VOL. 74, No. 1 JANUARY 1967

PSYCHOLOGICAL REVIEW

WORD-FREQUENCY EFFECT AND RESPONSE BIAS1

D. E. BROADBENT

Applied Psychology Research Unit, Cambridge, England

Many recent investigators have studied "Response Bias" theories ofthe perception of common vs. uncommon words. 4 different classesof theory are distinguished, and it is demonstrated that 3 of themare inconsistent with previously published and with fresh data.The 4th sense of response bias, however, leads to the prediction thatbias on correct responses may be greater than that on errors, and isvery accurately consistent with the data. This is the sense of responsebias as analogous to the bias of a criterion in a statistical decision.

During the past 15 years or so,very much research interest and efforthave been occupied with the compari-son of the perception of words whichare common in ordinary language onthe one hand, and those which areuncommon on the other. The fact thatcommon words are, other things beingequal, more easily perceived is perhapsonly a special case of the general influ-ence of probability on perception.From the time of the classic experi-ments on distortion in perception andremembering, such as those of Bartlett(1932), it has been common groundto most psychologists that a probableevent is easily perceived. The usefulfeature of the word-frequency effect isthat it allows quantitative studies,which are almost impossible in the caseof most other similar phenomena met

1 Thanks are due to Margaret Gregory forconducting the experimental work discussedin this paper, and to the British Medical Re-search Council for support. Some of theconcepts were presented in outline form in apresidential address to the British Psycho-logical Society in April, 1965.

in everyday life. It is hard to put anumber to the probability of perceivinga man in a bowler hat in the City ofLondon, as opposed to Manhattan.Consequently it is difficult to test anyprecise theory of perception choosingas stimuli pictures of men in bowlerhats. In the case of words, however,we can to some extent describe the rela-tive probabilities of different words inquantitative form. They thus providea convenient special tool for investi-gating the general question of prob-abilistic effects in perception.

In very recent years, a number ofwriters on the word-frequency effecthave considered the possibility that theeffect is due to a response bias, ratherthan to some feature of the input ofinformation to the organism. Unfortu-nately, the term response bias is itselfambiguous. There seem to be at leastfour different senses in which the termhas been used, each implying a differentdefinition of it. Definitions have not,however, usually been given, and theterm has been used as self-explanatory.It seems worthwhile, therefore, to dis-

1

D. E. BROADBENT

tinguish these possible definitions. Aswill be seen, when this is done the ex-perimental evidence suggests that threeof the definitions are inadequate as ex-planations of the word-frequency effect.The fourth, however, is very adequate.This fourth sense, admittedly, is notthe one which has been most frequentlyused in the past. Thus it is not verysurprising that several authors haveconcluded that response bias was notan adequate explanation (e.g., Brown& Rubenstein, 1961; Zajonc & Nieu-wenhuyse, 1964).

A convenient starting point for themodern interest in response bias maybe taken as the paper of Goldiamondand Hawkins (1958), who showedthat when a tachistoscope was flashedat experimental subjects (Ss) withoutany word actually being presented, andwhen the responses were scored as ifsome particular word had indeed beenpresent, they were scored as beingmore accurate in identifying thosewords which had in a preliminary ex-periment been more frequently pre-sented. Since there could be nosensory component in this experiment,the effect could legitimately be de-scribed as response bias. In addition,it seems that the presentation of a fixedset of alternatives between which 5"has to choose, rather than an open-ended type of test, markedly reducesthe word-frequency effect (Pierce1963; Pollack, Rubenstein, & Decker1959). Thus the effect certainly de-pends upon an adjustment of the or-ganism which can be fairly rapidlyeffected, and which is not inherent inthe nature of the stimulus. The useof the term "artifact" by Pierce showsthat such a process of adjustment isnot to all ways of thinking a genuinelyperceptual effect at all. In brief, how-ever, all the following different possiblehypotheses seem to be consistent withthe phenomena so far cited; each of

them implies a different definition of"response bias."

Pure Guessing

On this model, 5" perceives a pro-portion of the stimuli correctly, andguesses on some or all of the remainingtrials. If his guesses are more fre-quently common words rather than un-common words, he might by chancescore some correct responses on com-mon words which would enhance hisapparent performance.

Sophisticated Guessing

A more complex model is one inwhich, even when a stimulus word hasnot been correctly perceived, the in-formation which has arrived at thesenses nevertheless rules out someEnglish words as being impossible, andleaves a restricted set of alternativesas still consistent with what has beenheard. If now S chooses at randomout of this restricted set, but with abias towards the more probable words,he will, just as in the simple model,score some correct answers on commonwords by chance.

Observing Response

In attempting to identify the wordwhich has been presented, £ may ad-just his sense organs or his centralmechanisms so as to maximize the ef-fects of stimuli which he expects, at thecost of being badly adjusted to detectimprobable stimuli. This might be de-scribed as a kind of "observing re-sponse" model: Its predictions will ofcourse be closely similar to those of aview which regards the word-fre-quency effect as purely perceptual withno response component. However,this view does make it clear that theperceptual effect depends upon the ad-justment of the observer and so maybe less in forced-choice situations. Itis therefore included as a possible vari-

WORD-FREQUENCY EFFECT

ety of "response bias" theory, despiteits similarity to nonresponse theories.It is worth noting, however, that evi-dence inconsistent with this theory mayalso exclude a "pure perception" viewof the effect.

