Memory & Cognition1978, Vol. 6 (4) 446-453

Attention demands of visual search

GORDON D. LOGANErinda/e College, University of Toronto, Mississauga, Ontario, Canada L5L 1C6

The relation between attention demand and the number of items in the array (array size)was investigated by engaging subjects in a primary search task and measuring spare capacityat different points in time, with a secondary tone task that occurred randomly on half of thetrials. The major variables in both tasks were array size (4, 8, or 12 letters) and stimulus onsetasynchrony (SOA: -400, -200,0,200,400, and 600 msec). Subjects were able to perform thetasks quite independently, and most of the interference that resulted from nonindependenceappeared in tone-task performance. The amount of interference (i.e., maximum tone reactiontime) was independent of array size, but the duration of interference (i.e., the number of SOAsat which tone reaction time was elevated) increased with array size. The findings were inter­preted as supporting unlimited-capacity models of visual search performance.

When a person's attention is engaged in searchingfor a target in a. visual array, to what extent are theattention demands of searching determined by thenumber of items in the array (array size)? This questionhas stimulated thought and research for several years(for a review, see Smith & Spoehr, 1974), yet remainsunanswered. The earlier efforts have made it clear,however, that more is required than a simple accountof the observed increase in reaction time and errorrate with array size. Assuming that attention demandsincrease with array size can lead one to predict thesame increase in reaction time and error rate as assumingthey do not. Moreover, assuming the items are processedsimultaneously, in parallel, can lead to the samepredicted array-size effect as assuming items areprocessed one at a time, in series. These points havebeen demonstrated formally by Taylor (1976) andTownsend (1974), leaving the search literature in astate of seemingly permanent uncertainty:

The present paper adopted a different strategyfor measuring attention demands, motivated bytechnical advances in the attention literature. Theidea was to vary attention demands and array sizeindependently by engaging people in a demandingconcurrent task while searching. The relation betweenattention demand and array size may then be revealedby changes in the array-size effect in search performancecorresponding to changes in the attention demands ofthe concurrent task, or by the effect of array size itselfon performance in the concurrent task, or both. If largerarrays do demand more attention, they should suffer

This research was supported in part by Grant AO 127 fromthe National Research Council of Canada to Albert S. Bregmanat McGill University. I would like to thank Jane Zbrodoff,Alan Quapick, Morris Moscovitch, and Bruce Schneider forcomments on the manuscript. Requests for reprints may beaddressed to Gordon D. Logan, Department of Psychology,Erindale College, University of Toronto, Mississauga, Ontario,Canada L5L IC6.

more interference from concurrent activity and interferemore with the concurrent task (for a full development ofthis argument, see Logan, 1978). Using this technique,predictions may be developed to distinguish the fourclasses of models that predict identical array-size effects.

Interference between tasks will be stronger the morethe demands on attentional capacity exceed the supply.Since people are flexible in their allocation of capacity,able to change it in response to instructions or expectedvalue (e.g., Shulman & Fisher, 1972), it is convenientto designate one of the tasks as primary, so that italways receives sufficient attention for optimalperformance, and the other as secondary, so that it mayonly draw on spare capacity left over from the primarytask (Kahneman, 1973; Posner & Boies, 1971). Underthese conditions, the effects of concurrent activity aremost prominent in the secondary task. Moreover,predictions derived with search as the secondary taskshould converge on predictions derived with search asthe primary task.

First, consider changes in the array-size effect whensearch is the secondary task. Limited-capacity parallelmodels must predict a larger array-size effect withconcurrent activity than without. They rest on theassumption that all items are processed simultaneouslyand draw on attentional capacity simultaneously, sothat attention demands increase with array size.Assuming further that the speed and accuracy ofprocessing the target are reduced in proportion to theload on capacity, these models predict the observedarray-size effect (Atkinson, Holmgren, & Juola, 1969;Nickerson, 1972; Rumelhart, 1970). When capacity isconsumed by concurrent activity, proportionately lesscapacity is available for processing each item, so reactiontime and error rate should increase further in proportionto array size. This prediction is illustrated graphicallyin Figure lA.

