A comparison of five methods ofillusion measurement

STANLEY COREN*The Graduate Faculty of the New School for Social Research

New York, New York 10011and

JOAN S. GIRGUSThe City College of the City University of New York

New York, New York 10031

The relative efficiency of five techniques of illusion measurement were testedon parametric variations of the Mueller-Lyer and Ebbinghaus figures. Themethods of average error, reproduction, and selection from a graded series allshowed significant effects of configurational variations. The subjective scalingtechniques each failed to measure adequately changes in illusion magnitude forone illusion configuration. The suitability of the tested measures for groupadministration is also discussed.

Ever since the tum of the century,when Judd (1899, 1902,1905), Lewis(1908, 1909), and Seashore and hisassociates (Seashore & Williams, 1900,1902; Seashore, Carter, Farnum, &Sies, 1908) were beginning theparametric quantitative study of visualgeometric illusions, the method ofaverage error (sometimes called themethod of adjustment) has been themost frequently utilized method ofmeasurement. In this method, S setsan adjustable figural component tomatch a corresponding componentdistorted by the illusion. Thepopularity of this method of illusionmeasurement has persisted over thelast 70 years, although many othermeasures of illusion magnitude haveappeared in the literature since theseearly investigations.

A random sampling of 60 recentillusion articles reveals an interestingdistribution of measurementtechniques. These articles wereselected from the American Journal ofPsychology, Journal of ExperimentalPsychology, Perception & Psycho­physics, Perceptual and MotorSkills, Psychonomic Science, QuarterlyJournal of Experimental Psychology,and Scandinavian Journal ofPsychology, between 1967 and thefirst three months of 1972. Themethod of average error stilldominates, as is evidenced by its use in45% of the sampled articles. All of theexperiments in the sample that utilizedthis technique tested Ss individually.This method has been used to measureillusions of extent (Burnham, 1968;Coren, 1970b), direction (Coren,1969; Coren & Girgus, 1972), andcontour or curvature (Coren, 1970a).A typical example of its use is foundin Festinger, White, & Allyn (1968),

*Mailinll addreu: 66 west 12th Street.New Yolk, New Yolk 10011.

among others. In this situation, theapparently longer half of aMueller-Lyer figure is made adjustablein length. S's task is to set thisadjustable portion of the figure until itappears to be equal in length to theapparently shorter half of theconfiguration. One persistent problemwith the method of average error is thedifficulty in constructing apparatusthat permits variation of certainstimulus dimensions, such as curvatureor shape.

The second most prevalent form ofmeasurement in the sample is basedupon S's ability to reproduce theperceived illusory distortion either bydrawing it or by marking off anappropriate extent on a comparisonfigure. This method was employed in12% of the sampled experiments. Atypical example of its use in an illusionof extent is found in Erlebacher andSekuler (1969), who required Ss tomark off the apparent length of theshaft of a projected Mueller-Lyerfigure on a line provided on a sheet ofpaper in front of them. Pressey andSweeney (1969) have adapted thismethod to measure an illusion ofdirection. One of the advantages of themethod of reproduction is that itrequires little apparatus. In addition, itmay be used for group presentations.

The methods of constant stimuliand paired comparison account for10% of the studies surveyed. Thesemethods usually involve successivecomparisons of pairs of figures eitheragainst a standard or against otherforms of the illusion. Typically, thisprocedure is used in attempts todemonstrate the existence of anillusion, and thus it is rarely used tomeasure the magnitude of thedistortion as a function of variousstimulus attributes. An example of thismethod is found in Bolles (1969), whosimply asks Ss to judge the apparently

longer section of the Mueller-Lyeragainst the apparently shorter in orderto ascertain whether the illusion stillexists when the configuration is ofsub foveal size. One of the problemswith paired comparison methods is thelarge number of judgments (and henceexposures) needed to obtain accuratedata. Since many illusions are knownto decrement with repeated exposures(Coren & Girgus, 1972), one is apt toget underestimations of the illusoryeffect using these techniques.

