CHRISTOPHER A. BAYERt and A. W. PRESSEYUniversity of Manitoba, Winnipeg, Canada

Geometrie illusions as a funetion ofpigmentation of the Fundus oculi

and target size*

A within-race design was employed in which two forms of the Mueller-Lyerillusion and the vertical-horizontal illusion were studied as a function ofpigmentation density of the eye and target size. It was found that the illusionsdid not vary as a function of pigmentation density. In addition, with an increasein target size the ingoing Mueller-Lyer and vertical-horizontal illusions remainedrelatively constant but the outgoing Mueller-Lyer illusion decreased.Explanations are offered for both sets of results.

In 1967 , Pollack and Silvarmeasured the outgoing form of theMueller-Lyer illusion in children (8 to14 years of age) who differed inpigmentation of the Fundus oculi.They concluded that degree ofpigmentation was highly related tomagnitude of illusion; Le., deeplypigmented Os exhibited a smallerillusion than did lightly pigmented Os.However, scepticism about such aconclusion is generated by the kind ofexperiment they conducted. For onething, Pollack and Silvar employedwhat is, in essence, a between-racedesign. Eighty-seven percent of the Osin the darkly pigmented group wereNegro, and 95% of the lightlypigmented group were Caucasian. It ispossible that racial and culturalvariables other than pigmentationproduced the differences that theyobtained. A second weakness in theirexperiment is that they failed toprovide measurements of a control linein the different pigrnentation groups.A control condition is especiallyimportant when organismic variablesare being investigated. For example, itis possible that pigmentation affectsmeasurernents of nonillusory targets.If lines alone are overestimated bylightly pigmented Os, then the resuItsobtained by Pollack and Silvar wouldbe explained without any reference toillusions. The major purpose of thisexperiment was to measure geometricillusions only in Caucasian Os whovaried in degree of pigmentation andto provide control conditions to assesswhether measurements of nonillusoryt a r ge t s vary as a funetion ofpigmentation.

*This studv is based on a Master's thesissubmitted bv C. A. Bayer to the Unive rsitvof Manitoba. It was supported in part bv aNational Reserach Council of Canada grant(APA-177) to the second author.

tRequests for reprints should be sent toChristopher A. Bayer, Departrnen t ofPsychology, University of ManitobaWinnipeg 19, Canada. '

Psychon. Sei., 1972, Vol. 26 (2)

A second objective was to assess thegenerality of Pollack and Silvar'sfindings. Specifically, we sought todetermine whether pigmentationaffects different types of illusions andwhether pigmentation interacts with astimulus variable which is known tohave a strong effect on magnitude ofillusion-rviz, target size. The types ofillusions chosen were (1) the outgoingM u e l l e r-Ly e r , (2) the i n go in.gMueller-Lyer, and (3) thevertical-horizontal illusions.

SUBJECTSSeventy-four men enrolled in

introductory psychology at theUniversity of Manitoba served as Os.The sampie was restricted to CaucasianManitobans between the ages of 18and 22 years who had normal visionwith or without glasses. The mean agewas 20.4 years, and Os who normallywore glasses did so during testing.

APPARATUSThe apparatus consisted of a white

target holder, 36.8 cm wide and39.5 cm high. The face of the holderwas tilted backward 20 deg from theperpendicular. A chinrest was placedin front of the holder (andperpendicular to the line of sight) sothat the distance between O's eyes andthe face of the frame was about41 cm. One lamp (lit by a 100-W bluelight bulb) was placed on each side ofthe target holder about 25 cm awayfrorn, but perpendicular to, the side ofthe holder.

Nine illusory targets and threecontrol targets were prepared withblack ink and printed separatelyon21.5 x 28.0 cm sheets of white paper.Three ingoing and three outgoingforms of the Mueller-Lyer illusion, invertical orientation, were used. Thedistance between apices .for each formwas 10, 35, and 60 mm. The obliqueswere one-quarter of the lengthbetween apices and the interior anglesformed by the obliques were 90 deg.Each target was centered on animaginary point 60 mm from the top

and 14 cm from either side of thesheet. A dot was located directly tothe right and slightly below the topapex of each target for the purpose oforienting O's response, since a methodof production was employed. Forexample , in the 10-mm target the dotwas 10 mm to the right and 2.5 mmbelow the top apex. As target sizeincreased, the dot was moved so that itwas in the same relative location foreach target.

Three t a r g e t s of thevertial-horizontal illusion were used.The lengths of the horizontalcomponents (which were drawnparallel to the top of the sheet) were10, 35, and 60 mm. A dot was drawnin the middle of each horizontal line,and this dot corresponded to theimaginary center employed in theMueller-Lyer targets, The three controltargets were identical to theMueller-Lyer targets, except that theobliques were replaced by dots. Thedistances between dots were 10, 35,and 60 mm.

