Signal Detection Theory and Modularity

8/12/2019 Signal Detection Theory and Modularity

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Jou rna l of Experimental Psychology:H u ma n Perception an d Performance1995, Vol.21, No. 4,935-939Copyright 1995 bv theAmerican Psychological Association, Inc.0096-1523/95/$3.00

OBSERVATIONSignal Detection Theory and Modularity: On Being Sensitive to the Powerof Bias Models of Semantic Priming

Dennis NorrisMedical Research Council Applied Psychology UnitG. Rhodes, A. J. Parkin, and T. Tremewan (1993) have shown that semantic priminginfluences signal detection theory measures of sensitivity in visual word recognition. Fol-lowingan argument presented by M.Farah(1989), theysuggested that thisisevidence thatsemantic information influences perceptual encoding, and that such an influen ce represents aviolation of modularity.This article shows that, contrary to M.Farah's claim, measures ofsensitivity cannot be assumed to reflect the operation of perceptual encoding. Simulations arepresented to demo nstrate that modular criterion-bias models o f priming in which p riming hasnoeffect on perceptual encoding predict thesame sensitivityeffects thatG.Rhodesetal. takeas evidence against modularity.

Can the standard signal detection theory measures ofsensitivity and bias be used to address the question ofwhether perceptual processes are modular or not? Rhodes,Parkin, and Tremewan(1993) suggested thattheycan. Theyreported a series of experiments in which they demonstratedthat semantic priming can lead to increases in sensitivity invisual word recognition. They claimed that their findingsrepresented achallenge to modularity (Fodor, 1983, 1985).The basis of this claim rested on the argument that ifsemantic priming leads to an increase in sensitivity, asindicated by signal detection theory measures of d'', thensemantic information is influencing the early perceptualprocesses in word reco gnition. Any such top-down effect ofsemantic inform ation on perceptualprocessing is clearly aviolation of the modularity view, which would hold thatsuch processes are an informationally encapsulated andcognitively impenetrable module.Rhodes et al. (1993) are following a line of reasoningpresentedby Farah (1989). Farah stated that Signal detec-tion theorycan be used todistinguish between the effects ofattention on the sensitivity of an encoding process and onthe bias of an encoding process. Changes in these twoparameters reflect the operation of qualitatively differentmechanisms (p. 189). Farah argued that measuresof sen-sitivity can be used to determine whether perceptual andsemantic priming share a common underlying mechanism.Based on a review of the literature, she concluded thatalthough perceptual priming produces effectso nsensitivity,semantic priming produces only effects on bias. Perceptualand semantic priming a re therefore based o n different un -derlying mechanisms. Rhodeset al.accepted Farah's claimthat signal detection theory measures of sensitivity reflectthe operation of encoding processes but then proceed to

Correspondence concerning this article should be addressed toDennis Norris, Medical Research Council Applied PsychologyUnit, 15 Chaucer Road, Cambridge, CB2 2EF, En gland.

show tha t seman tic priming can influ ence sensitivity as wellasbias.Both Farah (1989) and Rhodes et al. (1993) appear tohave made the mistake of assum ing that the standard signaldetection theory measure of sensitivity can be directly in-terpreted as an index of the sensitivity of early perceptualprocesses. Signal detection theory can indeed give us aninsight into the workings of psychological processes bu tonly if we can besure thatth epsychological m odel implicitin signal detection theory ca n safely be applied to theprocessesunder investigation. Theproblem is thatthe the-oretical assumptions implicit in standard unidimensionalsignal detection theory are not actually shared by any cur-rent model of word recognition. Co ntrar y to Fara h's claim,sensitivity and bias do not necessarily reflect the operationof qualitativelydifferent mechanisms. A single mechanismcan simultaneously influence both bias and sensitivity. Inthis article, I show that in criterion biasmodels such as thelogogen model (Morton, 1969) and the checking model(Norris, 1986), priming can produce a change in both biasand sensitivity even though priming has no effect whatso-ever on early perceptual processing. Not only can bias andsensitivity effects have a common locus but, contrary toFarah's claims, the locus may have nothing to do withperceptual encoding. If changes in sensitivity need not re-flect changes in early perceptual processing, then measuresof d' will be unable to tell us whether those perceptualprocesses are modula ror not .Both the logogen model and the checking model arecriterion bias models in which priming has its effect on thedecision process rather than earlier perceptual analysis.However, in contrast to the bias ofstandardunidimensionalsignal detection theory, which simply reflects the position-in g of a single response threshold, bias inthese models ca nbe set differently fo r different words in the lexicon. Effec-tively, these models can be seen as extensions of signaldetection theory to the case of m ultiple mu ltidimension al