A technique that seems to embodysome of the advantages of the methodof average error but that requires lessin the way of apparatus involves theuse of a graded series of comparisonstimuli. The S's task is to select thecomparison stimulus that most closelymatches the test stimulus along thecritical dimension. This methodclosely resembles a recognition ormultiple choice paradigm, since the Ssimply looks over the simultaneouslyvisible array until he finds thecomparison figure that he feels is mostsimilar to the test element. Thisprocedure was used in 7% of thestudies sampled. An example comesfrom Virsu (1971), who used theprocedure to measure a curvatureillusion by asking S to select a circlefrom a graded series of circles, allvisible simultaneously. The selectedcircle was to look like a continuationof the degree of curvature of apreviously viewed arc. One of theproblems with this type ofmeasurement lies in the fact that Sstend to select items from the middleof the series. There is also a propensityto select the same stimulus repeatedlyin order to maintain apparentconsistency. Ease of presentation andadaptability for group presentationsare obvious advantages of this method.

Two subjective measurementtechniques, which allow relativejudgments but which, unfortunately,do not allow translation of responsesinto a physical metric, also appear inthe sample. The first is a rating scaletechnique that asks S to choose averbal label that most clearly describesthe figure that he is judging. Thistechnique accounts for 8% of thestudies reviewed. Restle and Merryman(1968) use this procedure to measurethe magnitude of the Baldwin illusion(a size contrast figure). Ss are requiredto indicate whether the stimulus thatthey are viewing is "very long, long,moderately long, moderately short,short, or very short. .. The secondsubjective measure found in thesample is the method of magnitudeestimation. This technique simplyrequires S to assign a numberproportional to the perceived size,curvature, etc., of the critical elementin the illusion figure. This technique,

240 Bebav. Rei. Meth. & Inatru., 1972, Vol. 4 (5)

Fig. 1. A-The Mueller-Lyer configuration in which both horizontal lines areof equal length, although the line with the outgoing wings is apparently longer.B-The Ebbinghaus illusion in which both central circles are equal in sizealthough the one surrounded by the larger circles is apparently smaller than theone surrounded by the smaller circles.

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used either with or without a standard,accounts for 7% of the studies. Anexample of the use of this method isprovided by Virsu (1967), whomeasured the magnitude of theMueller-Lyer, the filled space-openspace illusion, a perspective illusionand a variant of the Ebbinghausillusion. Ss were simply required toestimate the apparent size of thecritical elements in centimeters. Bothof these techniques can be used ingroup paradigms and require littleapparatus.

The remainder of the sampleconsisted of one crossmodal matchingstudy (Moses & Disisto, 1970) and anumber of demonstrational papersthat involved no direct measurementsand account for the final 10%. It is ofinterest to note that only 9% of thestudies surveyed tested more than oneS per session, despite the fact that 44%of the studies sampled used methodsthat could easily be adapted to grouppresentation. This is probably due, atleast in part, to a general suspicionabout the adequacy and accuracy ofgroup measures of illusion magnitude.

Given the variety of methods ofillusion measurement found in thissample of the literature, it might besomewhat difficult for an investigatorto decide among them, especially giventhe fact that few studies exist that testthe relative efficiency of the variousmethods under comparable conditionsand with comparable stimuli. In order

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to provide such a basis for choice, itseemed desirable to studysystematically the sensitivity andefficacy of various measurementtechniques in assessing parametricdifferences in illusion magnitude. As asecondary goal, it seemed desirable toassess whether measures of illusionstrength suitable for groupadministration are presently available.

METHODSSubjects

Twenty-six undergraduatevolunteers, participating for pointcredits in introductory psychology,served as Ss.

StimuliSince we are attempting to assess

the usefulness of various methods usedin parametric studies of illusionmagnitude, two illusions whosemagnitude can be varied systematicallywere selected: the Mueller-Lyer, whichhas long been known to vary instrength as a function of the anglebetween the wings (Lewis, 1909;Dewar, 1967) and the Ebbinghausillusion (frequently called Titchener'scircles), in which the apparent size of acentral circle varies as a function ofthe size of a number of surrounding orcontext circles (Girgus, Coren, &Agdem, 1972; Massaro & Anderson,1971). These configurations are shownin Fig. 1.

