g- Mean f 8 Observers -- Selected Single Observers 7 I I I Relevant Set Size "2.0 Figure 11. xperiment 6: The bld curve is the mean length difference threshlds as a functin f the relevant set size; the dtted curves are the threshlds fr selected individual bservers; and the displayed set size is always fur. (see dtted curves). In particular, the bservers with the highest and lwest threshlds are shwn alng with the bservers with the smallest and largest effect f relevant set size. The relevant sesize effect was reliable fr 6 and marginally reliable fr 1 f the 8 bservers. 2 In summary, the manipulatin f relevant set size frm tw t fur prduced effects similar t the sesize effects f xperiment 1. This supprted an attentinal hypthesis fr the sesize effect. xperiment 7 Attentinal hyptheses predict that unattended stimuli shuld be perceived and remembered less well than attended stimuli. In ther wrds, instructins t attend t ne stimulus and nt attend t anther shuld decrease perfrmance fr the secnd stimulus. In xperiment 7, perfrmance was measured fr such unattended stimuli. Methd Fur cnditins were included in tw different blcks f trials. In the sesize blcks, tw cnditins replicated the set size 2 and 4 cnditins f xperiment 1. These were presented in a mixed-list fashin and included a neutral plus cue at fixatin similar t that 2 The remaining bserver, Observer 6, reprted using the categrizatin strategy described with the cntrls f xperiment 1. It seems likely frm thse cntrls that if similar cntrls were used here, this bserver t wuld shw an effect f relevant set size t~ _ v t/) - t.j -..A

13 344 JOHN PALMR used in xperiment 6. In the cued blcks, the stimuli were similar t thse used in the relevant set size 2 cnditin f xperiment 6. Hwever, the cue was invalid n 25% f the trials and ne f the tbe-ignred stimuli was tested. Observers were instructed that despite ccasinal tests f the uncued lines, their pririty task was t d as well as pssible n the cued lines. In particular, they were challenged t d as well under these cnditins as with the 100% valid cues f xperiment 6 that they had just cmpleted. Three bservers participated in fur sessins. The number f trials per cnditin per bserver was 320 fr the sesize cnditins, 480 fr the valid cue cnditin, and 160 fr the invalid cue cnditin. Results In Figure 12, the bld curve is the mean length difference threshld as a functin f set size and cue validity. The setsize effect was nce again replicated. The new result is the large effect f cue validity. Fr the valid cues, the mean difference threshld was _ lg arc rain; in cntrast, fr the invalid cues the difference threshlds were t large t calculate accurately (.1.7 lg arc min). Thus, the effect here is n the rder f a lg unit f threshld. A last cmparisn is that perfrmance in the valid cue cnditin was intermediate between the set size 2 and 4 cnditins. Thus, the cue uncertainty in this experiment made the cues less effective than in xperiment 6. Als shwn in Figure 12 are the threshlds f the three bservers, each f which replicates the sesize effect and shws the large cue validity effect. T make a quantitative cmparisn between the cue validity cndi- A -.m a~ v - 0 r" 03 I- O t.) Mean f 3 Observers... Single Observers 10" fr all bservers / 11 r tl:l.._ 0 t/} I--- - tins, the estimated prbability crrect fr a length change f 16 arc min was calculated and is shwn in Figure 13. Here, prbability crrect is graphed as a functin f cue validity. The mean prbability crrect was fr the invalid cnditin cmpared with fr the valid cnditin, t(2) = 5.5, p <.05. In terms fa d' measure, this was a fivefld change in perfrmance. By any measure, the discriminatin was pr fr the stimuli that were nt cued. Discussin xperiment 7 demnstrated pr perfrmance fr a stimulus that was t be ignred accrding t instructins. This prvided further evidence fr an attentinal explanatin f the sesize effects. Mre generally, the last three experiments were all cmpatible with an attentinal explanatin f the sesize effect. xperiment 5 ruled ut sensry explanatins and xperiments 6 and 7 shwed that attentin instructins prduced effects similar t displayed set size. General Discussin The experiments in this article have demnstrated an effect f set size in a variety f situatins. It ccurred with several kinds f stimuli and judgments; it ccurred with a variety f delays and threshld criteria; and it ccurred with sets defined by instructins as well as with sets defined by the display itself. The sesize effect was measured in terms f difference threshlds that increased by a