Criterion Bias in Decision

Lastly, the situation might be viewedas analogous to a statistical decision,in which the stimulus presented pro-vides evidence pointing to a greater orlesser extent to each of the words in5"s vocabulary. If 5 were biased insuch a way as to accept a smalleramount of evidence before deciding infavor of a probable word rather than animprobable word, the word-frequencyeffect would be obtained. This lastapproach is probably the least used ofthe four, but it is nevertheless the onewhich the present paper will attemptto support.

To clarify the differences betweenthe models, let us think of the follow-ing hydraulic analogy. Let us supposea vast array of test tubes, each partlyfull of water, and each corresponding toa word in the language. The choiceof one tube corresponds to perceptionof a word, and the probability of choiceof any tube is greater when the waterlevel in it is higher.2

On Model 1, presentation of a stim-ulus has no effect on the water levels,but all "high-frequency" tubes start offwith more water than "low-frequency"tubes. Thus a high-frequency choiceis more probable.

On Model 2, presentation of a stim-2 To be precise, the level of water in a

tube shall be proportional to the logarithmof the probability of choice of that tube, aswill appear later. Furthermore, in Models1 and 2 there may also be occasions whenthe presentation of a stimulus determines acorrect choice perfectly, with no probabil-istic element. These occasions, however, areindependent of word frequency and can beignored for the moment.

ulus raises the water level in a smallproportion of tubes. This subsampleincludes the correct tube, but that tubereceives no more water than each ofthe others in the subsample. Choice iseffectively restricted to the few tubesselected by the stimulus: Within thesefew, a high-frequency choice is moreprobable because the initial level inthat class of tubes was higher.

On Model 3, presentation of a stim-ulus adds more water to the correcttube than to any other. This addi-tional amount is itself greater whenthe tube is "high-frequency" than whenit is low, perhaps because funnels arefitted to that class of tube to catchevery possible drop. Correct choicesof such tubes will therefore be morefrequent even if the initial difference inlevels is small or absent.

On Model 4, presentation of a stim-ulus again adds more water to the cor-rect tube than to any other, but theadditional amount is the same what-ever the class of tube involved. Since,however, the initial level in high-fre-quency tubes is greater, a high-fre-quency choice is more probable.

The following points should be noted.First, the four models differ largely inthe way in which the effect of thestimulus combines with that of theclass of response. Second, responsebias corresponds in Models 1, 2, and 4to an initial difference in water level;while in Model 3 it may do so but alsocorresponds to a difference in thechange of level produced by a stimulus.Third, in Models 3 and 4 the presenceof a real stimulus, no matter how faint,always increases the probability of acorrect perception.

DETAILED IMPLICATIONS or THESETHEORIES

Pure GuessingThis sense of "response bias" has

been clearly stated by Dember (1960,

D. E. BROADBENT

p. 287), and is that which one wouldnaturally infer from the papers ofGoldiamond and Hawkins (1958) andPierce (1963). (Throughout thispaper it should be remembered thatprevious authors may have been op-posing the value of response bias intheir use of the term, and also mayhave changed their usage in later ref-erences.)

This simple theory implies that if

Pc = apparent score correctpc = truly perceivedPF = probability of apparently cor-

rect response by guessing inthe absence of a stimulus

then Pc = pc 4- (1 — pc) pF.

We may define "response bias" inthis case as the difference in PF be-tween common and uncommon words:If pc is the same for all words, a greaterPF for common words would give agreater Pc for those words. But thismodel immediately involves us in ri-diculous impossibilities. For example,even if no guesses of uncommon wordsare made at all, it means that .S" has avery high probability of guessing acommon word correctly by chance. Inan experiment to be reported later,there is a difference of approximately.2 in the probability of correctly per-ceiving a common as opposed to an un-common word, and this means that theprobability of guessing a common wordcompletely correctly must be greaterthan .2. Since, however, this can beshown for more than five commonwords, the model is manifestly absurd.The word-frequency effect is muchtoo large to be explained by supposingthat the listener simply picks a wordout of his whole vocabulary of commonwords whenever he fails to perceivecorrectly.

In addition, this model of perceptionis inconsistent with the effect on Pc

which can be produced by presenting a

fixed vocabulary of possible words andvarying the size of this vocabulary. Ifpure guessing were the explanation ofthe improved performance which isshown with a smaller vocabulary, thenthe gain in correctly perceived wordsshould always be smaller than the in-crease of probability of a completelyrandom choice turning out correct.Thus a reduction in vocabulary sizefrom 100 words to SO should producean improvement in performance of, atmaximum, .01: but this is considerablyless than that actually attained.