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936 OBSERVATIONsignals in which each possible signal (word) has itsown bias and sensitivity. Other extensions of signal de-tection theory can be seen, for example, in Treisman's(1978) perceptual identification theory and in Ashby andTownsend's (1986) General Recognition Theory. However,throughout this article the term signal detection theory isused to refer to the more famil iar unidimensional form ofsignal detection theory used by Rhodes et al .(1993).In both the logogen model and the checking model,semantic priming alters the amount of perceptual evidencerequired to recognize a word without altering either thequantity or the quality of the perceptual evidence deliveredfrom perceptual encoding. Simulations are presented thatshow thatthese models can produce the pattern of sensitiv-ity effects shown in the experiments by Rhodes et al.(1993). As the checking model is a modular, bottom-upmodel, this demonstrates that sensitivity effects producedby priming are entirely compatible with the modularityhypothesis. Indeed, such effects were predicted by Norris(1986).

Signal detection theory attempts to provide the simplestpossible characterization of an observer detecting a signalagainst abackgroundo f noise. According to this character-ization, the behavior of the observer can be described bytw o statistics representing sensitivity and bias. Sensitivityrefers to the distance between the signal an d noise distribu-tions. The further apart these distributions are the moresensitive the observer is, and the easier it will be for theobserver to discriminate between signal an dnoise. To dis-tinguish between signal andnoise, theobserver needsto seta response threshold somewhere on the signal-noise con-t inuum. However, when setting this threshold the observerma y have abias to respond signal or to respond noise.If the assumptions of signal detection theory are satisfied,measures of sensitivity (d1) and bias (beta) can be derivedfrom the observer's hi t ra tean d false-alarm rate, an d thesemeasures are independent of one another.Because of this ability to separate bias from sensitivity,the signal detection theory statistics provide a valuabledescription of observers' behavior in a wide range of per-ceptual tasks. However, the claim thatchanges in measuredsensitivity are a direct reflection of changes in the sensitiv-ity of some early perceptual process is only true under thespecific set of assumptions made by signal detection theory.Signal detection theorystatisticsonlyprovideadescriptionof the observer's behavior. A measured increase in sensi-tivitysimply tells us that the observer is behaving as if thesignal andnoise distributions had moved further apart in asystem that makes response decisions in exactly the wayproposed by signal detection theory. In other words, thedecision to apply classical signal detection theoryto a set ofdata carries with it a set of theoretical assumptions about theprocesses being studied. If these assumptions are not met,then th e signal detection statistics will be misleading. Fo rexample, it might be the case that investigators had goodreason to believe that the lexical decision task involvedmaking a decision based on a set of orthogonal word de-tectors producing an output that could be represented on aunidimensional word-nonword (signal-noise) cont inuum.