factr f 2 when there are fur stimuli rather than ne. This means that fr the finest details f a scene, nly ne stimulus can be accurately discriminated. On the ther hand, fr carse size and shape infrmatin, at least fur stimuli can be accurately discriminated. Specifically, if fur lines are presented at 3* eccentricity, then lengths f arc min are distinguished 98% f the time. Such a dependence n the stimulus was freshadwed by William James: "The number f things we may attend t is altgether indefinite, depending n the pwer f the individual intellect, n the frm f the apprehensin, and n what the things are [italics added]" (James, 1890, p. 405). This last dependence is partly spelled ut by these experiments.. m a e-- c-.._1, //,,//, Valid 2 4 Invalid Cue Cue Set Size 0.5.~- Figure 12. xperiment 7: The bld curve is the mean length differenee threshlds as a functin f the set size r the cue validity; the dtted curves are the threshlds fr individual bservers. (Fr cnditins in which the cue validity was manipulated, the set size was always fur. Ntice that the values fr the invalid cue are nly a lwer bund.) 0.0.J r- Alternative Hyptheses fr the SeSize ffect Many factrs limit perfrmance in perceptual tasks: sensatin, decisin, memry, and attentin. T what extent did the partial discriminatin paradigm succeed in islating a setsize effect that depended n nly attentinal limitatins? Sensry hyptheses. Sesize effects can ccur frm sensry phenmena such as lateral masking. Such hyptheses were tested in three ways. First, specific sensry effects that might prduce sesize effects were cntrlled in the design f the experiments. These factrs included eccentricity and psitinal uncertainty, which therwise are cnfunded with set size. Secnd, cntrl experiments were cnducted t rule ut specific sensry hyptheses such as eye mvements and illu-

14 ATTNTIONAL LIMITS 345 Figure 13. xperiment 7: The estimated prbability crrect f individual bservers is shwn as a functin f cue validity. (This analysis assumes a single length change f 16 arc min.) sins between multiple stimuli. These cntrls shwed that little, if any, f the sesize effect was due t these surces. Third, mre general sensry hyptheses were tested by uncnfunding the number f stimuli displayed and the number that were relevant t the task. The number displayed was shwn t have n detectable effect. This is particularly imprtant because previus experiments have ften nt satisfied this criterin (e.g., riksen & Lappin, 1967). Thus, even thugh sensry effects d limit perfrmance under less cntrlled cnditins, it is nt the mediatr f sesize effects bserved here. Decisin hyptheses. Sesize effects can ccur frm a decisin prcess that cmbines infrmatin frm multiple nisy surces (e.g., Shaw, 1982). The mst well-understd case is what Shaw called infrmatin integratin tasks, which include mst detectin and search tasks. Determining whether such decisin prcesses play a rle here is addressed in tw steps. First, I argue that partial discriminatin is designed t avid limitatins f decisin as specified in previus theries. Secnd, I extend the decisin theries t include the partial discriminatin task and shw that fr reasnable assumptins the sesize effect is nt due t decisin. Tasks that require infrmatin integratin necessarily have decisin prcesses that can be affected by set size. Increasing the set size increases the number f infrmatin surces, which in turn increases the nise that cntributes t the decisin. In shrt, set size affects the decisin prcess. In cntrast, the partial discriminatin task prvides a cue that specifies nly ne surce f infrmatin as relevant t the decisin. Changes in set size d nt change the number f infrmatin surces relevant t the test. Given that set size des nt affect decisin, then decisin cannt mediate the setsize effects. This argument can be stated in anther way by using the task dichtmy f Sperling and Dsher (1986). They distinguished between tw kinds f tasks: A cmpund task has a respnse that depends n multiple stimuli, and a cncurrent task has independent stimuli and respnse sets. In ther wrds, cmpund tasks require infrmatin integratin, whereas cncurrent tasks require separate infrmatin prcessing. Sesize effects can be mediated by decisin in cmpund tasks but cannt be mediated by decisin in cncurrent tasks. The partial discriminatin task falls acrss this dichtmy. It is a cmpund task in that the respnse depends n the cue prvided by the lcatin f the test stimulus. Hwever, it is a cncurrent task in that the separate study stimuli must be prcessed independently, and a crrect