Lastly, even if the foregoing reasonsare not regarded as sufficient to ex-clude this model, it makes the follow-ing prediction which, as we shall see,turns out to be unjustified. Supposewe examine the errors which each 6"makes and divide them into commonand uncommon words. Now when thestimulus word itself is common, someof the occasions when 6" guesses acommon word will be scored as cor-rect answers and not as errors. But ifthe stimulus was in fact a commonword, naturally none of the guesses ofuncommon words can possibly bescored by the experimenter as correct,and all of them appear on the answersheet as errors. When, however, thestimulus is an uncommon word, thesituation is reversed, and every guessof a common word is entered as an er-ror. It may even be the case that anoccasional guess taking the form of anuncommon word does turn out to becorrect, and thus there may even befewer recorded uncommon errors inthis case than when the stimulus is acommon word. Certainly, however,there will be more recorded errors ofcommon words. If, therefore, we ex-amine the error words and divide theminto those words which are commonin the language and those which arenot, the ratio of occurrence of the for-mer to the latter should be greater if

WORD-FREQUENCY EFFECT

the actual stimulus was uncommon thanif the stimulus was common. (See Table1). The effect must be a substantialone, if the word-frequency effect itselfis large, since the entire advantage ofthe common words is derived from thefact that some common guesses are notscored as such. This prediction there-fore serves as a test of this type ofmodel.

Sophisticated Guessing

This theory is much less clearly ab-surd than the previous one. It hasbeen upheld by Solomon and Postman(1952), Newbigging (1961), J. T.Spence (1963), and Savin (1963),among others. Brown and Ruben-stein (1961) also used a formulationof response bias which is in some waysof this type. (The latter authors, how-ever, found that the effect was toolarge for a model of this type. Theycontended that the number of re-sponses, including error responses,which were of the same frequency classas the stimulus, was larger than itwould be by chance, and they conse-quently suggested that 5" was receivingsome information from the stimulusabout the extent to which the actualword was common or uncommon.)

The theory can be represented by anequation closely similar to that for theprevious case, namely

Po =

where

+ (1 —N

PF X — ;

inN = total number of wordslistener's vocabulary

n = number of words still possibleafter reception of a stimulus.

Response bias is defined as previously,as the difference in pF between commonand uncommon words. This would beperfectly capable of giving rise to aword-frequency effect of the magnitude

TABLE 1GUESSING THEORIES OF WORD-

FREQUENCY EFFECTS

S's performance

TruePerception

x%

High fre-quency guessesY% ( = a + b)

Low fre-quencyguesses

z%

Apparent score in experiment

HF stimulusLF stimulus

CorrectX + aX

HF errorb

a + b

LF errorZz

actually observed, since the additionalNterm — could well be substantialn

enough to make the word-frequency ef-fect considerably larger than the purerandom probability of guessing a par-ticular high-frequency word out of allthose in the English language. Forsimilar reasons, this model is capableof dealing with the large improvementin performance which occurs when thevocabulary of possible words is knownand is small. Recently Stowe, Harris,and Hampton (1963) have produceda version of this model which predictsan exponential relationship of the form

Po = PF1/K

and have presented data fitting suchan equation.

It may be added that a similar typeof model can be used to account for thelarge improvement in performancewhich occurs when a few words ofcontext are given before a somewhatnoisy stimulus word. In such a case,the listener may be able to say correctlywhat the target word is on quite a highproportion of occasions, even althoughhe has quite a low chance of doing sowith either of the two sources of in-formation by itself. Empirically, this

D. E. BROADBENT

effect also can be fitted by an exponen-tial relationship (Pollack, 1964; Ru-benstein & Pollack, 1963; Tulving,Handler, & Baumal, 1964).

Leaving aside the support or criti-cism which earlier papers provide forthis model, it will be clear that it makesa prediction similar to the model pre-viously discussed. That is, for com-mon stimulus words some of the ap-parently correct answers were in factguesses, and therefore there should befewer common words among the errorsto such stimulus words than thereshould be to uncommon stimuluswords.

Observing Response Model

This view has been most baldlystated by Broadbent (1958, p .54) forthe case of perceptual defense ratherthan the word-frequency effect. Itwould naturally arise, however, froma motor theory of speech perception(Liberman, Cooper, Harris, & Mac-Neilage, 1963), and is included amonga number of other mechanisms byBruner (1957, p. 138). The essentialfeature of this third class of theoriesis that the input to the perceptual mech-anism is regarded as flowing dispro-portionately from those characteristicsof the stimulus which are especially in-dicative of common words. For ex-ample, peripheral or central adjust-ments might orient the system towardsreceiving acoustic cues relevant to thedistinction between P and D, and notthose cues relevant to the distinctionbetween X and Z. Since the formerletters, and perhaps their correspond-ing phonemes, are more common thanthe latter, this might give more ac-curate perception of common words. Anumber of well-known experimentsshow adjustment towards selective per-ception of some inputs rather thanothers (Broadbent, 1958). However,such a theory would not imply the

same predictions as Models 1 and 2concerning errors. One might on thecontrary expect that detection of theabsence of common phonemes wouldbe especially efficient, as well as thatof their presence. Thus common wordswould not occur often as errors, com-pared with their occurrence as correctresponses.

