Perception & Psychophysics1975, Vol. 18(6}, 379-388

Memory and display searchin binary classification reaction time

PETER HOWELLUniversity College London, Gower Street, London, W. C.l. England

and

JANET E. STOCKDALELondon School ofEconomics and Political Science. London, England

Character classification tasks and "same"-"different" judgments of letter strings were examined withreference to major experimental findings and the models proposed to explain them. An experiment isreported which was designed to investigate similarities between these two paradigms. The subject's taskwas to scan a display and decide whether all the items in the display belonged to a criterion set; thelocation of the items in the display was irrelevant to the decision. Two classes of model were considered.First, for models in which display encoding time increases as a function of the number of items on display.an exhaustive-memory/exhaustive-display model offered a reasonable explanation of the data. Second.for models in which display encoding time is a constant, examination of the data in terms of thehypothetical number of memory and display comparisons demanded by the task revealed that negativeresponses were lengthened relative to positive responses. A one-processor model which postulates anexhaustive-memory self-terminating display search followed by a rechecking process on those trials inwhich a negative outcome ensues satisfactorily explains the latency and serial position data.

In a recent authoritative review. Nickerson (1972)divides binary-classification experiments into charac­ter classification and "same"·"different" judgmenttasks. The majority of character classification and"same"·"different" experiments use reaction time(RT) as the dependent variable but differ with respectto the decision rule the subject must follow: characterclassification requires a decision as to whether one ormore displayed characters. sometimes termed the testset (TS) and usually alphanumeric. are or are notmembers of a criterion set (CS): "same't-vdifferent"tasks require a decision whether two stimuli are thesame or different with respect to a preselected set ofattributes. The stimuli in the "same't-t'different" taskare usually non alphanumeric. but Bamber (1969) hasreported. an experiment in which the attributes werethe individual alphabetic characters making up astring. An attribute can then take one of two valuesdepending on whether the same or a different itemoccupies a given position in the display. The limitingcase of the character classification task is where boththe CS and the TS contain a single item. This is. then.logically similar to the limiting case of the

Requests for reprints should be sent to Peter Howell. who is nowat the Laboratory of Experimental Psychology. University ofSussex. Brighton BNI9QG. England. This research was supportedin part by a Science Research Council grant to Professor R. J.Audley. and by a grant to the second author from the SocialResearch Division of the London School of Economics. Thanks aredue to E. J. Hammond for programming on-line control of theexperiment and to Professor R. J. Audley, D. J. Caudrey. and Dr.D. J. Powell for comments during the preparation of this paper.

"sarne't-rdifferent' judgments of letter strings [oneletter (or attribute) in the CS which is same ordifferent from the one letter (attribute) in the TS].

The hypotheses usually offered to explain theresults of these two types of experiment are the foursearch models resulting from the possiblecombinations of the two conceptual contrasts serial orparallel and exhaustive or self- terminating. Serial orparallel refers to whether memory representations ofcharacters or attributes are compared with theprocessed TS one at a time or simultaneously.Exhaustive or self-terminating refers to whether allpossible comparisons of the encoded representation ofthe CS with the processed TS are made. or only asmany as are needed to enable a decision to be made.

Character classification experiments have. in themain, employed the Sternberg paradigm. Accordingto this paradigm. a set of elements is selectedarbitrarily from a detined stimulus ensemble andconstitutes the CS or positive set which is presented asa list for the subject to memorize. 'The size of thepositive set may be varied and defines the memoryload (M) imposed on the subject. On each trial. asingle TS is presented and the subject's task is tomake a positive response if this is a member of the CS.or if it is not then to make a negative response.

Typically. character classification results show thatRT increases linearly with M at the same rate forpositive and negative responses, with only an interceptdifference between the two kinds of response. Fromthe linearity of the functions. Sternberg (1966) hasargued for a serial process. and from the equal slopes.

379

380 HOWELL AND STOCKDALE

for an exhaustive scan. since. if the memory scan hadbeen self-terminating. positive trials would haverequired on average only half the comparisonsdemanded by negative trials.

In an extension of the basic character classificationtask. Sternberg (Note 1) presented subjects with fromone to four digits to memorize and then presentedtachistoscopically a linear array of one. two. or threedigits. The subject makes a positive response if the CSand TS have any elements in common and otherwisemakes a negative response. The presence of a positiveset item is. then. sufticient for a decision to be made.To aid our analysis. we define a decision item as onewhose value on the scanned dimension is sufticient toenable classification of that dimension. under optimalsearch conditions. In the modified characterclassification task. a positive item acts as a decisionitem in both memory and display.