For the Mueller-Lyer, the

apparently longer half of theconfiguration was used as a teststimulus. The shaft was 8 em long andthe wings were 2 em long. The anglebetween the wings was 15, 45, or75 deg. For the Ebbinghaus figure, thecentral test stimulus was an outlinecircle 14 mm in diam. Four contextcircles were arranged around thecentral circle at a distance of 6 mm.These context circles could havediameters of 5, 10, 18, or 23 mm.

ProcedureThe methods of measurement to be

evaluated ithis study are the methodof average error (adjustment),reproduction, selection from a gradedseries, rating scale, and magnitudeestimation. These five methodsrepresent the procedures used in 89%of the studies surveyed above,excluding those that utilized no formalmeasurement procedures.

Method of Average ErrorFor the Mueller-Lyer figure, Ss were

required to adjust a variable line untilit matched the length of a linedistorted by the illusion. The variableline was drawn in black ink and set ina heavy pasteboard tongue and groovearrangement. A scale affixed to thesliding portion of the apparatusallowed readings to be taken inmillimeters.

For the Ebbinghaus illusion,judgments were made by rotating awheel that presented singlecomparison circles (with nosurrounding circles) ranging indiameter from 8.0 to 19.5 mm in stepsof 0.5 mm. The circles appeared one ata time in a 26-mm aperture cut intothe apparatus.

Reproduction MethodFor the Mueller-Lyer, the stimuli

were printed one to a page. On eachpage, a 12-cm line was placed 10 emdown and somewhat to the right ofthe stimulus. S was required toestimate the apparent length of theshaft of the illusion by marking off theappropriate distance on this line. Theprocedure was similar for theEbbinghaus figures, only here S wasasked to indicate the apparentdiameter of the test circle by markingoff the appropriate length on the line.

Graded Series MethodAgain, all test stimuli were printed

one to a page. For the Mueller-Lyer,the set of comparison stimuli consistedof 27 line lengths (numbered 1 to 27)that ranged in size from 5.6 to10.6 cm in 2-mm steps. Thecomparison stimuli were presented inan ordered array on a separate page,with the shortest line at the top of thepage and the longest at the bottom. Ss

Behav. Res. Meth. & Instru., 1972, Vol. 4 (5) 241

Fig.2. A-The apparent size of the shaft of the Mueller-Lyer illusion incentimeters plotted as a function of angle size for the methods of average error(AE), reproduction (R), and selection from a graded series (GS). B-The relativesize of the shaft of the Mueller-Lyer judged against a standard line measured viamagnitude estimation (M) and rating scale (RT).

Magnitude EstimationAs in the rating scale procedure,

each Mueller-Lyer stimulus appearedon the same page as an 8-cm standard,only now the standard was labeled

are manifested; (2) whether theobtained results are stable enough toyield statistically significant effects asa result of the parametricmanipulations; and (3) the nature ofthe relationship between themagnitude of the observed effects andthe variability of measurement. Wewill consider each of these points inturn.

The first point concerns whethereach of the methods produces theexpected results. For the apparentlylonger segment of the Mueller-Lyer,the data of Lewis (1909) would leadus to expect that the apparent lengthof the shaft will decrease as the anglebetween the wings increases. For theEbbinghaus figure, the extant datalead us to expect that the perceivedsize of the central test circle will varyinversely with the size of thesurrounding circles.

Unfortunately the data cannot allbe presented on anyone graph, since itis impossible to convert all of the datato any single metric. Although themethod of average error, reproduction,and selection from a graded series allallow the direct translation ofjudgments into physical equivalents,the rating scale and method ofmagnitude estimation do not. For thisreason, the data from the former threemethods will be presented on onegraph while the data from the lattertwo methods will be plotted on aseparate graph. Figures 2a and 2bpresent the data from theMueUer-Lyer, and Fig. 3a and 3bcontain the data from the Ebbinghausfigure.

It is clear from the figures that theexpected ordinal relationships doappear in all of the measurementmethods tested. All five methods showa decrease in apparent size of theMueller-Lyer shaft with larger anglesbetween the wings. Similarly, theapparent size of the central test circlein the Ebbinghaus configuration variesinversely with size of the inducingcircles. The only perturbations appearin the Ebbinghaus figure where themethods of selection from a gradedseries and magnitude estimation fail toshow a difference between the 18- and23-mm inducers.