In support of this analysis, one maycite an experiment on division of at-tention which has been analyzed by thetechniques of signal-detection theory(Broadbent & Gregory, 1963). Theexperiment involved a man listeningfor a tone in noise in one ear, while heeither memorized six digits arriving atthe other ear, or else ignored them toconcentrate upon the tone. Using sig-nal detection theory, it is possible tocalculate, from true and false responsesin a psychophysical situation, a param-eter (d') which can broadly be de-scribed as signal-noise ratio, and it wasshown that concentration of attentionupon one sensory channel improvedthis ratio. Thus the general predic-tion of the third theory would be thatthe parameter corresponding to signal-noise ratio, in a detection theory analy-sis, should be greater for commonthan for uncommon words: Responsebias is here defined as a differencein d'.

Response Bias as a Criterion Placement

This view has been most clearlystated by Goldiamond (1962) but isconsistent with other lines of theoriz-ing such as Treisman (1960) andBroadbent and Gregory (1963).

Signal detection theory, which hasbeen briefly mentioned above, is nowwidely familiar (Swets, 1964). Inbrief, the basic suggestion is that someprocess varies randomly within the ner-vous system about a mean which isshifted in value by the arrival of asignal. In the case of yes-no detection

WORD-FREQUENCY EFFECT

of a single signal, some critical levelof the process has to be exceeded fordetection of the signal to occur, and itis obviously possible to produce a highrate of detections either by a large shiftin the mean value of the process whenthe signal occurs, or else by a low valueof the critical level. In the latter case,there will (other things being equal)be large numbers of false alarms.Nevertheless, a low critical level maybe rational if signals are very probable,and it has been shown experimentallythat the changes in performance pro-duced in psychophysical situations bychanges in the probability of a signalappear to correspond to changes in thecriterion level. They do not corre-spond to changes in d', the shift of themean value of the internal processwhich is produced by a signal.

The latter parameter is the onewhich was mentioned in the last sec-tion as corresponding to signal-noiseratio, and it would appear thereforethat experiments on the detection ofsimple tonal signals of different prob-ability lead us to a prediction diametri-cally opposed to the one derived fromthe previous model. If one couldanalyze the perception of speech on thebasis of signal detection theory, thismodel would suggest that the word-fre-quency effect would correspond to adifference in the critical level necessaryfor a word to be perceived.

The perception of speech involveschoice from many alternatives ratherthan the simple yes-no detection of asignal. Signal-detection theory hasbeen extended to the forced-choice case,and when the resulting mathematicsare applied to experiments on the per-ception of words drawn from knownvocabularies of different sizes, the mag-nitude of the effect is satisfactorily ex-plained without needing to suppose anychange in the parameter correspondingto signal-noise ratio (Swets, 1964, p.

609). There thus appears to be areasonable case for examining theword-frequency effect using the meth-ods of signal-detection theory, and at-tempting to decide which of the crucialparameters is changed when commonwords are perceived rather than un-common ones.

Unfortunately, it is difficult, usingthe methods of signal-detection theory,to handle the case in which a numberof different responses (decision out-comes) have different degrees of biasattached to them. Accordingly, a freshanalysis has been made using a pro-cedure suggested by Luce (1959), andthis will now be explained. It shouldbe emphasized that the method sug-gested by Luce derives from a differentaxiomatic approach from the earliersignal-detection theory, but the presentauthor does not intend to support oneset of axioms or the other. The twocalculations lead to approximately sim-ilar conclusions in most instances, butin the present case the method of Luceis considerably more convenient.

THE ANALYSIS OF MULTIPLE CHOICESITUATIONS WITH VARYING BIASES

The normal analysis of the forced-choice situation, from the point of viewof signal detection, is to suppose thatthere are a number of different vari-ables, equal to the number of alterna-tive choices, and each varying nor-mally and with unit variance about amean which is zero for all alternativesexcept the correct one. For the correctalternative, the mean value is d'. Oneach trial, one sample is drawn fromeach of the resulting distributions, andthe largest value determines the alter-native which is chosen for response.The correct response, therefore, clearlyhas the greatest probability of occur-rence, but there is some chance thatone of the other alternatives may,through ill fortune, reach a high value

8 D. E. BROADBENT

when the correct alternative happensto have taken on a low value.

Biases are introduced into the situ-ation by supposing that some alterna-tives have a mean which is greater thanzero even before a stimulus arrives andare shifted by a further amount d' ifthe appropriate stimulus occurs.

Let us start by taking the case of atwo-alternative forced-choice decision.In this case, we have two normal dis-tributions, each with unit variance, andone of which has mean zero while theother has mean d'. If a sample isdrawn from each distribution, the dif-ference between these samples is itselfdistributed normally with mean d'.Thus if the two processes are namedx and y, and if we take the differencex—y, there will be two resulting distri-butions, one with mean +d' when xis correct, and the other with mean—d' when y is correct. If now we de-cide in favor of one alternative when-ever x—y is positive, and the otherwhen x—y is negative, we obtain a per-centage of correct answers which canbe calculated from the properties of thenormal distribution, and which is con-vertible to d' by published tables.