For this type of task. Sternberg found that for allTS sizes greater than one. negative RTs increased at afaster rate than positive RTs with increasing length ofthe CS. He considered that these data demonstratedthat. while scanning of the CS is exhaustive for eachitem in the TS. scanning of the TS is self-terminating.This conclusion was supported by a reanalysis of asimilar experiment by Nickerson (1966). Thisinterpretation is not without its difficulties. First. noserial position effects (i.e .. no dependence of RT onposition of the common item in either list) werereported. which may be explained by the additionalassumption of a random order of search in theself-terminating model. and. second. quantitativeestimates of the slopes in the two experiments revealthat the negative slope is not twice the positive slopebut somewhat less than this.

This extension of the paradigm does. however.allow us to develop our analogy between characterclassification and "same"-"different" judgments ofletter strings. Consider first the task which subjectsencou ntered in the Bamber (1969) experiment.Subjects were required to judge whether or not twosuccessively presented horizontal rows of letters.containing equal numbers of letters. were identical(i.e.. contained the same letters in the same order).The length (I) of the letter strings was varied from oneto four items and the number of different items fromone to I. As soon as an item. which was not containedin the CS is processed. a decision can be made. In"same't-vdifferent" judgments. an item present in thedisplay. but absent from memory. acts as a decisionitem.

In the Bamber experiment. a plot of RT as afunction of I revealed a marked upward concavity forsame responses, which was interpreted by Bamber asinconsistent with any model which describes the datain terms of a single search process. "Different"judgments were consistent with a self-terminatingmodel. but "same" responses were faster than

predicted. This "fast-same" phenomenon has beenreported by a number of experimenters who haveemployed multidimensional stimuli in "same"­"different" tasks (see the review by Nickerson. 1972).

These data led Bamber to propose a model in whichtwo stimulus-comparison processors. one fast and theother slow, arc assumed to operate simultaneously.When the CS and TS are the same. the fast processoris able to operate on the basis of the simple identity ofphysical stimulus characteristics. When the twostimulus sets are different. the fast processor is unableto operate and negative responses must rely on theoutput of the slow processor. This model thereforeexplains why the negative RTs arc consistent with aserial sclf-terminating model, but the positiveresponses are faster than predicted. The model wastested in experiments carried ou t by Bamber (1972)and Bamber and Paine (1973). Both experiments weredesigned to eliminate the intervention of the fastprocessor so that both positive and negative responseswould be initiated by the slow processor. For example.Bamber (1972) required subjects to judge whether twoletters. which were always physically different. werenominally the same or different. If it is assumed thatthe fast processor is incapable of making nominalidentity judgments. then both positive and negativeresponses should be consistent with a serialself-terminating model. However. positive responseswere still taster than predicted. implying that the"fast-same" phenomenon is not merely the product ofa physical match. The experiment of Bamber andPaine also failed to dissociate the two processors, andso the results of both experiments cast some doubt onthe validity of the model.

Consideration of character classification tasks and"same"-"diITerent" judgments has led us to devise atask in which the subject searches the TS in order todecide whether or not it contains all the members ofthe CS, the CS and TS being of the same length. Inthis task. the nature of a decision item is the presenceof an item in the display which is absent frommemory. i.e .. the same as in the "same"-"different"judgment task. The proposed task deviates from thetraditional "samc"-"different'· judgment of letterstrings. in that. as in the modified characterclassification task. position of the items will berandomized.

In designing our task. an important proceduraldifference between Sternberg (Note 1) and Bamber(1969) emerges. In the character clas­sification task used by Sternberg (Note 1), therewas a maximum of one decision item in the TS, RTbeing investigated as a function of position of thatitem. In contrast, the "same"·"different" judgmentof letter strings in the Bamber (1969) experimentcould contain from one to I decision items, RT beingexamined as a function of the number of decisionitems. However. in the Bamber experiment. the

number of decision items for a fixed list length isconfounded with the position of these items (i.e .. asthe number of decision items increases. theprobability of encountering a decision item in a givenposition also increases). For this reason. in the presentexperiment, when the TS differed from the CS. it didso with respect to one item only. position of thedecision item being controlled. Stimulus material waschosen so as to avoid possible ordinal position effects.arising from natural sequencing inherent in thestimulus set. Such effects create problems inproviding an adequate model for search tasks. Forexample. there is evidence that search times dependon whether or not items are formed into organized sets(Rosenbaum. 1974).

A major point of interest in the present experimentwill be the nature of the functions fitted to the RTs ofnegative and positive responses. If it is assumed thatinformation in memory is compared with individualdisplayed items, not in a one (memory) to one (dis­play) fashion, as is assumed by "same" -"different"theorists. but by means of an exhaustive orself-terminating comparison for both memory anddisplay. the relation between RT and M would beexpected to be positively accelerating. This would beconsistent with the upward concavity reported inBamber (1969. 1972).