It is interesting to note that all ofthe curves for the Ebbinghaus figureshow underestimation relative to theactual physical size of 14 mm, Thus,although the expected relative sizechanges appeared in the data, the usualabsolute changes did not. However, aspointed out by Massaro and Anderson(1971) and Girgus etal (1972), thisprobably indicates a constant errorthat is due to contextual effectsoperating on the comparison circles aswell as on the test circles. Theseeffects do illustrate that in situations

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"100 units." Using this as a modulus,Ss were required to estimate the lengthof the shaft of the illusion in arbitraryunits. A similar procedure was used inthe Ebbinghaus illusion, only here thestandard was a 14-mm-diam circle thatwas labeled "100 uni ts. "

The stimulus materials were boundinto booklets, each of which consistedof one set of illusion stimuli and onemeasurement technique, preceded by apage of instructions. Within eachbooklet the stimuli were randomlyordered, and the illusions andmeasures were randomly ordered perS. In addition, there were a number ofinterpolated filler tasks, such as linebisection of direction estimates. It washoped that these would provideintervals between successive measuresof the same illusion so as to minimizeany decrement of illusion magnitudethat might occur with prolonged orrepeated exposures to the testconfigurations. Ss were tested ingroups ranging from two to six innumber and were allowed to set theirown working pace. On two occasionsduring the session, as the S reached theend of a set of measures, he wasstopped and individually tested on oneof the illusions using the method ofaverage error. One measurement wastaken from each S on each illusionstimulus, under each of the fivemeasurement procedures.

RESULTS AND DISCUSSIONOur consideration of the efficiency

of these five methods of illusionmeasurement must focus on threeissues: (1) whether or not theexpected trends in illusion magnitudewith variation of stimulus parameters

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were asked to remove this page fromtheir booklets so that it could beviewed easily at the same time as theillusion stimuli. They were required tojudge which line most closelyapproximated the length of the shaftof the illusion figure. For theEbbinghaus illusion, the graded seriesconsisted of 17 circles, numbered from1 to 17 and arranged in a similargraded series, with the smallest circleat the top of the page and the largestat the bottom. The circles ranged insize from 11 to 18 mm in steps of0.5 mm, Ss were required to indicatethe number of the circle that mostclosely approximated the size of thetest circle.

Rating ScaleFor the Mueller-Lyer, in addition to

the single illusion stimulus on eachpage, 10 em down and to the right ofthe figure there appeared an 8 em line(equal in length to the shaft). At thebottom of the page there was a 7-pointrating scale labeled "very much larger,

. much larger, larger, equal, smaller,much smaller, very much smaller." Sswere required to check the point onthe scale appropriate to theirperception of the relative size of theillusion test element compared to thestandard. A similar procedure wasfollowed for the Ebbinghaus figure,only here the standard was a14-mm-diam outline circle.

242 Behav. Res. Meth. & Instru., 1972, Vol. 4 (5)

squares of the means, over the totalsum of squares, with both valuescorrected for the magnitude of theerror variance (Hays, 1963). Thecolumn marked w' . in Table 1contains these values. For theMueller-Lyer, the indication is that themethod of average error demonstratesa very strong effect, producing resultsin which the variation of anglesexplains some 23.3% of the variance.The method of reproduction andmagnitude estimation are onlyone-third as efficient, handling some7% of the variance, and the gradedseries explains only 3%. (Note that, fornonsignificant F ratios such as thatmanifested by the rating scale data,w 2 is automatically set to zero.) Forthe Ebbinghaus figures, the gradedseries is actually the most efficient,with 18% of the variance explained bysize of the inducer, and the method ofaverage error and rating scale areequivalent to each other, with 14% ofthe variance explained.