Unlimited-capacity parallel models predict no changein the array-size effect with concurrent activity. Items

446

ATTENTION DEMANDS OF SEARCH 447

~..... ~

~ ~ ~ /;;;:/ ~

Figure 1. Possible outcomes in concurrent-task searchexperiments. (Panels A and B represent search-task data whensearch is the secondary task. Reaction time and array size arethe coordinates; the top lines represent concurrent-activity trials,the bottom lines, single-task trials. In A, attention demandsincrease with array size; in B, attention demands are constantfor all array sizes. Panels C, D, and E represent secondary-taskdata when search is the primary task. Reaction time and stimulusonset asynchrony are the coordinates; solid lines = 4-letterarrays; broken lines =8..Jetter arrays; dotted lines =l2-letterarrays. The contours need not peak at a point nor increase anddecrease linearly around the peak; these aspects of Panels C,D, and E are for graphic convenience. The models predict onlymonotonic increases and decreases that are gradual ratherthan abrupt to account for statistical variation in the durationof attention demand. In C, the amount and duration of attentiondemand increases with array size; in D, the amount and durationof attention demand are constant for all array sizes; in E, theamount of attention demand is constant, but the durationincreases with array size.)

are assumed to be processed simultaneously, but withoutdrawing attentional capacity. Each item is thought toadd noise to a decision process, and since speed andaccuracy of processing the target are reduced inproportion to the total amount of noise, the array-sizeeffect is predicted (Estes, 1972; Gardner, 1973; Shiffrin& Geisler, 1973). Since the processes underlying thearray-size effect do not demand attention, concurrentactivity cannot change the array-size effect, althoughit may increase reaction time by a constant amountfor all array sizes, as illustrated in Figure 1B.

Serial models predict the array-size effect byassuming that items are processed one at a time, so thatprocessing time (and thus reaction time) must increasewith array size. Limited-capacity serial models assumethat processing each item requires attention (e.g.,Shiffrin & Schneider, 1977), so that attention demandsincrease with array size. When available capacity isreduced by concurrent activity, each item will requiremore time to be processed, so that the array-size effectwill become stronger, as in Figure 1A.

Unlimited-capacity serial models assume thatprocessing each item does not require attention;attention demands should be constant for all array sizes,so the array-size effect should not change withconcurrent activity, as in Figure 1B. However, serialprocessing must require a certain amount of book­keeping, at least the system must determine when it

AS

UPUP;USLS

LS;US

Possible Outcomes

A+D A+E B+C B+D B+EA+CAssumptions

No Bookkeeping LPBookkeeping LP;LS;US

Note-Columns represent all possible combinations of outcomesin primary- and secondary-task search data. A, B, C. D, and Erefer to outcomes illustrated in Figure 1. The entries representthe models predicting the outcomes; L = limited capacity;U = unlimited capacity: S = serial; P = parallel.

has finished processing the current item and which itemto process next, and it is possible that this bookkeepingrequires attention.

With this assumption, unlimited-eapacity serialmodels would predict a larger array-size effect withconcurrent activity, as in Figure lA, since the number ofbookkeeping operations would increase with array size.Note that this assumption does not change thepredictions of the other models: In parallel models,the amount of bookkeeping required is independentof array size, so the predicted effects would not change.Serial limited-capacity models already predict a largerarray-size effect with concurrent activity; bookkeepingwould enhance the effect, but the data should still looklike Figure IA.

I have reported a series of experiments in which visualsearch was the secondary task, performed in theretention interval of a primary short-term memorytask (Logan, 1976, 1978). In all experiments, aconcurrent memory load increased reaction time,but the array-size effect remained unchanged; theresults resembled Figure IB (also see Logan, 1976,Experiment 2). These findings reduce the field ofavailable models, supporting unlimited-capacity parallelmodels and the unlimited-capacity serial models thatassume no bookkeeping (see Table 1).

The present study was designed to reduce the fieldfurther. Visual search was the primary task, so that theattention demands associated with array size wouldbe revealed most prominently in secondary-taskperformance. People were engaged in a visual searchtask in which they determined whether an array of4, 8, or 12 letters contained an A or a V. At the sametime, they performed a secondary, simple reaction timetask, responding to a tone presented at one of sixstimulus onset asynchronies (SOAs) defined relativeto the onset of the array. Under these conditions, thefunction relating secondary-task performance to SOAdefines, for the primary task, a "contour" of attentiondemand over time, which may be used to comparemomentary demands of the same task at differentpoints in time, or to compare the demands of differentversions of the primary task. This procedure andrationale was first used by Posner and Boies (1971)

Table 1Predictions with Search as the Primary Task

and the Secondary Task

SOASOA

"I!XX\" "11'\'\'\ eL.L.:~ / ~

AS

SOA

~. c

~ E~······....Y~

448 LOGAN

and has since gained wide currency (e.g., Comstock,1973, 1975; Ells, 1973; Millar, 1975; Posner & Klein,1973; Proctor & Fisicaro, 1977; Shwartz, 1976).