In the experiments of Nickerson (1966) andSternberg (Note 1). Sternberg observed that there is acommon intercept for both positive and negativeresponses as the number of items on display increases.Another feature of these two experiments is thatdisplay and memory comparisons require the sameamount of time (Nickerson. 1972). Assuming thatdisplay encoding time is a constant. our inclusion of acontrol condition in which memory load is varied butdisplay load is constant provides a baseline againstwhich to examine the intercepts and slopes of the RTfunctions for positive and negative responses whenboth memory and display loads are varied.

This approach permits a stage analysis of the"fast-same" phenomenon. Differences in comparisontime between positive and negative responses wouldlead us to conclude that the "fast-same" phenomenonis a feature of the search stage. any other differencesthat it is a feature of one of the other stages involved inc1assitication.

METHOD

SubjectsEight subjects. four male and four female. participated in the

experiment. Each subject was paid a total of £.2 for the two I'/l-hsessions. No practice was given. but all of the eight subjects hadpreviously performed in RT experiments.

Stimulus MaterialsThe stimulus ensemble comprised the eight letter-like shapes

shown in Figure I. The shapes were constructed from the elementsof a 4 by 6 dot matrix. 7 mm in height and varying in width from

MEMORY AND DISPLAY 381

• •• • ••• • •• •••• • ••••• • •••• • •• • • • ••••• •• • • •

•• • •• •• ••••• •• • •• • •• • ••• • •• • • • • •• •• • •• • •••••• • •• •• •

Figure 1. The stimulus ensemble of eight letter-Uke shapes.

6 mm (one character) to 28 mm (four characters). These weredisplayed on a 36-cm osciloscope, which the subject viewed from adistance of approximately 60 cm.

ApparatusThe experiment was run under the control of a POP-12 computer

connected with a Teletype. an oscilloscope. and two pairs ofresponse keys. one set for responding and the other to terminate theCS. Response latencies were measured to an accuracy of 1 msec.

Experimental ConditionsAll subjects received two conditions. One condition (0 = l)

represented a replication of the basic Sternberg character­c1assilication task in which. following the presentation of a CS ofsize M. a single test item is displayed. Under this condition. thememory load. M. was varied but the display load. O. remainedconstant at a single item. The subject's task was to decide whetheror not the single TS was a member of the CS. Under the othercondition (0 = M). both the memory and display loads werepermitted to vary. but on any given trial the display load was alwaysequal to the memory load. In this case. the subject's task was todecide whether the identity of the items in the TS was the same asthose in the CS.

Within each condition. memory loads of 1.2.3. and 4 were used.Under each of the two experimental conditions. subjects received %trials at each of the four memory loads. and of these 50% required apositive and 50"70 a negative response.

DesignEach subject participated in two experimental sessions. The

order of the two conditions. 0 = I and 0 = M. wascounterbalanced across the two sessions. Trials with the samememory load (M = I. 2. 3. and 4) were all grouped together in ablock. and the order of presentation of the four blocks of trialswithin an experimental session were determined by reference to aLatin square in the following way. Each of the four subjectsperforming condition 0 = I in the first session was allocated to oneorder of a Latin square which defined, within the first experimentalsession. the order of presentation of the four blocks of trialsrepresenting the four different memory loads. This square wasreplicated across the four subjects performing condition 0 = M inthe first session. In the second session. subjects were assigned todifferent orders within the Latin square with the constraint that allorders were represented. Four subjects made a positive responsewith their right hands. four subjects with their left hands. and thiswas counterbalanced across order of conditions.

Stimulus SequencesFor the 0 = I condition. a population of M + 4 stimulus

elements was defined prior to a block of trials with a given value ofM. On any trial. the CS was randomly selected from this ensembleand presented as a horizontal display on the computer oscilloscope.The subject was instructed that he could look at this set of stimuli aslong as he wished. In order to terminate the memory display and tocommence the trial. he was to use his thumbs to depress two keyswhich were used for no other purpose in the experiment. Onesecond later. the single TS was displayed. The subject was

382 HOWELL AND STOCKDALE

RESULTS

DISCUSSION

factorial design was performed for positive andnegative responses separately, using data fromindividual subjects. A significant main effect ofM wasfound for both negative (F = 7.3; df = 3,21; P < .01)and positive responses (F = 13.3; df = 3,21;P < .01). Both positive and negative responses weretested for a quadratic component, which was found tobe significant at the 5% (F = 4.7; df = 1,21) and 1%(F = 8.3; df = 1,21) levels, respectively. It is againstthese data that models of the processes underlyingsearch tasks will be evaluated in the discussion.

The data for negative trials under the D = Mcondition were further analyzed by plotting individualRT as a function of the position, Pi of the negativeitem, for each value of M. Examination of theseindividual data revealed that three of the eightsubjects show clear serial position effects. These dataare shown in Figure 3.