respnse t ne is independent f the thers. Thus, if the cue is assumed t be accurate in indicating nly ne infrmatin surce fr decisin, then partial discriminatin is a cncurrent task with sampled stimuli. In ther wrds, bservers must perceive and remember each stimulus independently, but then memry is randmly sampled fr ne stimulus. One might still argue that the task is nt cncurrent because the infrmatin frm the cue is nt used accurately t indicate a single infrmatin surce. This seems very unlikely because f the very distinct cue lcatins. In additin, analyses f xperiment 1 (cnfiguratin effects cntrl) have shwn nne f the cnfusin errrs expected if the test lcatin is uncertain. Furthermre, such a failure f using the cue makes anther predictin that can be shwn t fail. When the wrng surce f infrmatin is selected, then perfrmance is based n the wrng stimulus and the respnse can be n mre accurate than a guess. Thus, the prbability f cue failure limits the best pssible perfrmance. Cnsequently, the psychmetric functins must asymptte fr a large stimulus t a level dependent n set size. Let ~b(n,x) be the psychmetric functin fr set size n and stimulus x. One then expects that a failure prbability f f with set size n results in a change f the psychmetric functin shape given by ~(n,x) = (1 -f) ~b(l,x) +fg, (1) where g is the respnse prbability with randm guessing (g =.5 here). In ther wrds, any trial is based n ne f tw states. With prbability (1 -f), the crrect surce f infrmatin is sampled and perfrmance is as with set size 1; with prbability f the incrrect surce f infrmatin is sampled and ne must guess. The verall prbability is the cmbinatin f these tw kinds f trials. This equatin is an applicatin f a standard mixture mdel ften discussed in the attentin literature (see the Type 1 mixture mdel in Shaw, 1980; r fr a general review, see Swcts, 1984). quatin 1 predicts the asymptte fr any given sesize effect. A twfld increase in the difference threshld as fund in xperiments 1 and 2 requires that the asymptte drp frm 1.0 t.8. The best bserved perfrmance measured in xperiment 2 was arund.98, which is much larger than the predicted.8. Thus, this decisin hypthesis can be rejected. In summary, it is nt likely that decisin mediates the setsize effects. This cnclusin is based n tw arguments. First,

15 346 JOHN PALMR the partial discriminatin task prevents set size frm affecting the decisin prcess by its sampling f a single surce f infrmatin. Secnd, if the sampling prved t be inaccurate, then the effect n decisin wuld cause a change in the asymptte that was nt fund. Thus, ne can reject any rle f decisin prcessing. Memry versus perceptual limitatins? One can imagine that the limitatin n perfrmance bserved here is due t prcesses f either perceptin r memry. With n definitive definitin f these cncepts, n clear cnclusin is pssible. Hwever, ne kind f memry hypthesis can be ruled ut. Suppse that the sesize effect depends n memry prcesses that ccur during retentin intervals n the rder f 1 s r mre. Fr example, suppse frgetting frm shrterm memry was mre rapid fr larger set sizes. This predicts that the sesize effect wuld be small fr very shrt retentin intervals and wuld grw with retentin intervals. This is cntradicted by the bservatin f similar sesize effects fr delays between study and test f 0.5 and 8.0 s, as fund in xperiment 4. Because sesize effects are established within a half secnd f stimulus ffset, this implies that perceptin r memry prcesses within that half secnd are respnsible fr the effect. This argument was pursued further fr intervals f less than 0.5 s by using a partial-reprlike methd (Palmer, 1988). The results indicate that the lss f infrmatin is very early, but it still des nt distinguish between perceptin and memry hyptheses. There are several pssible suggested hyptheses. Perceptin itself may have a limitedcap~icity t establish the precisin f size and shape (e.g., Rck & Gutman, 1981); perceptual memry may degrade befre items can be encded int mre durable memries (e.g., Sperling, 1960); encding t mre durable memries may be limited in ther ways (e.g., Wlfrd & Hllingswrth, 1974); r finally, the mre durable memries themselves may have limited capacity (e.g., Frick, 1988). Attentin hyptheses. Althugh the exact lcus f the limit n infrmatin prcessing is unknwn, there is evidence that it is attentinal. Specifically, the relevant set size was shwn t be the critical variable in the sesize experiments. Thus, the prcess that limits perfrmance is under instructinal cntrl t select sme stimuli. This is taken