In thatcase,itwouldbe entirely appropriate toperform thekind of analysis presented by Rhodes et al. (1993).However, no current theory does actually embody suchassumptions.If these assumptions are not satisfied, then a change inmeasured sensitivity need not imply that the observer'sperceptual processes have changed in any way at all . Inmore complex systems, changes ina pparen t sensitivity ca nalso come about through changes in the decision processesor biases involved in response selection.Although no models of word recognition share the as-sumptions of classical signal detection theory, many doshare a set of assumptions broadly similar to those firstexpressed in the logogen model. As already stated, thelogogen model can be considered to be an extension ofsignal detection theory to the case of multiple multidimen-sional signals. In the logogen model, changes in responsecriteria caused by semantic priming can produ ce exactly thepattern of data observed by Rhodes et al.(1993).Perhaps the best way to illustrate the behavior of morecomplex criterion bias systems like the logogen model orthe checking model is to consider how it is that in thesemodels semantic priming can lead to changes in sensitivityin the lexical decision task.For thepresent purposes bothofthese models are equivalent. In both m odels, semantic prim-ing has the effect of lowering the effective response thresh-o ld fo r primed words. In the logogen model, this occursbecause semantic features increase the feature counts, oractivation levels, of primed logogens. In the checkingmodel, the response criterion for primed candidate words isreduced directly. Whether the feature counts of primedwords are increased, or the criterion is reduced, the neteffect is identical;less perceptual evidence is required torecognize primed than unprimedwords.1Note that one of the most important characteristics ofthese criterion b ias mo dels isthat thereductionin responsecriterion isspecific to a limited set of words. Fo r example,the word street might only prime the word road.Standardunidimension al signal detection theory has no way to mo delthis selective reduction in criterion. Th e signal detectiontheorycriterion shift is an across-the-board shift: a tendencyto respond to every word in the lexicon on the basis of lessinformation. This means that signal detection theory iscompletely unable to explain even the standard effect ofsemanticpriming in aspeededlexicaldecision task (Meyer& Schvaneveldt,1971).Aglobal shift incri ter ion fol lowingaprime would mean that allwords were always respondedto with equal speed.Rhodes et al. (1993) constructed the stimuli in theirexperiment so that the nonwords were always only a singleletter different fromthe words(e.g.,road-voad). It is tempt-ing then , in tryin g to predict the behavior o f a criterion biasmodel, to think only of what happens to the activationlevels, o r feature counts, for the target word itself and toignore the effects ofo ther wordsin the lexico n. If we ignoreThe logogen model is usually described as havinga singleresponse criterion . Ho wever, this criterion iseffectively modulatedon awo rd-by-word basis by priming from semantic features.


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OBSERVATION 937the impact of other words in the lexicon, then we are ledalong the following path of reasoning: When the word ispresented it will produce a given amount of perceptualevidence in favor of that word (road). The matched non-word (voad) will produce somewhat less featural evidencein favor of the same word. If we now prime the word, thetotalamounto fevidence infavorof theword will simplybeincreased by some constant regardless ofwhetherthewordor nonword is presented. Priming will therefore increaseactivation of the word road produced by both the wordsroad and voad. The amount of evidence in favor of bothwords and nonwordswill increase without actually increas-ing their discriminability. T he differen ce between the aver -agefeature countsfo rwords andnonwo rds willbe thesamewhether they areprimed or not.The flaw in this analysis is that, in forcing criterion biasmodels intoastandard signal detection theory framewo rk,itomits to take account of the effects of other words in thelexicon that ma y have a different criterion (amount ofpriming) from the target word itself. The impact of otherwordsin thelexicon isseen mainlyin the way nonwordsa retreated. Given that stimuli in the Rhodes et al . (1993)experiment were presented briefly, followed by a patternmask, and that accuracy was less than perfect, one canassume that the featural representation of the input is de-graded in some way. Both word and nonword inputsmayactually produce their maximum activation in aword otherthan the matched word. If features are removed from theword input,itwill generally tendtomatchth erepresentationof the target word at least as well as any other word .2However, iffeaturesareremovedfrom thenonword,it mayactivate the lexical representation of another word morestrongly thanthe representationof theword towhich it wasoriginally matched (e.g., voad could become vo??, whichwould match words such as vole better than road). In theabsence ofpriming,itdoesn otmatter whethervodematchesroad or some other word. However, if road isprimed, thenthe nonword will no t display any effect of priming if deg-radation causes it to most closely resemble another wordthat is notprimed. Therefore, because of the effect of otherwords in the lexicon, priming will not haveasmuch effecton the activation levels producedby nonwords as bywords.The effect of priming on nonwords will be reduced to theextentthat nonwords aremore likely than words toactivatewords other than the primed word.Exactly the same argument applies even if the input isdegraded bynoise tha t alters rather than deletes features.Aslonga s thenonwordismore likely thantheword toactivatea wordotherthan the targetword,criterionbiasmodels willproduce effects ofsensitivityas well aseffectsof bias in asimple lexical decision task.A more concrete impression of the behaviorof the logo-gen model and the checking model can be realized byperforming a simple simulationof the lexical decision taskan d two alternative forced choice (2AFC) task used byRhodes et al. (1993). The words and nonwords in thefollowing simulations were constructed in a manner ana lo-gous to the stimuli used by Rhodes et al. in their first twoexperiments. InRhodese tal.'sfirstexperimentinwhichthe