Subject 2 (Figure 3a) and Subject 4 (Figure 3c)showed a left-to-right scanning order, with RT fastestfor D = 1 increasing with increases in display load toD = 4. Subject 3 (Figure 3b) appeared to· scanoutwards from a central position of the display, halfthe time in each direction. Thus it is likely that theoverall lack of serial position effects arose from theuse of different strategies across subjects. The lack ofa serial position effect in an individual subject's datamay be explained by a random order of search. Thethree subjects who did exhibit serial position effectsall used their right hands to indicate a positiveresponse. It may be noted that key-to-responseassignment apparently has some strategic importancein uncovering self-terminating search processes. Forexample, Atkinson, Holmgren, and Juola (1969)reported an unpublished study in which differences inRT/ display-size slopes were observed betweensubjects making a negative response on the left and onthe right. These differences in slope have beenrevealed by key positioning and tend towards thepredictions of a self-terminating model.

The data were subjected to an error analysis, anderror rates across the two conditions were comparable(5.4% for D = M and 5.5% for D = 1). Error datadependent on M for the D = M condition are shownin Figure 4. The major features of these data were theincrease in the probability' of a false negativeresponse, i.e .. a negative response when a positiveresponse would be appropriate, with an increase in Mand the greater incidence of false negative over falsepositive responses for values of M > 1.

,I.

1// '

1// '

1/I,'

i'I}'t'

t,.,,1 RT_=567+147(M) a

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Positrve responses 0Negative responses []

0=1:

D=M: Po&rt'ive responses .---eNegative responses .- - __

1000

2000

3000

instructed to decide whether or not the TS was a member of the CSand to respond as quickly and accurately as possible by depressingone of two keys, on which he rested his index fingers, one keysignaling a positive and the other a negative response.

For the D = M condition. a similar procedure was adopted.except that the TS now contained the same number of stimulusitems as displayed in the CS. The test items were displayed inrandom order. and the subject's task was to decide whether theidentity of the items in the TS was the same as those in the CS. Thelocation of the items was irrelevant to this decision. A negative trialwas defined by the presence of a single negative set item, i.e., anitem not previously displayed in the CS. and the frequency withwhich a negative item appeared at each serial position was equatedover the sequence of 96 trials within each memory load. One secondafter the subject's response a new CS was presented and thesequence of events was repeated. At the end of a block of 96 trials.the subject had a break of approximately 10 min.

uI!....0::

::I 0..1.-----,---,.--_---,__----,

The relation between mean correct response latencyand memory load, M, is shown in Figure 2.Considering the D = 1 condition, the results show asignificant linear relation (for positive responses, F =51.6; for negative responses, F =37.1; df = 1,3;P < .01) but no significant quadratic component ineither case. The best fitting straight lines for thepositive and negative responses were approximatelyparallel, the ratio for the slopes of positive to negativeresponses being 1.05. .

For the D = M condition, positive and negativeresponses clearly exhibit deviation from linearity,being concave upward. An analysis of variance for a

Figure 2. Relation between RT and M for poIItive and negativeI'eIpOn_ under the D = 1 and D = M condltlolll. The IUlid line.under the D = 1 condition nprelent the best fitting Itndght linel totbeIe data obtained from eight lubjects.

1Memory load. M

2 3 4

Analysis of the D = 1 ConditionIn the simple character classification task, as we

stated in the introduction, four models are usuallyconsidered. These arise from the combination of thetwo conceptual contrasts, serial or parallel and

3000

2000

1000

MEMORY AND DISPLAY 383

a. Subject 2 • b. Subject 3 c. Subject 4

O;op.y load (0)

/• 0=1 •x 0=2 \/ /.C 0=3

• 0=. .../ ./.:

/0/ ->C _____~

C~

~~ x----" x---

• ••

t-lll:c:.•~

P, Pz P3 P4 PI Pz P3 P4 P1 Pz P3 P4Negative item position

Figure 3. Relation between RT and position, Pb of the negadYe Item under the D = M condition for each value of D, for three individual .subjects.

Figure 4. Probability of falle positive and fa1Ie negativerespon_ as • function of memory load, M, under the D = Mcondition.

plot of RT vs. M for the D = 1 condition gave a linearfunction which Sternberg interpreted as support for aserial scan of memory. Similarly, Atkinson et al.(1969) interpreted their display scan study asconsistent with a serial scan of display. Theseconsiderations eliminate all but the serial-memory/serial-display models. While the linearity of the

exhaustive or self-terminating. The linear relationbetween RT and M observed in this experiment iscongruent with other findings using a similar task. Aspointed out earlier. no significant quadraticcomponent was found. The existence of a negativelyaccelerated quadratic component would haveindicated a logarithmic relation between RT and Mwhich has been reported by some experimenters(Joh nsen & Briggs. 1973). The observed linearitytogether with the comparability of slopes for positiveand negative responses have been interpreted assupport for a serial exhaustive search of the memoryset (Sternberg. 1966).