In the present study, the range of SOA extendedfrom -400 to 600 msec, Pilot data had suggestedthat this range would capture the onset and offset ofattention to the search task, so that a complete contourof attention demand could be obtained for each arraysize. Two aspects of the contour, its height and breadth"are important, as they represent, respectively, themagnitude and duration of the attention demands ofsearching.

Again, predictions may be developed for each of thefour models: Limited-capacity parallel models predictcontours that are higher and broader the larger the array,reflecting, respectively, the greater momentary demandsof the larger arrays and the longer time spent in activeattention to the array to meet the greater demand.The predicted contours are illustrated in Figure 1C.

Unlimited-capacity parallel models predict contoursequal in height and breadth for each array size, sincethe attention demands of searching do not increasewith array size and search need not require attentionuntil the target has been determined, after which theattention-demanding processes should be equal induration for each array size. Because it will take moretime to determine the target in a large array, searchwill begin to demand attention later, and the peak ofthe contour should appear later in time, further to theright on the SOA axis. These contours are illustratedin Figure lD. It is possible, however, that the onsetof the array might evoke attention-demanding processesother than those designed to determine which targetwas presented (i.e., the bookkeeping processesmentioned earlier). Perhaps the normal responsetendencies of the visual system must be changedtemporarily to best discriminate the targets; themaintenance of such a set might constitute attention­demanding bookkeeping (Logan, 1978). Similarly,the response tendencies of the hands might be altereddynamically (since people do not ordinarily pressbuttons when they see letters), and the maintenanceof the new set might require capacity (Klapp, 1976).These processes would begin to demand attention oncethe array appeared and would continue to do so until aresponse was made. The time to respond depends on theduration of the unlimited-capacity target-determiningprocess which, in turn, depends on array size. Thus,the duration of attention demand would necessarilyincrease with array size, although the amount demandedwould not. The predicted contours, assuming book­keeping, appear in Figure 1E. Note that the bookkeepingassumption does not change the predictions of limited­capacity parallel models, since they already predictthat the duration of attention demand should increasewith array size.

Limited-capacity serial models predict contoursequal in height, with breadth increasing with array

size because momentary demands are constant acrossarray size (since only one item is processed at a time),yet more time must be spent attending to the array(processing items) the larger the array. The predictedcontours are illustrated in Figure IE. The predictionsmayor may not be changed by assuming bookkeeping,depending on the nature of the assumed bookkeeping.Minimally, the system must be able to determine whenit has finished processing the current item (so the nextitem can be selected) and to select the next one. Serialscanning theory holds that scanning is efficient in thatitems are only processed once (see Nickerson, 1972;Sternberg, 1975), and this imposes further constraintson bookkeeping. The items selected may be kept trackof dynamically, perhaps by remembering the ones thathave been selected (or equivalently, the ones that havenot). In this case, momentary attention demands wouldincrease with array size, and performance wouldresemble Figure 1C. Alternatively, the data structurein which the items are held might be exploited so thatit keeps track of the items that have and have not beenselected; selection might be based on some localproperty of the data structure that permits exhaustivesampling without replacement. For example, a circulararray of letters has a ring-like structure that may besampled exhaustively by iteratively selecting the nextitem clockwise from the current one. In this case, thephysical array provides the organization-the spatialstructure of the world constrains the activity of theperceptual system-and attention demands would beconstant across array size. Performance would resembleFigure IE.

Unlimited-capacity serial models predict contoursequal in height and breadth, as in Figure ID, sinceneither the amount nor the duration of attentiondemand vary with array size. Assuming bookkeepingthat concerns only the current item and the next one tobe processed, performance would resemble Figure IE.Assuming bookkeeping that concerns all unprocesseditems, performance would resemble Figure 1C.