By adopting a decision rule whichchanges from one alternative to theother when x—y equals zero, we havetaken a situation of zero bias. It wouldof course be equally possible to adoptthe rule that we decide in favor of onealternative when x—y is greater thanor equals C, and in favor of the otheralternative when x—y is less than C.This would introduce a bias in favor ofone alternative or the other, whichwould be precisely analogous to the cri-terion setting adopted in the yes-nocase.

The approach adopted by Luce(1959) depends upon the followingvaluable approximation. If we have aprocess of the type already mentioned,normally distributed with zero mean,

and if there is some critical value of theprocess at a value C, then to a reason-able approximation

log = KG

where

PF = probability that process willnot attain C

PS = probability that process willexceed C

K = a constant, which may beeliminated by using appro-priate units for scaling thevalue of the process.

This approximation allows us to workout very simply the consequences of atwo-alternative decision, such as theone considered above.

Thus if

mean of distribution correspondingto Alternative 1 correct = log amean of distribution correspondingto Alternative 2 correct = — log aCriterion level = + log V (i.e., abias in favor of Alternative 2),

then when Alternative 1 is presented

Probability of Response 1 _ aProbability of Response 2 V'

and when Alternative 2 is presented

Probability of Response 1 1Probability of Response 2 a V

This analysis can now be extended tothe case of more than two alternatives,by use of the principle that the relativeprobabilities of any two alternatives areunaffected by the presence or absenceof other alternatives. In the case ofspeech, this principle appears in generalto be approximately valid, as has beenshown by Clarke (1957). We maytherefore draw up a table in which thecolumns represent responses and therows stimuli; within each row, the ra-

WORD-FREQUENCY EFFECT

TABLE 2

RELATIVE STRENGTHS OF FOUR RESPONSESIN THE PRESENCE OF EACH OF FOUR

STIMULI, TO ILLUSTRATETHE NOTATION

Stimuli

i234

Responses

1

aiViViViVi

2

V2a2V2

V2

V2

3

VsV3

«3V3

Vs

4

V4V4V4

OtiVt

tio of the numbers in any two columnsrepresents the ratio of the probabili-ties of those two responses when thestimulus appropriate to that row hasbeen presented. That is, the entriesin the table correspond to the quantitiesa and V of the example already given.For the four-choice case, see Table 2.Notice that each response may possessa different bias, and in addition thatthe effect of the correct stimulus maybe different for each of the possiblestimuli.

Turning now to the word-frequencyeffect, let us consider for simplicity twoclasses of words, one consisting of high-frequency words and the other of rela-tively low-frequency words. Againfor simplicity, we may suppose thateach of the former possesses a constantresponse bias V relative to each of thelatter. Table 3 shows a section of thetable for this situation. There wouldof course be many other possible re-sponses, some of them lying outside thetwo frequency categories altogether,but, as already argued, this would notaffect the relative probabilities in-volved. The probability of respond-ing with any one particular erroneousword is of little practical use. Itis, however, of interest to consolidateall the error responses in the high-fre-quency class with which we are con-cerned, which we may suppose to con-

TABLE 3

RELATIVE STRENGTHS OF THE CORRECT RE-SPONSE AND OF EACH OF Two ERRORS, IN

THE CASE OF SPEECH PERCEPTIONWITH COMMON AND UNCOMMON

STIMULI

Stimulus

High frequencyLow frequency

Correctresponse

aaV(XL

One par-ticular highfrequency

error

VV

One par-ticular lowfrequency

error

11

tain NH different words, and also thosein the low-frequency class, which wemay suppose to contain NL differentwords. Table 4 illustrates this change.

Table 4 will hold both for Model 3and for Model 4: Model 3 holds if<XH > a^, and Model 4 holds if OH =«L and V > 1.

To clarify the meaning of the table,let us consider a few illustrative pre-dictions from it. Suppose «H = «L = 1,that is, no stimulus effect occurs at all(the Goldiamond and Hawkins situa-tion). Let us also put NH = NL = 4,that is, consider a small fixed vo-cabulary like that of Goldiamondand Hawkins in which no responsesoccur outside the vocabulary. Then ifV > 1, say V = 4, the probability ofa correct response to an HF stimulus

is 4 + 3 X 4 + 4 = '2' While the

probability of correct response to an

TABLE 4

FINAL TABLE OF RELATIVE STRENGTHS FORCORRECT RESPONSES AND FOR TWO TYPES

OF INCORRECT RESPONSE, IN THECASE OF SPEECH PERCEPTIONCONSIDERING ALL WORDS IN

THE LANGUAGE

Stimulus

High frequencyLow frequency

Correctresponse

«HVox

Errors ofhigh

frequency

(NH-1)VNHV

Errors oflow

frequency

NL

NL-1

10 D. E. BROADBENT

1LF stimulus is 7—. . . . . , „ — .^.