Analysis of the D = M ConditionExtending the task by requiring classification of

more than one character gives rise to a further set ofmodels for this additional dimension. In order toconsider models for how these characters are scanned,theorists have usually assumed display encoding andmemory comparison do not overlap in time. -If wemake this assumption. no further elaboration of themodels is required and we have the 16 modelsresulting from the combination of the 4 models of thesimple character classification task and the 4 modelsfor the additional dimension in the modified task. Theserial exhaustive-memory/self-terminating-displaysearch model proposed by Sternberg (Note 1) toexplain his data and outlined in the introduction is anexample of one of these models.

In order to simplify consideration of the models. wewill first make the assumption that memory anddisplay scan are serial. This can be justified in that a

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False negatives

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3 4Memory load. M

384 HOWELL AND STOCKDALE

Positive responses:

t 1- > t 2­

t H > t 2+

t 1- > t2­

t 1+ > t 2+

t 1- > t 2-

t 2+ = 2t 2_

t 2+ = t 2_

Predicted Relations Between t1 and t 2

Table 2Predicted Relations Between the Linear (t,) and Quadratic

(t 2 ) Components for Positive (+) and Negative (-) Responses

Model(Memory Search/Display Search)

Exhaustive/ExhaustiveSelf-terminating/ExhaustiveExhaustive/Self-terminating

Self-terminating/Self-terminating

Note- These predictions are derived from models involving serialscanning of both memory and display items, in which displayencoding time increasesas a function of the number of items ondisplay.

as to whether or not individual subjects show adefined or random order of search. When there is adefined order of search. the probabi lity ofencountering a decision item at the tirst to the M-thscanned position is the same since this isexperimentally controlled. With a random order ofsearch. the probability of encountering a decisionitem at the first to the M-th scanned position is againthe same. if order of scan is independent of thedecision item position.

Functions of the form given in Equation 2 weretitted using a polynomial regression technique. forpositive and negative responses separately, givingvalues as follows:

RT = 314.25 + 140.15(M) + 122.75(Mz) (3)

Evaluation of Models for the D = M ConditionInitially, let t 1 be the time to encode an item from

the display and tz be the time to compare an encodedrepresentation against a memorized item.

Assuming serial interrogation of display (D) andmemory (M), a general equation relating RT to D andM can be derived (Equation I).

simple memory and display scan functions has beeninterpreted as support for a serial process, a parallelscanning model may also predict a linear increase inboth positive and negative RT with the task variable(memory or display comparisons), as Atkinson et al.(1969) have shown. It should be noted, however, thatthe model outlined by Atkinson does require anexhaustive scan, and an exhaustive scan of adimension does not permit any definitive conclusionsabout the serial or parallel nature of scanningprocesses for that dimension. For example, the datawhich Sternberg explained in terms of a serial­exhaustive - memory/serial- self-terminating - displaymodel can equally well be explained in terms of aparallel- exhaustive -memory/serial - self-terminating­display model.

where f1(D ) weights the number of items encodedfrom the display for a given value of D, fz(M) weightsthe number of comparisons of the encodedrepresentation against the memorized items for agiven value of M, both of which depend on the type ofresponse and exhaustive or self-terminating nature ofprocessing for the dimension under consideration. Rrepresents the time required to produce a response.

In this experiment. the general equation can beexpanded as a quadratic:

(2) Negative responses:

Table IFunctions for Display and Memory Conceptual Contrasts

The functions for the conceptual contrast(exhaustive vs. self-terminating) are presented inTable I separately for display and memory and forresponse type.

It should be noted that predictions for displayself-terminating models do not require qualification

Self-terminatingNegative

ExhaustivePositiveNegative

Positive

r, (D)

DD

D

D+l

2

MM

M + 1

2

M+l M+l M---+-

2 zrr, D) r, D

RT = 459.00 + 111.20(M) + 109.00(MZ) (4)

Suhstituting into Equation 2 the expressions for Dand M as demanded by the exhaustive andself-terminating cases enables predictions concerningthe relative magnitude of the linear and quadraticcomponents to be derived. These are presented inTable 2.

These predictions are difticult to evaluatestatistically given the Latin square design and theattempt to prove the null hypothesis in some cases.However. among the alternatives, one may supposethat the exhaustive-memory/exhaustive-display mod­el is favored. Thus, t1+ is approximately equal to t 1 ­

and t2+ is approximately equal to t2-. Theexhaustive-exhaustive model is the only one to givethese predictions, as indicated in Table 2. The timetaken for comparing an encoded display item against

MEMORY AND DISPLAY 385

P(false positive)

p(false negative) = I - [1 - (I - p+)M-lp_] M

where M is the number of memory items; P+ is theprobability of a false match when comparing twodifferent items: p. is the probability of a falsemismatch when comparing two matching items.