lexical decision task was used, target words could be pre-ceded by related, unrelated,or neutral primes. Three non-word conditions were constructedfrom the word conditionsbychanging asingle letterin thecorresponding word target.The simulation used a set of 500 words and 500 non-words. All stimuli took the form of a 30-element vector inwhich each element was intended to represent an ortho-graphic feature of the stimulus. Each word or nonwordcomprised 20features drawnfrom thetotal featureset of 30features. Thefeaturesineach word were selected randomlywiththeconstraint thata llitemsdiffered fromeach otherbyat least 4 features (the maximum possible difference is 20features). Each nonword was constructed by changing 4features in one of the words, again with the constraint thatthe nonword differed from al l words by at least 4features.Because all stimuli differ from each other by at least 4features, we can consider the 4-feature difference to beequivalent to a single letter difference. Because all wordsare constructed to have 20 features and to differ fromnonwords by 4features,w e could arrange fo r lexical deci-sion performanceto beperfect bysetting the thresholdfor a yes response to be 17 featu res. In the Rhodes et al.(1993)experiment, participants were induced to make errors bypresentingthetargetfor 50ms followedb y apattern mask.To introduce errors in the simulations, target items weredegradedbyeliminating each feature withafixed probabil-ityof 0.3. Featuresin thetarget item activate correspo ndin gfeatures in each of the 500 words in the lexicon. If thenumber offeaturesin anywordin the lexicon exceeded theresponse threshold, the system responded yes ; otherwiseit responded no . The baseline response threshold was setso as to try andequate performance onwordsandnonwordspresented in a neutral context. Priming wa s simulated byreducing the threshold fo rprimed words by 1 feature (i.e.adding 1 to the feature count of primedwords).Becauseitis unclear how m any words should be primed, two versionsofthesimulationarepresented,one inwhich onlyone o f the50 0wordsin thelexicon wasprimed on apriming trialandone in which 50 words were primed. On unrelated primetrials, the primed words were chosen at random with theconstraint that the matched related target word was neverprimed. No words were primed on a neutral trial.Table 1 shows the results of the simu lation safter 100,000lexical decision trials in each of three word and threenonword conditions. Table 1 also presents values for thenonparametric sensitivity statisticA' (MacMillan & Creel-man, 1990; Rae, 1976)and thebias statisticB (Grier, 1971;MacMillan & Creelman, 1990) used by Rhodes et al.(1993).Thesestatisticsar ecomputed bycom paring perfor-mance ineach of the word conditions withthe correspond-in g nonword condition. For reference, Table 1 shows thedatafrom theRhodeset al.experiment.Intheir analysis,thedifference in sensitivity between the related andun related

2Note that, depending on the featural analysisassumed,somewords ca n lose features and appear similar to other words. Forexample, thewordEARcouldloseafeature an dmatch FA R betterthan EAR.


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938 OBSERVATIONTable1Hit and False Alarm Rates Produced by LexicalDecision Simulation in Each of the Three Wordand Nonword Conditions

ConditionOne word primedA'BHitsFalsealarmsFifty words primedA'BHitsFalse alarmsData for250-msSOAaA'BHitsFalse alarms

Neutral0.680.000.610.390.680.000.610.390.73-0.020.630.36

Prime typeRelated

0.70-0.340.890.720.69-0.170.770.660.73-0.410.860.61

Unrelated0.67-0.010.590.410.61-0.030.620.490.69-0.030.640.41

Note. SOA = stimulus onset asynchrony.3From Rhodesetal.(1993).

conditions wassignificant but theneutral conditionwas notsignificantly different from the other tw o conditions.The simulations show adifference in sensitivity betweenrelated andu nrela tedof about 0.03 when 1word isprimedan d about 0.08 when 50words areprimed.This compareswithadifference insensitivityof about 0.04 in the data.Inthe data, the main effect of sensitivity appears to be due tothe unrelated condition being worse than the neutra l andrelatedconditions.Thisisalso trueof thesimulations when50words are primed,but when only 1wordis primed thesimulations show a much smaller effect of inhibition.The reason why we see an increased effect of inhibitionwith a larger set of primed words is quitesimple.If only o neword is primed, an unrelated nonword will only be influ-enced by priming if it happens to match the single primedword in the lexicon. If many words are primed, then thenonword response will be influenced by priming if itmatches any one of these primed words. Therefore, themore words that are primed, the greater will be the detri-mental influence of priming on unrelated nonwords. Anunrelated word is much less likely to match one of theseprimed words and will therefore be little influenced bychanges in the size of the priming set. In the relatedcase,both words and nonwords are more likely to match theprimed word (o n average itwill be the most similar wordan d italsohas theadvantageofpriming)an d thedetrimentaleffect of increasing the number of primed words will besmaller.Even this very simple model demonstrates a pattern ofbehavior quite contrary to that predicted by Farah (1989).Changes taking place entirely within the decision-makingcomponent of the model can simultaneously influence stan-dard measures ofboth biasandsensitivity. In terestingly,thechange inbias issmaller in the simulations thanin thedata .When 50 words are primed, the change in sensitivity is