1 + 4 X 4 + 3Thus the Goldiamond and Hawkinseffect will occur.

In the same situation, suppose astimulus of moderate strength isapplied, so that «H = at = 6. (As-suming Model 4). Then correct HFresponses have probability

2424 + 1 2 + 4

and correct LF responses have proba-

bility 6 + 16 + 3 = -24'

Notice that the difference in probabil-ity of the two types of correct responsebecomes greater when a stimulus ispresent, an effect which has sometimesbeen regarded as excluding a response-bias interpretation. On the other hand,if the stimulus is exceedingly strong,«H = «L — 400, the difference in cor-rect responses becomes slight again.

HF correct responses then

16001600 + 1 2 + 4 "

LF correct responses then

400400 + 16 + 3 -.95.

In other words, with a strong stimulusprior biases are effectively overruled,and one perceives what is really present.

While these implications of the anal-ysis help one to understand it, the twomain questions are whether the factsof perception are consistent with thisanalysis rather than with Model 1 or 2;and, if this analysis is appropriate,whether Model 3 or 4 is the morenearly correct. To test these ques-tions, two further predictions may bedrawn from Table 4, for the case whenNH and NL are large.

1. On Models 3 and 4, the ratio oferrors of high frequency to errors of

low frequency will be approximatelyconstant, whatever the frequency classof the stimulus, provided that NH andNL are large. This is quite contrary tothe prediction of the two guessingmodels, since, as already indicated,these models cannot allow large valuesof NH and NL.

2. If, for each class of stimulus, wedivide the correct answers by theerrors which were of the correct fre-quency class, we obtain for the high-

frequency stimulus r: - r , and forIN ii — 1

the low-frequency stimulus r; - r .J.NL — iDividing one of these ratios by the

other thus gives us — X r; - r . IfIN ii — 1

we can determine TT— by some inde-INH

pendent means, then if the two ratiosare equal, this implies that an = «L.This in turn means that the "observ-ing response" class of interpretation(Model 3) is not valid. It will also ex-clude purely perceptual theories of theeffect. In that event, the response biasV must count for the entire word-frequency effect that is present.

AN ILLUSTRATIVE EXPERIMENT

MaterialsTwo lists of 60 monosyllabic words and

one of 60 disyllabic words were prepared.Each list was prepared as follows. A groupof 20 high-frequency words and anothergroup of 20 low-frequency words were se-lected, new groups being used for each list.The list of 60 was then compiled by drawingwords at random from the two groups of 20subject to the restrictions that each word oc-curred at least once and not more thantwice, that there were equal numbers ofhigh-frequency and low-frequency words andalso that not more than three successivewords were drawn from the same frequencygroup.

The high-frequency words all had frequen-cies of at least 100 occurrences per millionwords (AA in the Thorndike-Lorge, 1944,

WORD-FREQUENCY EFFECT 11

count). They were selected by taking thefirst monosyllable or disyllabic, as appropri-ate, on every tenth page of the Thorndike-Lorge word count. The low-frequencywords had frequencies of not less than 10and not more than 49 per million. (That is,they were in fact within the vocabulary ofall normal adults.) They were selected bya similar procedure, the first word being se-lected on a different page from the firsthigh-frequency word. Proper names, wordssuspected of having very different frequen-cies in English and American usage, andwords beginning with a vowel were excludedfrom both the high-frequency and the low-frequency groups; also excluded from thelow-frequency group were words havinghomonyms with higher frequencies.

The lists were recorded on one channel ofa twin-channel Ferrograph recorder, eachword being preceded by a serial numberwhich served as a ready signal; a gap ofabout 12 seconds elapsed between successivewords. Electronically generated wide-bandnoise was recorded on the second channel.The tape was played back with the outputsfrom both channels fed into a single externalloudspeaker. The gain levels were adjustedso that the speech was reproduced at com-fortable listening level (mean peak read-ings of 83 db. re .0002 dynes/cm2). Thenoise level was set by trial-and-error in pre-liminary experiments to allow about 30%correct responses in an open-ended situationwhile not resulting in perfect performance ina forced-choice: in fact the S/N ratios thatresulted were in the region of 0 db.

All 5s were British housewives from theApplied Psychology Research Unit panel be-tween the ages of 20 and 50.

Procedure

(a) Monosyllables. The 5s were tested ingroups. One group of 12 5s heard List 1of monosyllables and a second group of 12on a subsequent occasion heard List 2. Six5s of each group gave forced-choice re-sponses while the other six gave open-endedresponses. The "forced-choice" 5s weregiven two matrices, one with the 20 high-frequency words corresponding to the rowsand the other with the 20 low-frequencywords. (They were not informed of thedifference in frequency between the twolists.) The columns of each matrix werenumbered to correspond with the test num-ber on the tape. They were told that eachtest word, according to its number, wouldbe a member of one of the lists and that

they should respond by ticking in a cellon the appropriate matrix, also that theyshould avoid leaving blanks. The 5s makingopen-ended responses were told that all thewords were monosyllables and that theyshould write down whatever word theythought that they had heard even if theywere unsure about it. However, blanks wereallowed if 5 was really uncertain.