These expressions are the same for the exhaustiveand self-terminating cases. since the only difference

between exhaustive and self-terminating processing isthat in the former case processing continues aftersufficient information for a response has beenobtained. If P+ = P-, then the error rate is the samefor both response types, but if p_ > P+, the predictederror probabilities show qualitative similarities to thedata. The error data do not allow us to discriminateamong the models.

The exhaustive-memory/ exhaustive-display modelhas difficulties in dealing with serial position effectsand differences in slope between response types andcomparison of the slopes under the D = M andD = 1 conditions. Final rejection of the model willhave to await an experiment in which D > M. wherethe predicted differences in latencies permit moredefinitive conclusions.

Although the weight of the evidence against theexhaustive-exhaustive model is in no way conclusive,we extend our treatment by making the assumption,outlined in the introduction. that display encodingtime is a constant. The implication of this is to makef1(D)t 1 in Equation 2 a constant.

Making this assumption. the positive and negativeresponse data for the D = M condition werereexamined in terms of the number of comparisonsdemanded by the various models. The logic for thisreanalysis is that in the simple character classificationand display scan studies the task variables arememory and display comparisons. respectively. Dataanalysis for these tasks usually proceeds by plottingRT vs. M or D for positive and negative responsesseparately. The form and slope of the resulting plotsare then compared with those predicted by theproposed models. In the present task. going from amemory and display load of M = N to M = N + 1clearly gives an additional display item as well as anadditional memory item. Display and memorycomparisons therefore interact multiplicatively in themodels considered here but possibly with differentweighting factors for the two response types.depending on whether the dimension underconsideration is examined exhaustively or inself-terminating fashion. The predicted number of Dwith M comparisons for each of the alternative modelsmay be computed as the weighting factor for t 2 , i.e.,the value which is formed by the product off1(D) . f2(M) in Equation 2.

Table 3 presents latencies and the predictednumber of comparisons for the various models. If thepositive and negative response latencies are plottedagainst the hypothesized number of D with Mcomparisons. then all four models provide asatisfactory linear fit. This supports a serial process ora parallel model of the type presented by Atkinsonet al. (1969). On the basis of the reanalysis of thedata. the resulting functions for positive and negativeresponses should be parallel; however. in all cases. theslope for positive responses is significantly greater

(6)

(5)

RT = 567 + 147(M)

RT = 479 + 154(M)

Positive responses for D = 1 condition:

Negative responses for D = 1 condition:

a memorized representation (tz) takes 122.75 and109.00 msec/comparison for positive and negativeresponses. respectively. The time to encode displayitems (t 1) takes the values 140.15 and 111.20 msec/item for positive and negative responses.

It is not apparent why positive and negative probesrequire different amounts of time to encode. nor whythere is a difference in comparison time. Thecomparison times could be made congruent byassuming that rechecking takes place on positive trialsinflating the observed comparison time. Thecomparison times show marked discrepancies with theD = 1 condition. If. as has been found. memory anddisplay comparison times are equal (Nickerson.1966). we would expect the comparison times for theD = M and D = 1 conditions to be the same.Comparison times for the D = 1 condition are 154and 147 msec/item, as indicated in Equations 5 and6. This prediction. therefore. is not fulfilled.

If the exhaustive-exhaustive model is favored. then itmust be shown why some subjects exhibit serialposition effects. One possibility is to attribute theeffects to a compatibility artifact. For example.Holmgren (1974) entertained 'he hypothesis thatwhen a decision item is detected on the left side of thedisplay. a left-hand decision response is made fasterthan a right-hand one. with the reverse being truewhen the decision item is on the right of the display. Ifthis were the case in the present task. apparent serialposition effects might arise. However. these would beexpected in different directions for the two keyassignments.

Consideration of the error probabilities shows that.for all four models. the probability of false negativeand false positive responses are given by the followingexpressions (assuming independent comparisons):

386 HOWELL AND STOCKDALE

Table 3Observed Latencies for Positive (+) and Negative (-) Responses for Each Value of Memory Load (M) Under

the D = M Condition and the Corresponding Predicted Number of Comparisons

Model (Memory Search/Display Search)

Exhaustive/ Exhasutive/

Exhaustive/Self-terminating Self-terminating

Response Self-terminatingf Exhaustive/ Self-terminating/ + Recheck + RecheckM Latency Exhaustive Exhaustive Self-terminating Self-terminating (i.e., Model 1) (i.e., Model 2)

+ + + + + + +

1 574 673 1 1 1 1 1 1 1 1 1 2 1 12 1075 1136 4 4 3 3.5 4 3 2.25 2.75 4 5 4 53 1830 1755 9 9 6 7 9 6 4 5 9 9 9 94 2842 2654 16 16 10 11.5 16 10 6.25 7.75 16 14 16 14

Note- These predictions are derived from models involving serial scanning of both memory and display items, in which displayencoding time is assumed to be a constant.

than that for negative responses, as shown in Table 4.Thus, no model as it stands can adequately accountfor the obtained latency data.