here as the criterin fr cnsidering a phenmenn t be attentinal. The analysis that fllws cnsiders alternative attentin hyptheses in tw parts. The first part analyzes the chice between switching and sharing hyptheses. The secnd part describes a particular versin f the sharing hypthesis that is cmpatible with the current results. These attentinal hyptheses can be cmbined with any f the perceptual and memry lci discussed earlier. A first cnsideratin in attentin thery is whether attentin is a matter f switching between a few states r a matter f sharing ne r mre cntinuusly valued quantities. Fr example, is nly ne item prcessed in any display with attentin switching between displays, r d multiple items share prcessing within a display? A test f the simplest switching mdel is pssible by using the psychmetric functins measured in xperiment 2. By an all-r-nne attentin switching hypthesis (cf. Shaw, 1980, Type l mixture mdel; Swets, 1984), attentin cnsists f nly tw states, attending r nt attending. If ne des nt allw switching within a trial, the mdel predicts discriminatin in the same way as quatin 1, which was used t cnsider a decisin hypthesis in which respnses were based n a mixture f crrectly selected stimuli and incrrectly selected stimuli. The same mdel can be applied here by assuming that ne selects a single stimulus and guesses if anther is tested. Cnsequently, the prbability f guessingfis 0 fr set size 1,.5 fr set size 2, and.75 fr set size 4. This predicts that perfrmance cannt be better than.625 prbability crrect fr set size 4. The best bserved perfrmance btained in xperiment 2 is repltted in Figure 14. The panels are fr separate bservers and the pints shw the best bserved prbability crrect fr each set size. Fr bth panels, the prbability crrect is mre than.95 fr Observer 11 and mre than.9 fr Observer 13. The lines shw varius mdel predictins, with the lwest being the allr-nne switching mdel. The predictins are calculated by assuming an verall guessing prbability frm the set size 1 cnditin and then estimating the reduced perfrmance fr set size 4 frm the particular attentin mdel. Clearly, the mdel with nly ne attended lcatin can be rejected. A mre interesting analysis is t cnsider the switching mdel that allws a maximum f three stimuli t be prcessed in any display. quatin 1 can be applied t this case by assuming fr set size 4 that there is a.75 chance that the tested stimulus is ne f the three that were prcessed. The predictins fr this mdel are the middle dtted curves in Figure 14. This predictin can als be rejected. This implies that all fur stimuli must receive sme prcessing n each trial. In ther wrds, there is partial infrmatin available abut the size r shape f at least fur bjects in a brief display. This analysis can be extended ne step further by calculating the prprtin f the trials that might be based n n infrmatin. In ther wrds, hw ften des ne knw nthing abut ne f the stimuli in the set size 4 display? The asympttic values f the psychmetric functin prvide a bund n the prprtin f times that the bservers knew nthing abut an item. Using quatin 1 and an asymptte f.98 yields an fparameter f.04. Thus, ne stimulus f set size 4 is "cmpletely missed" less than 5 % f the time. Clearly, attentin must be shared acrss the stimuli. Given shared attentin, the next issue is what kind f sharing metaphr is apprpriate. Pssible metaphrs include switching between stimuli within a trial r the sharing f resurces (Kahneman, 1973). Distinguishing these pssibilities is beynd the experiments reprted here. Instead, I describe a specific mdel f attentin sharing that is cmpatible with the bserved sesize effect. The mdel was called the sample size mdel by Shaw (1980; see als Lindsay, Taylr, & Frbes, 1968; Lute, 1977). In the sample size mdel, attentin is mediated by the allcatin f samples t nisy perceptual attributes. That is, any unidimensinal percept is the aggregatin f several samples frm an underlying unidimensinal randm variable representatin. When a single stimulus is t be attended, all samples can be taken frm that stimulus. When tw stimuli are t be attended, the samples must be divided between the stimuli. Assume that each stimulus attribute is characterized by an independent Gaussian randm variable. Then the mean f the samples f that variable will have a variability that is