In order to avoid confusion arising from5s losing their places and not being surewhat serial number of response they shouldbe completing (the numbers were given onthe tape but were heard against the back-ground of noise) the experimenter presentedeach number visually while the correspond-ing signal was being heard.

(6) Dlsyllables. The procedure for thelist of disyllables was similar. Two groups,one of 11 and the other of 13, heard the samelist on separate occasions; five 5s madeopen-ended responses in one group and sevenin the other, the remaining 5s in each casemaking forced-choices. The 5s were in-formed that all the words would have twosyllables.

Scoring

For each 5 in the open-ended conditionsix scores were taken: (a) the number ofcorrect high-frequency responses, (6) thenumber of wrong high-frequency responses(of the same number of syllables as thestimulus) made to high-frequency stimuli,(c) the number of wrong low-frequency re-sponses made to high-frequency stimuli, (d)the number of correct low-frequency re-sponses, (e) the number of wrong high-fre-quency responses made to low-frequencystimuli, (/) the number of wrong low-fre-quency responses made to low-frequencystimuli. A high-frequency response was anyresponse word having a frequency of 100or more per million. A low-frequency re-sponse was any response word having a fre-quency of between 10 and 49 per million.Responses having a number of syllables dif-ferent from the stimulus words were not in-cluded.

Those 5s who were presented with di-syllables made a fair number of incorrect re-sponses which consisted of a stem (usuallyhigh-frequency) followed by a common suf-fix, for example, "camp-ing." Such responseswere not counted as high-frequency or low-frequency errors if the stem word was withinthe correct frequency limits because thesewords are not given as such in the Thorn-dike-Lorge word book. They could not,

12 D. E. BROADBENT

TABLE 5

MONOSYLLABLES

Stimulus

High-frequency

Low-frequency

%Correct

32.SQA

12.77B

High-frequency

errors

32.25°

41.67D

Low-frequency

errors

15.83=

19.17*1

Note.- A XFC X B

No. of LF monosyllablesNo. of HF monosyllables

= 1.512. From Thorndike and Lorge:

' 1.42.

therefore, have been included in the samplecount made to establish the relative numbersof high-frequency and low-frequency words,nor sampled as stimuli. Whether for gene-rating stimuli, classifying responses, or count-ing vocabulary size, the Thorndike-Lorgecount was always used as the criterion.

Sampling Count to Establish the Rela-tive Numbers of High-Frequency andLow-Frequency Words

On page 5 and every subsequent fifth pagethroughout the book (41 pages in all) acount was made of the numbers of (a) high-frequency monosyllables, (&) high-frequencydisyllables, (c) low-frequency monosyllables,(d) low-frequency disyllables occurring onthat page. Proper names other than Ameri-can place names were included in the countbecause several of the 5s had given propernames among their responses.

RESULTS

Forced-Choice

This condition was included in orderto confirm that the percentage of cor-

TABLE 6DISYLLABLES

Stimulus

High frequency

Low frequency

%Correct

32.77A

ll.ll8

High-"frequency

errors

9.73°

9.17D

Low-frequency

errors

6.67E

14.44F

A X FNote.—r* v R = 4.38. From Thorndike and Lorge:No. of LF disyllablesNo. of HF disyllables : 5.39.

rect responses was indeed similar forthe high-frequency and low-frequencywords in these particular tape record-ings, and therefore that the randomsampling of stimuli had not resulted inone class of words being acousticallysuperior in intelligibility. Preliminarystudies had raised a suspicion that thiscan happen with nonrandom samplessuch as PB lists, but in the presentcase it did not and the two classes ofword were equally intelligible.

Open-Ended

The percentages of responses in eachof the six categories of interest areshown in the tables. It will be noticed(a) that the word-frequency effect ismarkedly present, amounting to a dif-ference in probability of correct re-sponse of about .2; (b~) the errors ofhigh frequency are, in the experimenton monosyllables, in a constant ratioto the errors of low frequency, regard-less of the nature of the stimulus.3 Inthe case of disyllables, there is somesign that low-frequency errors are morecommon to a low-frequency stimulus:this difference is not quite significant,being due to eight 5s out of the 12tested, and will be discussed later. Itis, in any case, in the wrong directionas far as the guessing models are con-cerned. Thus these data clearly dis-prove the two guessing models; (c)in both experiments, the ratio of cor-

3 My attention has been drawn by Harris.Savin to the prediction of Model 2 that er-rors to an HF stimulus will occur dispropor-tionately often to those stimuli which happento be very similar to other words of highfrequency, and this will oppose the predic-tion tested here. We have therefore re-analyzed the data, weighting errors fromeach stimulus inversely by the total numberof errors to that stimulus, but the resultsare unchanged. It will of course be evidentthat Models 2 and 4 are in some ways verysimilar, so that supporters of the former maybe happy to regard the latter as a modifica-tion of it.