It is important to consider these predictions ofsecondary-task performance when search is the primarytask in combination with the earlier predictions ofsearch performance when search was the secondary task.The two sets of predictions converge on the modelsand their assumptions; models may stand or fallon theirability to predict performance in both situations. Thepredicted combinations are summarized in Table 1,where columns represent possible combinations ofoutcomes with search as the primary and the secondarytask, the rows indicate whether or not bookkeepingis assumed, and the entries represent the models thatpredict the outcomes given the assumptions. Previousdata with search as the secondary task have shown thatthe array-size effect does not change with concurrentactivity, as in Figure IB (Logan, 1976, 1978). Thisrestricts the set of possible models to unlimited-capacityserial models that assume no bookkeeping and

unlimited-capacity parallel models that mayor maynot assume bookkeeping. From Table 1, the possibleoutcomes in the present experiment where search isthe primary task are (1) contours equal in height andbreadth for all array sizes (Figure lD), supportingunlimited-capacity serial and parallel models that assumeno bookkeeping, and (2) contours equal in height withbreadth increasing with array size (Figure IE),supporting unlimited-capacity parallel models thatassume bookkeeping. The first outcome would answerthe question that began this paper; it would indicatethat attention demands do not increase with array size.The second outcome would support one model uniquelyand suggest the importance of bookkeeping processes.

Finally, the procedure allowed an estimate of theeffects of concurrent activity on search performance.Since the tone for the concurrent task was presentedon only half of the trials, the difference between searchperformance on tone and no-tone trials may also revealthe attention demands of searching. If it is, indeed,appropriate to apply the previous results with searchas the secondary task to the present situation, oneshould expect that responding to the tone would notincrease the array-size effect. This prediction is, ofcourse, weakened because search was the primary task.Nevertheless, a larger array-size effect with concurrentactivity would be most informative.

METHOD

SubjectsTwelve graduate and undergraduate students and laboratory

staff from McGill University served as subjects. Four were maleand eight were female. None reported any perceptual defect,visual or auditory, and each was paid for participating in fourI-h sessions.

Apparatus and StimuliThe visual stimuli were arrays containing 4, 8, or 12 different

letters equally spaced around an imaginary circle centered onthe fixation point (see Logan, 1978, Figure 5). Each arraycontained one target letter, an A or a V. Each array size wasrepresented by 48 different arrays in which each target letterappeared in each position equally often. The same was true foreach nontarget letter (all remaining letters except Q), withinsampling limitations. The arrays were made from black upper­case Letraset (717) mounted on white cards. The exposureof the array was preceded and followed by a fixation fieldcontaining a small black dot in the center of a white field.

The stimuli were exposed in a Gerbrands three-fieldtachistoscope (Model T-3B-l) with a viewing distance of 80 ern.At this distance, each letter subtended about 26 by 26 min ofvisual angle, and the diameter of the imaginary circle on whichthe letters were placed subtended about 4 deg of visual angle.The luminance of fixation and array fields was matched at8 fL; during testing the room was dimly lit by a 40-W bulb. Eachday, 5 min were allowed for dark adaptation before testingbegan.

The auditory stimulus was a 1,000·Hz sine tone producedby an Electronic Institute tone generator (Model 377) andpresented binaural1y through headphones (Koss pro/4AA) ata comfortable listening level. The events on a trial began withthe closure of a switch, which initiated both the timer associatedwith the tachistoscope and a set of Hunter timers (Model 111-(',

ATTENTION DEMANDS OF SEARCH 449

Series D) that control1ed SOA and the duration of the tone.The array appeared in the tachistoscope 400 msec after theswitch closed. It remained on for 600 msec. The tone waspresented for 500 msec at one of six SOAs, which ranged from-400 to 600 msec in 200-msec steps (positive values of SOAindicate that the tone fol1owed the onset of the array).

Thus, the onset of the earliest tone immediately followedthe closure of the switch, and the onset of the latest tonecoincided with the termination of the array.

The tone was presented on half of the trials. Trial-to-trialvariation in SOA required that the Hunter timers controJlingSOA be reset before each trial. Because the adjustment wasaudible to the subjects, the timers were also reset before trialson which the tone was withheld. On those trials, the circuitfrom the tone generator to the headphones was broken by theoperation of a silent switch.