16 ne ATTNTIONAL LIMITS Observer " Observer I1. " L e~ P D.. 0.a ~ 0.7.i O t,n 0.6 Observer 11 attended lcatin... three attended lcatins... all lcatins attended..d O 0.6 m Observer ne attended lcatin... three attended lcatins... all lcatins attended Set Size Set Size Figure 14. On the basis f xperiment 2, the best bserved prbability crrect is shwn as a furlctin f set size fr Observers 11 and 13. (The lines are predictins frm three mdels explained in the text.) inversely prprtinal t the number f samples. With equal allcatin f samples, an increase in the set size decreases the number f samples prprtinally. Therefre, the variability f the sample mean is prprtinal t the set size. Cmbining this with a signal detectin mdel in which d' is inversely prprtinal t variability predicts that d' is inversely prprtinal t n 1/2, where n is the set size. Assuming further that the psychmetric functins are a cumulative nrmal, the predictin is then fr threshlds t be prprtinal t #/2 because threshlds are inversely related t d' fr any fixed stimulus. In ther terms, the lg threshld will be linear with lg set size and have a slpe f 0.5. Anther simple mdel that makes this same predictin is an infrmatin-theretic mdel in which ttal infrmatin transmissin capacity remains cnstant regardless f set size. Fr n stimuli, capacity fr any ne stimulus will be 1/n f ttal capacity. Under certain assumptins, d' squared varies prprtinally with channel capacity (Taylr, Lindsay, & Frbes, 1967), thus d' will be inversely prprtinal t #/2 as stated. In summary, bth the sample size mdel and the cnstant infrmatin transmissin mdel predict threshlds t duble fr any furfld increase in set size. This predictin can be cmpared with the results f xperiment I. The slpe in a lgarithmic plt was estimated t be lg arc min/set size. This slpe is nt reliably different frm the 0.5 predicted by the sample size mdel. All f the ther experiments shw rughly similar size effects. Althugh nne f these experiments were designed t distinguish these mdels frm ther detailed mdels, it is interesting that a mdel as simple as the sample size mdel can predict the magnitude f the sesize effect. Summary. Sensry, decisin, and shrterm memry frgetting can be ruled ut as mediatrs f the sesize effect. In additin, any attentin switching mdel can be ruled ut that des nt have sme infrmatin abut each stimulus. Of the mdels that remain, a particularly simple ne is an attentin sharing mdel in which samples are shared amng the stimuli. This sample size mdel predicts the functin and magnitude f the sesize effect. Generality Stimulus generality and categrizatin. The results fund here can be cmpared with previus experiments that have measured hw much infrmatin is perceived and remembered frm ther kinds f stimuli. The classic studies f span f apprehensin in the full reprt paradigm shw n effect f set size fr letters, wrds, r gemetric figures like squares and circles. The different result may be due t the full reprt impsing a ceiling n perfrmance fr small sets f items. In ther wrds, a single letter might be perceived better than fur letters, but either can be reprted perfectly. This idea finds sme supprt in the recgnitin experiments f Reicher (1969) in which there is a sesize effect f ne versus tw letters. Hwever, ther letter experiments have shwn that tw letters prduce similar perfrmance as a single letter (e.g., stes, 1972; Farrell & Desmarais, 1990). These studies differ in many ways, including the task, stimulus sets, and use f masks. If the ceiling effect is nt the explanatin, then ne alternative is the categrical nature f letter stimuli cmpared with the size and shape attributes studied here. Remembering categry labels may be different frm remembering fine detail. Indeed, a few; bservers in xperiment 1 reprted a strategy f using categrizatin that seemed t attenuate the sesize effect. In summary, differences between partial discriminatin and reprt may nt nly be due t ceiling effects, but may als be due t the categrizatin pssible with letterlike stimuli. Task generality and memry. Studies f visual search have shwn that under certain cnditins, very large set sizes can be prcessed as efficiently as small set sizes (e.g., geth et al.,