WORD-FREQUENCY EFFECT 13

rect responses to errors of the appropri-ate frequency class, when compared forhigh- and for low-frequency stimuli,gave approximately the correct predic-tion of the relative number of words inthe frequency classes according to theThorndike-Lorge word count. Thedifference from the correct value isnot, in fact, significant. If we work outthe value for each individual S, thenamong the group receiving monosylla-bles seven 5"s gave an estimate largerthan that from the Thorndike-Lorgeand five 5"s gave a smaller estimate,while among the group receiving di-syllables the numbers were five andseven. Thus it appears that there isno difference between high-frequencyand low-frequency words in the quan-tity corresponding to d' in signal-detec-tion theory: The entire word-frequencyeffect is due to Model 4.

CONCLUSIONS AND LIMITATIONS

The considerable number of experi-ments already in the literature on thistopic have not provided data analyzedin this way. Consequently they do notassist us in deciding whether Model 4explains the word-frequency effect inall cases, or whether the experimentcited is in some way peculiar. How-ever, the experiment appears reasonablyrepresentative, and the author has beenunable to find any feature of earlierresults which Model 4 is unable to ex-plain. Therefore, until some data areanalyzed in this way and give contraryresults, it would seem simplest to holdthat Model 4 has been operative in allexperiments on word frequency. Thismeans

(a) that the effect is not due tobiased guessing on trials when thestimulus has left correct and incorrectwords equally probable,

(b) that the effect is not due to anincrease of the stimulus contribution to

correct perception of high-frequencywords, but

(c) that the effect is due to a priorbias in favor of common words, whichcombines with sensory evidence favor-ing the objectively correct word.

It may be worth noting certainchanges in conditions which might beexpected to alter the pattern of results.For example, small values of NH andNL will tend to produce data which donot exclude Models 1 and 2. This isbecause the difference between NH andNH — 1 will then become important, sothat the relative number of errors whichare common words will increase if thestimulus is uncommon. We have foundthis to apply to forced-choice experi-ments, and also to visual rather thanauditory ones. In the visual case,errors usually have several individualletters in common with the stimulus,and this restricts the effective size ofNH and NL. One would expect a simi-lar pattern of results with an auditoryexperiment at high signal-noise ratios.

Experiments showing this featurewould, however, merely fail to disproveModels 1 and 2; they would not be evi-dence against Model 4. It is moreimportant to consider cases in whichModel 4 might be found insufficient.

One such case might be that in whichunwillingness to respond at all becomesa major factor. Absence of responsewas allowed in our experiment, and solong as 51 does not use this possibilitytoo often, the various ways in whichit might be included in the mathematicsdo not differ much in the predictionsthey produce. Some (not all) of themmight, however, require adjustment ofModel 4 to fit data in which absenceof response was common.

Perhaps more important is the pos-sibility that stimulus words may carryinformation about their frequency class.As already indicated, Brown and Ru-

14 D. E. BROADBENT

benstein (1961) concluded this, al-though providing data inconsistent withModel 3. Their conclusion is depend-ent, however, upon the particular as-sumptions implicit in their equations,and from our present point of viewthere is no need to accept it. Our re-sults on monosyllables positively opposeit. There was, however, an insignifi-cant tendency among disyllables forerrors to be more common in the fre-quency class of the objective stimulus.Furthermore, the phenomenon of the"descent of the median" (Pollack,1962) makes it seem likely that errorfrequencies sometimes change with thepopulation of words presented. There-fore, although there is no positive evi-dence on this point, it may be thatModel 4 may in some situations requiremodification by increasing V for HFstimuli.

Many, including the author, may re-gret the exclusion of any perceptualfiltering or observing response mecha-nism. As some consolation we mightpostulate that such a mechanism couldonly become operative if relatively fewcues were involved, that is, if NH andNL were small either through the useof a small vocabulary or through apowerful context. However, attemptsin Cambridge to find such an effecthave so far failed completely.

The supporters of a purely perceptualeffect might rather consider that theuse of the term response bias is per-haps misleading when it is applied toa model of the present type. It willbe clear that the bias which has beenpostulated is not something which af-fects only the final overt response ofwriting down or uttering the word, butrather a bias applied to some centralevent, which may or may not occurfollowing the delivery of a stimulus atthe sense organs. The author wouldnot think that a response bias in thissense can be described as an artifact.

Rather it is a particular part of theperceptual mechanism. The term re-sponse bias is also objectionable becauseit suggests a kind of peripheralist the-ory which is now clearly unsatisfactory.Nevertheless, the bias which appearsin the present model would explain re-sults such as those of Goldiamond andHawkins and the reduction of theword-frequency effect in forced-choicesituations, and these are the phenomenawhich have given rise to the usual useof the term response bias. It is to behoped that many of those who opposethe usefulness of the concept in itssense of pure or sophisticated guessingmay nevertheless welcome its appear-ance as a parameter in a theory of per-ception based upon signal-detectiontheory.

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(Received September 28, 1965)