Some conclusions andrecommendations can be drawn fromthese data and their analysis. First, itmust be made clear that the observerswho participated in this experimentwere experimentally naive and madeonly one judgment per figure permeasure. Thus, we are utilizing a verystringent set of conditions to measurethe effectiveness of the techniques.The fact that four out of five measuresproduced the expected results atacceptable levels of statisticalreliability for each illusion isheartening. The failure of one of thesubjective measures to demonstratereliable changes in illusion magnitudesfor each of the illusion figures isdistressing but may reflect thenecessity for pretraining before theactual measurement session ratherthan any inherent weakness in thesescaling procedures. Note, however,that any such pretraining mayintroduce the problem of illusiondecrement. In addition, the fact thatthe subjective techniques of ratingscale and magnitude estimation do notprovide a means of translation of thedata back into corresponding physicalunits renders it difficult to compareresults of studies conducted underdiffering conditions or in differentlaboratories.

Since the methods of average error,

Mueller-Lyer Ebbin&haua

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scaling procedures comes from Eyman(1967) who reports that sophisticatedand unsophisticated observers, testedon a magnitude estimation task, tendto give the same mean judgments butsignificantly different variability.

Studies such as these might lead usto expect more stable results on thesubjective scales if Ss were initiallypretrained or practiced. The necessityof such practice, however, presents thepossibility of contamination of thedata by illusion decrement withexposure, such as that observed byCoren and Girgus (1972). This wouldtend to attenuate the magnitude of theillusions and hence reduce anyobserved parametric variations in thestrength of the distortion.

One comparison of great interest inassessing the efficacy of any measure isthe question of the relationship of themeasured magnitude of the effect (thevariability of the means) and the over­all variability of measurement (thevariability of the Ss). Simply lookingat the standard deviations of the scoresdoes not give this answer. However,the answer to this question may beobtained by computation of w',which is an estimate of the amount ofvariance explained and is obtainedessentially by a ratio of the sum of

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Fig. 3. A-The apparent size of the central test circle in the Ebbinghausillusion in millimeters plotted as a function of the size of the surrounding circlesin millimeters for the methods of average error (AE), reproduction (R), andselection from a graded series (GS). B-The relative size of the central circlejudged against a standard circle measured via magnitude estimation (M) andrating scale (RT).

where absolute measurements areneeded (rather than relative illusionmagnitudes), a control figure with noinducing components should beincluded to provide a baseline.

The statistical results do not showas consistent a pattern as do thefigures. Table 1 presents theappropriate comparisons. The columnmarked "F" indicates the F ratioscomputed from analyses of varianceperformed on the data from eachillusion and each measure. Theserepresent the main effect of angle sizefor the Mueller-Lyer and of inducersize for the Ebbinghaus figure.

For the Mueller·Lyer, all of themethods show the expected variationof shaft size to be significant atp < .05 or better, except for the ratingscale data. For the Ebbinghausconfiguration, all of the methods showstatistical reliability at the 5% level orbetter except for the magnitudeestimation task. The reasons for thisrelative insensitivity of the subjectivescales are not immediately apparent.Certainly it is not the case that Ss didnot understand the task, since all thoseinterviewed after the sessions reportedno difficulty whatsoever. It is possiblethat experimentally naive Ss may needsome practice with these subjectiveprocedures in order to establish someframe of reference or internalmodulus. This is supported by the factthat Restle and M@rryman (1968),when using a rating scale to measurethe magnitude of the Baldwin illusion,felt it necessary to provide a practiceseries of judgments on the entire set ofstimuli, before collecting his data.Following this practice run, fairlystable data were obtained. A moredirect test of the stability of subjective

Behav. Res. Meth. & Instru., 1972, Vol. 4 (5)

reproduction, and selection from agraded series produced statisticallyreliable results for both configurations,one would be tempted to designatethem as the methods of choice. Theexpected, overwhelming superiority ofthe method of average error, basedupon its traditional use wheneverpossible, even in the face ofcomplicated apparatus difficulties, didnot emerge. Under the conditionstested, the methods of reproduction orselection from a graded series seem togive nearly equivalent results to themethod of adjustment. These lattertwo methods have the additionaladvantages of requiring little apparatusand being suitable for group testing.The fact that these data were actuallygathered in a group testing situationindicates that the traditional distrustof group measures may beunwarranted, at least if theappropriate measurement techniquesare employed.

In sum then, we can conclude thatthe methods of average error,reproduction, and selection from agraded series are efficient measures ofvariations in illusion magnitude, and,at least under conditions where nopretraining is available to theobservers, these measures are probablypreferable to rating scales or themethod of magnitude estimation.

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