In the search task, reaction time was measured from theonset of the array, using a digital timer. The timer began withthe onset of the array, and stopped when the subject pressedone of two bu ttons mounted on a panel placed in front of himor her. Pressing each button also illuminated a separate light sothat response accuracy could be monitored. In the tone task,reaction time was measured from the onset of the tone by asimilar digital timer that started with the onset of the toneand stopped when the subject pressed a third button. Allreaction times were measured in milliseconds.

ProcedureEach trial began with a verbal ready signal from the

experimenter ("ready?"), to which the subject responded"yes" if he or she had the fixation point in sharp focus. About.5 sec later, the experimenter closed the switch that initiatedthe events of the trial in the manner described above. Sincethe subjects could hear the click of the switch, it served as awarning signal, occurring reliably 400 msec before the onset ofthe array.

Each day, each subject completed 144 trials in four blocksof 36 trials. Each array size and target letter occurred equallyoften in each block. A tone occurred on half of the trials in eachblock, such that each SOA was paired once per block with eacharray size. Within these constraints, the order of conditions wasrandomized. One order of 144 trials was constructed, and itand its inverse were used throughout the experiment. Eachsubject alternated between the two orders day by day, halfof the subjects beginning with one order (i.e., ABAB), halfbeginning with the other (i.e., BABA).

Subjects were told to rest the middle and index fingersof their right hands on the two response buttons for the searchtask. They were told to press the left button with their indexfinger if the array contained an A, and the right button withtheir middle finger if it contained a V. To the left of thesetwo buttons was the response button for the tone task. Subjectswere told to rest the index finger of their left hand upon it,and to press it immediately when they heard a tone.

Before testing began, subjects saw and heard examples ofthe stimuli, and had the events on a typical trial described tothem in detail. The search task was defined as primary in that(1) after each trial subjects were told their reaction time andaccuracy in the search task, but not in the tone task, (2) thesearch task occurred reliably on every trial, while the tone taskoccurred randomly on half of the trials, and (3) subjects weretold that the search task was the more important of the two,and that they should concentrate on it, responding as quicklyand accurately as possible. They were told to respond quicklyin the tone task as well, but speed was not strongly emphasizedas it was in the search task. The subjects were told to respondto the tasks as independently as possible, and in particular,to avoid response-grouping strategies such as responding to thetwo tasks simultaneously on each trial. Each subject completedfour l-h sessions on successive days. No more than 2 days

450 LOGAN

-400 -200 0 200 400 600 0 200 400 600 800

RESULTS

elapsed between consecutive sessions. After the first session,the instructions were reviewed briefly during the dark-adaptationperiod to insure that the subjects still remembered them.

Figure 2. Mean reaction time in the tone task as a functionof stimulus onset asynchrony (panel A) and the time at whichthe response to the tone occurred (panel B). (Array size is theparameter; solid lines = 4-letter arrays; broken lines = 8-letterarrays; dotted lines = 12-1etter arrays. The vertical lines inPanel B represent mean search reaction times, across SOA,for trials on which the tone was presented.)

The Search TaskMean reaction times from concurrent-task trials

are plotted as a function of SOA in Figure 3. Each pointon the function for each array size is based on 144observations. Single points to the right of the functionsrepresent mean reaction times from no-tone trials. Eachof these points is based on 864 observations.

Performance in the search task was strongly affectedby array size [F(2,22) = 60.289, p < .001]. Reactiontimes increased monotonically with array size at eachSOA, and in the no-tone trials. However, SOA and theinteraction between SOA and array size also hadsignificant effects [F(5,55) =7.292, p < .001, andF(10,110) =2.937, p < .003, respectively]. This isdisturbing, since the interpretation of secondary-taskdata is clearest when the secondary task has no effecton primary-task performance (Kantowitz, 1974). But

responses to the array. Responses to tones presented200 msec before the array fmished some 400 msecafter the array began. Even with no interference, thefastest possible response to these tones (estimated fromthe fastest observed reaction time) would have finishedsome 120 msec after the array began. In either case,there is sufficient temporal overlap in the responsesto the tasks to have produced dual-task interference;one can feel confident that tone-task interferenceresulted from processing the array.

The temporal relation between secondary-taskinterference and primary-task events has not beenambiguous in previous studies because the intervalsbetween primary-task events have been large relativeto secondary-task reaction times (e.g., Posner & Boies,1971). Thus, either plot would lead to the sameconclusions.