larger than that observed in the data, despite a smaller shiftinbias.Note thatn o attempth as been made to fit the simulationto the data. The simulation is presented solely to demon-stratetheabilityo f criterion bias models toshow sensitivityeffectsdue topriming.Both Antos (1979) and O'Connor and Forster (1981)argued thatifnon words were very similar toprimed words,then it would be impossible to reduce the recognition cri-terion without a huge increase in errors. Norris (1986)presented a series of counters to these arguments.Norris'scounterarguments are reinforced by the present simulationsin which the stimuli are designed to reflect the structure ofitemsin the Rhodes et al.(1993)experiment inwhichallnonwords were constructed by changing a single letter inthe corresponding word condition.Rhodes et al.'s (1993) second experiment used a two-alternative forcedchoiceprocedure.Thishas the meritthatthe results are unaffected by signal detection theory bias(Sekuler&Blake,1990).Thatis,responsesareindependent

of the placement of the overall response threshold. In sucha procedure, asimplemeasure ofpercentagecorrectcan beinterpreted as an index of sensitivity and is equivalent to thenon parametric measure, the area un der the receiver-operat-ing characteristic curve (McNichol, 1972). The materialsan dprocedure for the two-alternative forced-choice exper-iment were similar to those of the lexical decision experi-ment, with the exception that on each trial a word andnonword were presented one above the other.This simula-tion was, likewise, very similar to the lexical decisionsimulation. However, on each trial the word and the non-word were both (after degradation by noise) matchedagainsteach wordin thelexicon.If thestrongest match(i.e.,numberof featuresin common plus priming) wa s producedby theword,the response was considered correct, otherwiseitwas incorrect. In the case ofties,a response was generatedat random. Table 2 shows the results of the simulation,again priming either1wordor 50words, along w iththedatafrom Rhodes et al. Once again, it is shown that the simplecriterion bias m odelproduceseffectso f sensitivity, this timein a task that is considered to be independent of effects ofbias.Incommon withthe lexical decision simulations, thesesimulations also show the shift toward more inhibition asthe num ber of primed words is increased. Themajor differ-ence between the simulation and the data is that, in the data,both primed and unrelated conditions produced lower sen-sitivity than the neutral condition. Rhodes et al. speculatedTable2Percentage of Correct Responses Produced bySimulations of Two-Alternative Forced Choice Experiment

ConditionOne wordFifty wordsData for 250-msSOA

Neutral656567

Primed696764

Unrelated646160

Note. SOA = stimulus onset asynchrony.Trom Rhodeset al.(1993).


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OBSERVATION 939that there may have been problems with their neutral con-dition. However, it is interesting to note that we couldengineer anoutcome thatwasmore similarto thedataif theprimedid not alwa ys succeed in priming the intended target.The primed condition would then move closer to the unre-lated condition.