The ability of the various models to explain theerror and serial position .data is also presented inTable 4. As pointed out earlier, the error data canequally well be explained by any of the four modelsand do not permit discrimination among them. Theserial position effects are not compatible with all ofthe four models but can be accommodated by theinclusion of additional assumptions. In the case of theexhaustive display models, it would be necessary toassume that the serial position effects are artifactual,and this artifact occurs for only one key assignment.For the self-terminating memory models, a randomorder of memory search would be required for thosesubjects not showing serial position effects.

All features of the data can be dealt withsatisfactorily by both the exhaustive-memory/self­terminating-display and self-terminating-memory/self-terminating-display models. Furthermore, anexhaustive-memory/self-terminating-display modelcan be made compatible with the observed differencesin latency of positive and negative responses if arecheck is proposed on those trials on which anegative outcome ensues.

The notion of rechecking to confirm the negative sethypothesis prior to emitting a negative response was

introd uced by Briggs and Blaha (1969) for characterclassification and Krueger (1973) for "same"­"different" judgments. Our view of recheckingassumes that the subject performs a recheck only ifhisfirst scan indicates that a negative response isappropriate. The recheck takes the form ofreaccessing the criterion set and performing anexhaustive search for the negative item.

In considering the RT data under the D = Mcondition in terms of the predicted number ofcomparisons, for D = M = 1 there are twoalternative models depending on whether or not therechecking process obtains. In this condition, we havea situation comparable with Sternberg's initialcharacter classification studies and also to Atkinson'sdisplay scan studies, both of which revealed anexhaustive scan which requires no recourse torechecking. Besides such empirical considerations asto the absence of a recheck, it is easy to conceptualizean underlying process. When D = M > 1, thesubject registers two kinds of information when hescans an item, that is position and identityinformation.

In contrast, when D = M = 1, the subject hasonly one kind of information, i.e., identity, and anexhaustive scan might be regarded as sufficientwithout a recheck. The models where rechecking is(Model 1) and is not (Model 2) involved for the case

Table 4Models in Which Display Encoding Tune is a Constant and Their Ability to Explain the Major Experimental Findings

Major Experimental Findings

Significance of the Difference inModel Slopes for Positive and Negative Error Display Memory

(Memory Search/ Responses (Student's t Test, Data Position PositionDisplay Search) Two-tailed, elf=7) (Figure 4) Effects Effects

Exhaustive/Exhaustive t =2.328 p < .05 t X (t) tExhaustive/Self-terlninating t =4.145 p < .05 t t tSelf-terminating/Exhaustive t = 5.210 p < .01 t X (t) X (t)SeIf-terminatingfSelf-terminating t =7.164 p < .01 t t X (t)Note- t and X refer to the model's successor failure, respectively, to explain the observed findings; tn means the model can explainthe findings ifadditional assumptions are made as outlined in the Discussion.

MEMORY AND DISPLAY 387

Model 2: RT = 443 + 153 C (8)

Modell:RT=319+165C (7)

D = M = I were both fitted to the data, and theequations for negative responses of the best fittingstraight lines were, respectively:

where C refers to the number of scanning comparisonsexecuted. This compares with the following equationof the line fitted to positive responses:

Implications of the Exhaustive-memoryjSelf­Terminating-Display Scan Model for CharacterClassification and "Same"-"Different" JudgmentTasks

Character classification. It was noted in theintroduction that a common feature of studies inwhich both number of items in memory and numberof items on the display are varied is that negativelatencies are not accurately predicted by a simpleexhaustive-memory/self-terminating-display model.The inclusion of an intuitively plausible recheckingscheme allowed accurate quantitative predictions ofresponse latencies to be made.

It was suggested that the lack of display positioneffects in other studies might arise from a failure toconsider the relation of negative and positiveresponses to the hands producing such responses andto different strategies used by subjects.

"Same"-"different" judgments of letter strings. Inthis study, a positive response is equivalent to a"same" response of the "same"-"different" judgmenttask. One common finding in such studies is that"same" responses are faster than "different"responses. Our analysis permits the dissociationbetween comparison and other stages involved inthese tasks. Our model suggests that there is alengthening of comparison times caused byrechecking. 1

One feature which puzzled Bamber was the upwardconcavity of "same" responses in his data. Fordifferent responses, he proposed a self-terminatingdisplay model. Our model proposes that the subjectdeals with one item at a time from the display andperforms an exhaustive search against memory andterminates as soon as a display item is found to be nota member of the CS. This is successful in predictingthe upward concavity observed here and in Bamber'sexperiments.