Inspecting Panel A, it is clear that performancewas strongly influenced by SOA [F(5 ,55) =30.131,p < .001] . Reaction time increased from the -400-msecSOA to the -200-msec SOA, reached a peak betweenSOAs of -200 and 0 msec, and declined thereafter.The contours for each array size differed systematicallyfrom each other, as indicated by the significant effectof array size [F(2,22) = 14.214, P < .001] and itsinteraction with SOA [F(IO,IlO) = 5.242, P < .001].The contours for each array size rose together andreached a peak at the same height (maximum reactiontimes were 607, 595, and 609 msec for 4-, 8-, and12-1etter arrays, respectively), but declined separatelysuch that the breadth of contour increased with arraysize. This suggests that the amount of attentiondemanded by the search task was independent of arraysize, but the duration of attention demand was not.It tended to increase with array size.

Errors were relatively rare in the tone task (meanproportion = .021), and virtually all of them weremisses. The proportion of errors for each array size andSOA appear in Table 2.

Response Time (rnsec}Stimulus Onset Asynchrony (rnsec)

A B,

~..-. 1-..

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~

.. , . I ,array . I . I array

Data AnalysisEach day, each subject completed four concurrent-task trials

at each combination of array size and SOA. The mean reactiontime in each combination was computed for each subject forboth the search task and the tone task. Each day, each subjectcompleted 24 single-task trials at each array size in the searchtask, and mean reaction times were computed there as well.The first session was considered practice, and only data fromthe last three sessions were analyzed. Since previous studies withthe same stimuli had shown that most of the improvementwith practice occurred between the first and second sessions,each subject's data were averaged over the last three sessions,and these scores were submitted to analysis of variance.

u8DO~S~600,::c.~400

oa:

200

The Tone TaskMean reaction times across subjects and days are

displayed in Figure 2. Each point in the figure is basedon 144 observations. Panel A presents the data plottedconventionally as a function of the time at which thetone was presented (SOA), whereas Panel B representsthe same data plotted as a function of the time at whichthe response to the tone occurred. The two plots arepresented because each misrepresents the temporalrelation between maximal interference and the onsetof the array. Panel A suggests that maximal interferenceoccurred before the onset of the array; Panel B suggestsit occurred around the termination of the array, aboutthe same time as a response occurred in the search task(vertical lines). This ambiguity arises because themeasure of interference is itself an interval of time,extending from the onset of the tone to the completionof the buttonpress response. Interference cannot berepresented as a point on the SOA axis because it itselfextends along the SOA axis. Thus, corresponding pointsin the two plots represent the ends of intervals duringwhich the tone task was subject to interference. It isclear from the two plots that the tone responses showingmaximal interference overlapped in time with the

ATTENTION DEMANDS OF SEARCH 451

Table 2The Proportion of Errors in the Tone Task, the Interresponse Intervals in Milliseconds, and

the Proportion of Errors in the Search Task, Each as a Function of SOA and Array Size

ArrayStimulus Onset Asynchrony

Measure Size -400 -200 0 200 400 600

4 .007 .007 .014 .007 .035 .021Errors (Tone Task) 8 .007 .014 .007 .035 .063 .042

12 .000 .007 .014 .035 .028 .035

4 -488 -163 - 27 90 223 476Interresponse Interval 8 -544 -287 - 81 35 167 338

12 -619 -364 -110 13 128 322

4 .104 .049 .021 .014 .049 .049Errors (Search Task) 8 .083 .076 .104 .063 .049 .035

12 .167 .188 .146 .118 .118 .076

Tone and Search Tasks TogetherSubjects were instructed to perform the two tasks

independently, and if they could not, to protect theprimary search task so that the ensuing interference

Figure 3. Mean search reaction time for trials on which atone was presented as a function of stimulus onset asynchrony.(Array size is the parameter; solid lines> 4-letter arrays; brokenlines =8-letter arrays; dotted lines =12-letter arrays. Singlepoints to the right of each function represent the correspondingmean reaction times from search trials on which the tone waswithheld.)

since the SOA effects on search performance wereneither large nor regular enough to yield a consistentinterpretation, it may be most reasonable to regardthem as noise.