17 348 JOHN PALMR 1972). Similarly, detectin studies f simple visual stimuli such as gratings have shwn n effect f attentin beynd an effect n decisin (e.g., Davis et al., 1983). Why are the current results different? The pssibility suggested in the intrductin is that memry plays a much smaller rle in visual search than in recgnitin. Certain kinds f perceptual prcessing may be pssible fr large set sizes, but remembering infrmatin frm that same set size may be impssible. This idea can be restated as the hypthesis illustrated in Figure 15. This is a schematic infrmatin flw diagram that illustrates the typical prcessing sequence f perceptin t memry t further prcesses leading t a respnse. The hypthesis is that the decisin critical t a task may ccur in ne f tw places. Fr tasks such as search r detectin fr simple targets, it may be pssible t make an early decisin befre the bttleneck f memry. Such a decisin wuld be the basis fr string infrmatin abut nly the target in a display and nt abut distractrs. In cntrast, tasks such as recgnitin require a memry fr each stimulus, and hence any decisin has t be after the bttleneck f memry. The details f this hypthesis are pen. Fr example, sme search tasks might require memry. The pint is that memry requirements are a likely surce f the differences in sesize results bserved between search, detectin, and recgnitin. Implicatins fr Scene Perceptin Tw pints f the current discussin have implicatins fr the larger issue f scene perceptin. One pint is the attentinal limits n perceptin and memry shwn here fr recgnitin. The ther pint is the hypthesis that tasks like Hypthesis IPe rceptin~ Me m ry,~p rfuertshserngl \/ \/ I Decisin ] I Decisin 'a" ] Search depends n early decisin prcessing Recgnitin depends n late decisin prcessing Figure 15. This infrmatin flw diagram illustrates the different ways that search and recgnitin tasks may relate t the prcesses f perceptin and memry. (The prpsal is that sme search tasks are mediated by an early decisin prcess, whereas all recgnitin tasks require a late decisin prcess.) search d nt have these attentinal limits because f different memry requirements. Fr scene perceptin, these pints suggest that searchlike tasks have a great advantage. By aviding the memry bttleneck, perceptin f smething abut many stimuli is pssible. If this is the case, an imprtant characterizatin f different aspects f scene perceptin is t what extent they require memry. This might be usefully incrprated int cmputatinal mdels f scene perceptin. These mdels ften attempt a rather cmplete representatin f the visual wrld. This may be apprpriate fr searchlike tasks, but the limits f memry suggest that nly a mre schematic representatin f the visual wrld is accumulated and maintained ver time. These ideas have a particular implicatin fr perceptins that ccur ver multiple eye fixatins. ye fixatins ccur ver time and thus must require sme kind f memry. Cnsequently, the current results suggest that tasks invlving multiple fixatins may resemble recgnitin rather than search. If s, nly a limited amunt f visual infrmatin can be remembered after a fixatin t integrate with future fixatins. This idea is cntrary t that f an integrative visual buffer in which a cpy f an imagelike representatin is integrated frm fixatin t fixatin (McCnkie & Rayner, 1976; Rayner, 1978). Indeed, the current results jin grwing evidence that relatively little visual infrmatin is integrated acrss eye mvements (e.g., Rayner, McCnkie, & Zla, 1980; Sun & Irwin, 1987). This suggests a thery in which nly mre abstract cdes are integrated frm fixatin t fixatin (e.g., Hchberg, 1968; Rayner et al., 1980; Rck et al., 1972). An initial attempt t measure the memry fr a previus fixatin can be fund in Palmer and Ames (1988). The measurements use the partial discriminatin paradigm in a situatin in which bservers make a sequence f eye fixatins. The initial results are cmpatible with the memry capacity fr infrmatin frm a previus fixatin being similar t the memry capacity measured in the current experiments. In summary, I suggest that the recgnitin paradigm may be an apprpriate way t study the perceptins derived frm multiple eye fixatins. Cnclusins The present experiments shw that size and shape cannt be perceived and remembered as well fr multiple stimuli as they can fr a single stimulus. Increasing the number f stimuli frm ne t fur dubles the difference threshld fr discriminating these attributes. vidence frm several such sesize experiments discnfirms accunts in which the setsize effect is due t sensry r decisin prcesses and supprts accunts in which the effect is due t attentin. Thus, althugh sme tasks such as visual search demnstrate great capacity in specialized prcessing f many stimuli, the recgnitin task studied here shws that the prcessing f perceptin and memry tgether is sharply limited in its capacity fr the precisin f visual attributes. This limit n hw much visual infrmatin is remembered frm a brief presentatin suggests a similar cnstraint n hw much visual infrmatin is remembered frm eye fixatin t fixatin.

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