The model's success in predicting the upwardconcavity would seem to highlight the similaritybetween our task and that of Bamber, but how mightwe generalize the model to a situation where positionis important as in Bamber's experiment? We can takea lead from an experiment by Bamber and Paine(1973). They focused their attention on certainmechanisms by which information is retrieved fromletter strings. Two types of information areavailable-position and identity. Bamber and Paineexplicitly made the assumption that the CS and TSare both encoded in the form of a-letter and positiontag. Ifwe make this assumption about the encoding ofitems in "same" -"different" judgments of letterstrings, then our model is directly applicable. Thescan would then be an exhaustive search of positionand identity pairs of the CS vs. each position andidentity pair of the TS until a decision ensued.However, it does not even appear to be necessary tomake this additional assumption. While different

(9)RT = 461 + lSOC

All three equations were significantly linear beyondthe 0.10J0 level (F = 1205, 217, and 1635,respectively; df = 1,3). No significant differences inslope were found between either of the two lines fittedto the negative responses obtained under the M = 1condition, and the slope of the line fitted to positiveresponses. There is a significant difference inintercept between the lines fitted to negative responsesunder Model I and to positive responses (t = 3.994;df = 7; P < .05, one-tailed test), but no significantdifference emerges when considering Model 2.

Comparison of the slope constants under theD = M condition for the proposed model and for thebest-fitting lines for the 0 = 1 condition revealedthat they are remarkably similar. (For negativeresponses, the difference is 6 msec, and for positiveresponses it is 4 msec). Of all the models considered,the exhaustive-memory/self-terminating-display mod­el with rechecking on negative trials when M > 1offers the most satisfactory account of the evidence.This model predicts a common slope for negative andpositive responses when plotted against the number ofcomparisons involved. The slope constants for theD = M condition under this model and for theD = I condition are very similar. In addition, themodel provides an explanation of the display serialposition effects. In contrast, the self-terminating­memory/self-terminating-display model would re­quire the additional assumption of rechecking on bothpositive and negative trials to explain the latency dataand seems implausible.

Under the 0 = M condition, a feature of the datawas the upward concavity evident in the relationbetween RT and M for both positive and negativeresponses. In order to confirm that this concavity hadbeen removed, a polynomial regression was performedon positive and negative responses separately afterstandardization of the abscissa in terms ofthe numberof scanning comparisons predicted by the modifiedexhaustive-memory/ self-terminating-display model.For neither positive nor negative responses did thequadratic component which reflects such concavityreach significance. Thus. the standardization wassuccessful in removing the upward concavity.

388 HOWELL AND STOCKDALE

items could be different with respect tojust position orjust identity. the former has usually not beenconsidered.

REFERENCE NOTE

I. S. Sternberg. Scanning a persisting visual image versus amemorised list. Paper presented at the Annual Meeting of TheEastern Psychological Association. 1967.

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BAMBER. D. Reaction times and error rates for "same"·"different" judgments of multidimensional stimuli. Perception &Psychophysics. 1969.6. 169-174.

BAMBER. D. Reaction times and error rates for judging nominalidentity of letter strings. Perception & Psychophysics.1972. 12. 321-326.

BAMBER. D.. & PAINE, S. Information retrieval processes in"same't-vdifferent" judgements ofletter strings. In S. Kornblum(Ed.), Attention and performance IV. New York: AcademicPress. 1973.

BRIGGS. G. E., & BLAHA, J. Memory retrieval and centralcomparison times in information processing. Journal ofExperimental Psychology. 1969. 79,395·402.

HOLMGREN, J. E. Visual search in a forced-choice paradigm.Perception & Psychophysics. 1974. 16, 253·258.

JOHNSEN. A. M.• & BRIGGs. G. E. On thl\ locus of displayload effects in choice reactions. Journal of ExperimentalPsychology. 1973. 99. 266·271.

KRUEGER. L. E. Effect of irrelevant surrounding material onspeed of "same"-"different" judgments of two adjacentletters. Journal ofExperimental Psychology. 1973. 98, 252-259.

NICKERSON. R. S. Response times with a memory-dependentdecision task. Journal of Experimental Psychology. 1966, 72.761-769.

NICKERSON, R. S. Binary-c1assitication reaction time: Review ofsome studies of human information-processing capabilities.Psychonomic Monograph Supplements, 1972, 4, Whole No. 65.

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NOTE

I. In the present experiment. for the D = M condition, theproportion of CS· TS pairs with respect to position and identitydecreases as M increases. It might be argued that this couldaccount for the faster positive responses. Our on-line analysis of thedata does not allow us to test this hypothesis. However. one couldquestion th is explanation in that for the D = I cond ition thedifference between positive and negative responses remainsapproximately constant despite the fact that identity between theCS and TS occurs only when M = I.

(Received for publication April 18. 1975;revision received July 28. 1975.)