This interpretation is supported somewhat by theoverall similarity of performance on tone and no-tonetrials. For tone trials, the mean reaction times (acrossSOA) for 4-, 8-, and l2-letter arrays were 532, 627,and 701 msec, respectively. The corresponding meansfrom no-tone trials were 524, 626, and 718 msec. Atno SOA was the array-size effect larger than the oneobserved on no-tone trials. Thus, there is no evidencethat performing the tone task while searching increasedsearch reaction time relative to no-tone trials by anamount proportional to array size.

The proportion of errors for tone trials in the searchtask appear in Table 2, representing each combinationof array size and SOA conditions. The proportion oferrors for no-tone search trials was .057, .056, and .119for 4-, 8-, and l2-letter arrays, respectively.

Stimulus Onset Asynchrony (msec)

would only be apparent in performance on thesecondary tone task. The significant main effect of SOAin the analysis of the tone data suggests that subjectswere not able to handle the tasks independently, andthe significant main effect of SOA and its interactionwith array size in the search data suggests that theywere not able to restrict the ensuing interference to thesecondary task. The purpose of this section is to reportmeasures of the relative strength of these effects. Thismay be done in two ways: (1) by comparing variancecomponents associated with main effects and inter­actions in the two separate analyses of the tasks, and(2) by examining trends and variance components in ananalysis of the interval between responses to the twotasks (interresponse interval, hereafter, IRI).

Variance components. The variance componentsassociated with each main effect and interaction in thetwo tasks were computed following the method ofVaughan and Corballis (1969) and appear in Table 3.

If subjects had been able to restrict concurrent-taskinterference to tone-task performance, the variancecomponents associated with SOA and with the inter­action between SOA and array size should be substantialin the tone task but negligible in the search task. Fromthe estimates in Table 3, it is clear that this was the case.The variance component associated with SOA wasabout 12 times larger in the tone task than in the searchtask, and the component associated with the interactionwas about twice as large. It would appear that, for themost part, subjects were able to protect the search taskas instructed.

Interresponse intervals. Following Kahneman (I973),IRIs were computed by applying the formula,IRI = Tone RT + SOA - Search RT, to the meanreaction times in each combination of array size andSOA conditions for each subject. The means acrosssubjects appear in Table 2. and the variance componentsfrom an analysis of variance on the IRI data appear inTable 3 (both main effects and the interaction weresignificant, p < .003).

If subjects had been able to perform the two tasksindependently, IRI should be a linear function of SOA

notone

,array _ L ....._ .....o 200 400 600

.···················~·····.··········· .. ·········..•12

.,,-.--""""-- '____-8--' "-----....----I. ' ,-400 -200

u~ 8005<lJ

~ 600cog 400<lJ

cr:

452 LOGAN

DISCUSSION

Table 3Variance Components of the Effects of Array Size (AS)

SOA,and Their Interaction in the Tone T-ask,the Search Task, and the JRI Analysis

This paper began by asking to what extent theattention demands of searching are determined by arraysize. An answer to this question was obtained by havingpeople respond to tones presented randomly at differentSOAs while they were engaged in searching arrays ofdifferent sizes for the presence of an A or a V. Thedata suggest that the people were able to perform thetwo tasks independently for the most part, and that theywere able to restrict most of the interference resultingfrom concurrent performance to the secondary tonetask. The small amount of interference observed in theprimary search task was not easily interpretable andperhaps should be regarded as noise. Given thesefindings, the functions relating tone reaction timeto SOA may be interpreted as measures of the amountand duration of the attention demands of searching.

with a slope of one (i.e., adding 100 msec to SOAwould add 100 msec to IRI). If, on the other hand,subjects could not perform the two tasks together, IRIshould be constant, independent of SOA, particularlyat short SOAs where interference is typically strongest(see Kantowitz, 1974). If either response was lengthenedat the shorter SOAs, the function relating IRI to SOAwould flatten. Indeed, if one response were to becomecompletely refractory, the (local) slope of the functionwould become zero. Since the range of SOA in thepresent experiment captured the beginning and end ofinterference, this local flattening should appear in themiddle of the function, with the ends linear with unitslope. Thus, independent performance on the two taskswould be seen as a linear trend in the IRI data, whereasinterference or dependent performance would be seenas a cubic trend (for a similar argument, see Kahneman,1973, Chapter 9).