The most important difference between standard signaldetection theory and the criterion bias models describedhere is that signal detection theory has a single responsecriterion that operates across-the-board. That is, on any o netrial, thechange incriterion placement mustbe thesamef orall wor ds in the lexicon. In these other models the responsecriterioncan be setdifferently fo reach word in thelexicon.Priming can then be used to set the thresholds so as toreflect the probability structureof the input. Because prim-ing in most lexical decision experiments reduces stimulusuncertainty,this information can be used to help the systembehave as though signal and noise distributions had beenmoved further apart.This distinction between a single cri-terion and a word-by-word criterion isvital to afull appre-ciation of the behavior of criterion bias models. For exam-ple, Antos(1979)and Schvaneveldt and McDonald (1981)discussed the application ofsignaldetection theory to stud-ies of semantic priming as though priming in criterion biasmodelscanonly produce effects ofbiasand not sensitivity.Their mistake seems to have been to equate the single criterion of signal detection theory with the more power-ful notion of criterion used in criterion bias models suchas the logogen model or the checking model.Along with Farah (1989), Rhodes et al . (1993) havemisunderstood the kind of inferences that can safely bedrawn from a signal detection theory analysis of primingdata.Their case against modularity dependson theassump-tion that sensitivity effects must be the consequence ofchanges in early perceptual analysis. The simulations pre-sented here show ho wchangesinsensitivitycanalsofollowfrom selective changes inrecogn ition criterion.Instandardunidimensional signal detection theory, these selectivechanges in criterion cannot be properly modeled simply bychanges inbias, andconsequently they manifest themselvesas achange insensitivity.Classical unidimensional signal detection theory can bemisleading if it is taken literally as the only possible psy-chological model.W e should not forget thatthere areothermodels andother extensions of signal detection theory thatma y be more appropriate. However, signal detection theorystill provides a valuable statistic even under circumstancesin which the underlying model might not be appropriate.Whenever the hit rate increases without a commensurateincrease in the false-alarm rate, it might seem perfectlyproper to describe the system as showing an increase insensitivity. But the crucial question is how does this in-crease in sensitivity come a bou t? What is the un derly ingpsychological model? Although signal detection theorycould be taken as a psychological model, and increases insensitivity couldbeattributedtochangesin theperforman ceof some early stage in perception, other models need notmake this assumption. In thesimple version of the logogen

or checking model described here, changes in sensitivitydue to priming come about purelyas aresult of changes inresponse bias or activation level of individual logogens.Priming has no effect whatsoever on the efficacy or sensi-tivity of early perceptual encoding.Finally, because changes in sensitivity can be due toresponse bias or decision level processes, rather than per-ceptual coding, it would be wrong to follow Rhodes et al.(1993)and take changes in sensitivity caused by primin g asevidence of a violation ofmodularity.

ReferencesAntos, S. J. (1979). Processing facilitation in a lexical decisiontask. Journal of Experimental Psychology: Human Perceptionand Performance, 5,527-545.Ashby, F. G., & Townsend,J. T.(1986). Varieties of perceptualindependence. Psychological Review, 93 ,154-179.Farah, M.(1989).Semantic an d perceptual priming: Ho wsimilarare the underlying mechanisms? Journal of Experimental Psy-

chology: Human Perception andPerformance, 15,188-194.Fodor, J. A. (1983). The modularity of mind. Cambridge, MA:MIT Press.Fodor, J. A.(1985). Precis of The mo dularity of mind. Behav-ioral and Brain Sciences, 8, 1-42.Grier, J. B.(1971).No npara metric indexes for sensitivity and bias:Computing formulas. Psychological Bulletin, 98 ,185-199.MacMillan, N . A., & Creelman, C. D. (1990). Response bias:Characteristics of detection theory, threshold theory, and non -parametric indexes. Psychological Bulletin, 107,401-413.McNichol, D.(1972).Aprimerofsignal detection theory.London:George,Allen & Unwin.Meyer, D. E., & Schvaneveldt, R. W. (1971) Facilitation in rec-ognizing pairs of words: Evidence for a dependence betweenretrieval operations. Journal of Experimental Psychology, 90,227-234.Morton, J.(1969).Interaction of information in word recognition.Psychological Review, 76 ,165-178.Norris, D. G.(1986). Word recognition: Context effects withoutpriming. Cognition, 22,93-136.O'Connor , R.E.,&Forster,K . I.(1981).C riterion biasa ndsearchsequence bias in word recognition. Memory Cognition, 12 ,470-476.Rae, G.(1976). A no n-para metric measure of recognition perfor-mance. Perceptual and Motor Skills, 42, 98.Rhodes, G. , Parkin, A.J., & Tremewan, T. (1993). Semanticpriming an d sensitivity in lexical decision. Journal of Experi-mental Psychology: Human Perception and Performance, 19,154-165.Schvaneveldt, R. W., & M cDona ld, J. E.(1981).Seman tic contextan dtheencoding ofwords: Evidencefor twomodeso fstimulusanalysis. Journal of Experimental Psychology: Human Percep-tion andPerformance, 7,673-687.Sekuler, R. ,& Blake, R.(1990).Perception(2nd ed.). New Yo rk:McGraw-Hill.Treisman, M.(1978). A theory of the identification of complexstimuli with an application to word recognition. PsychologicalReview, 85 ,525-570.

Received September 7, 1993Revision received January20, 1994Accepted August1,1994

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Signal Detection Theory and Modularity