Only the linear and cubic trends were significantin the analysis [F(1,55) = 517.944, p<.OOI, andF(1 ,55) =6.164, P < .050, respectively]. The linearwas the stronger of the two, accounting for 98% of thevariance component due to SOA, while the cubic trendaccounted for 1%. It appears that, although subjectsdid experience some interference when performing thetwo tasks concurrently, they were able to perform themquite independently.

The data (see Figure 2) Clearly indicate that the amountof attention demanded was the same for each array size,but the duration of attention demand increased witharray size. Thus, the initial question is answered.

The answer, combined with previous data obtainedwith search as the secondary task, may reduce thefield of possible models to one, the unlimited-capacityparallel models that assume bookkeeping. By themselves,the data from the present tone task are consistentwith (1) limited-capacity serial models with andwithout bookkeeping assumptions, (2) unlimited­capacity serial models with bookkeeping assumptions,and (3) unlimited-capacity parallel models withbookkeeping assumptions. These models predict theobserved constant attention demands, which werelonger in duration with larger arrays. By themselves,the previous data with search as the secondary task(Logan, 1976, 1978), and indeed, the present searchdata support (1) unlimited-capacity serial modelswithout bookkeeping assumptions and (2) unlimited­capacity parallel models with and without bookkeepingassumptions. These models predict the observedconstancy of the array-size effect under varyingconditions of attention. The two sets of data togetherare more consistent with the unlimited-capacity parallelmodels that assume bookkeeping than with any othermodel, as only they predicted observed combinationof outcomes (see Table 1).

The possible nature of bookkeeping processes invitesspeculation. In serial models, some bookkeepingprocesses are obvious-those keeping track of the serialcomparison process. In the favored parallel models,bookkeeping might involve maintaining a set todiscriminate the targets (Logan, 1976, 1978) and main­taining the appropriate responses in a state of readiness(Klapp, 1976). More generally, one might expect thatthe momentary organization and coordination ofcognitive resources sufficient to perform the task woulddemand attention. Many of the resources called upon inlaboratory tasks have been practiced extensively in othercontexts and might function automatically, at least infamiliar contexts. What is new in the laboratorysituation is the constellation of resources required forperformance, and this constellation might not beautomatized (i.e., people know how to recognize lettersand how to push buttons; what they must learn is topush buttons in response to letters). In search tasks,then, the sets to discriminate and respond must beprepared and maintained by attending. Since preparationis the same for all array sizes, the amount of attentiondemanded should be independent of array size.However, the duration of attention demand shouldincrease with array size: The set to discriminate andrespond must be maintained until a response occurs,so the duration of attention demand will depend onreaction time. Since reaction time is determined byautomatic letter-recognition processes whose duration

199.835411.264277.264

ASx SOA

Effect

SOA

591.3417,030.866

90,097.817

4,724.824386.456

2,552.970

ASAnalysis

Search TaskTone TaskInterresponse Interval

increases with array size, the duration of attentiondemand depends, albeit indirectly, on the number ofitems in the array.

This interpretation illustrates a recent view ofcognitive resource allocation that holds that theattention demands of performance are determinedprimarily by control processes that organize andcoordinate the more elementary processes that actuallydeal with information (e.g., Logan, 1978; Newell, 1973;Posner & Snyder, 1975). From this view, controlprocesses organize the elementary processes in responseto instructions or intentions to produce behaviorappropriate to the situation. The elementary processesare relatively permanent residents of the mind and nolonger require attention to be maintained. Theirorganization, however, is transitory, designed only tomeet the needs of the moment, and so must be achievedand maintained by attending judiciously. A majorempirical implication is that attention demands aredetermined by the control processes, not by theelementary processes they coordinate, nor even theinformation being processed. The present study, infinding no relation between attention demand and theamount to be processed (i.e., array size), is consistentwith this general view. A major theoretical implicationis that the problem of control must be taken seriously.Previous efforts have focused on processes in isolationor in some particular task environment. While this workis important, it ignores or deemphasizes the possibilitythat one process can serve many goals, and does little tospecify the procedures by which processes are selectedand combined to cope with new task environments.It is known from practical experience that humancognition is tremendously versatile; human subjectscan perform virtually any task asked of them, oftenon a moment's notice. Perhaps by examining theprocesses of attentional control more directly than hasbeen done in the past, psychologists will come tounderstand such versatility.

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(Received for publication November 15.1977;accepted March 28,1978.)