PROCEDUREThe Os were divided into five

groups on the basis of relativeperceived darkness (density) of thepigmentation of the Fundus oculi. Thearea of the retina viewed was betweenthe maeula lutea and the optic disk ,This area was chosen for two reasons:(1) the relative absence of bloodvessels on the retinal surface, and(2) the ease with which this area eanbe loeated eonsistently and foeusedupon. An optometrist.! using abattery-handle May ophthalmoscope,perforrned the ratings in a dark room.The c at e go r i zation of Os wasjudgmental. In i t i a lly, Os weredistinguished on a 3-point basis:"light," "medium," and "dark." Asthe number of Os examined increased,"light-medium" and "medium-dark"eategories were also able to beincluded. There were 15, 9, 21, 15,and 14 Os in Groups 1 (light) to 5(dark ), respeetively.

The Os sat in front of the apparatusand were shown the 10-mm version ofeach target. For the Mueller-Lyertargets, it was explained that the taskwas to mark a point directly below thedot so that the distance he produceda p p e ared equal to the distaneebetween apices, For the horizontalline, he was asked to draw a dotdirectly below the bisecting dot sotha t the distance between dotsappeared equal to the horizontal line.For the control cards, the sameresponse was required, exeept that thedistance between dots was to bereproduced. It was emphasized thatonly one response could be made oneach target and that judgments were tobe made visually, i.e., arm movementsto aid the judgment of length were not

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Fig.l. The vertical-horizontal andMueller-Lyer illusions as a function oftarget size.

22 c]­

20 5~!

change as target size increases, but theo u t go i n g Mueller-Lyer i l l usiondecreases.

DISCUSSIONThe results of this study do not

support the conclusion by Pollack andSilvar that fundus density affects themagnitude of geometrie illusions. Thisdifference could be due to the factthat, in Pollack and Silvar's study, thecritical variable was not pigrnentationof the Fundus oculi but some otherracial or cultural variable. It could alsobe argued that, within a Caucasiangroup, pigmentation does not varye n o u g h to prod uce significantdifferences in illusion. However, if thiswere so, it would be extremelydifficult to test the relationshipbetween pigmentation and illusionwithout confounding other variables.Indeed, the strategy of blocking Os onthe basis of rated pigmentation wouldnot be an appropriate one.

One might also argue that thedifference between the two studies isdue to the different populationsemployed. However, conversion ofPollack and Silvar's data (i.e., themean magnitude of illusion) intopercent illusion form indicates thatlightly pigmented children yielded a17.68% illusion on the outgoingMu e l l er-Lyer form, while darklypigmented children yielded a 12.86%illusion on the same form. In thepresent s t udy, Caucasian adultsyielded a 14.50% illusion on theo u t go i n g Mu e l ler-Lyer form ofapproximately the same visual angle(i.e., the 10-mm form) as that used byPollack and Silvar. The Mueller-Lyerillusion is a Plaget (1969) Type I

illusion--it de creascs with age. Thisfinding is based on data mainly fromCaucasian populations. Since Pollackand Silvar 's lightly pigrnented groupwas 95% Caucasian, the expecteddccrease in illusion (from 17.68% to14.50%) with age is demonstratedwhen the previous study's data iscompared to the data presented here.Based on this comparison, it seemsreasonable to assurne that the data ofthe present study is reliable.

Finally, it could be argued that thedifference between the two studies isdue to the different psychophysicalmethods e mployed. It is notimmediately obvious whypigmentation should interact withpsychophysical method, but even if itwere true, the results of this studywould indicate that pigrnentationplays a role only under very limitedconditions and, as such, is probablynot an important variable in theperception of illusions.

The results on the effects of targetsize are consistent with previousfindings, but they also throw new lighton the matter. Begelman & Steinfeld(1967) in vestigated the effect 0 f targetsize on the vertical-horizontal illusionand concluded that the illusiondecreases as a function of size if thehorizontal portion is the variablestimulus but r ernains relativelyconstant if the vertical line is variable.Since in this study judgments weremade (of a horizontal standard) alonga vertical dime nsion, the results areconsistent with those obtained byBegeiman and Steinfeld.

Two studies have been carried outin which target size was varied in theMueller-Lyer illusion (Binet, 1895;Heymans, 1896). Both of theseinvestigators used a method ofmeasuring the ingoing illusion with theoutgoing illusion, or vice versa, andboth concluded that the Mueller-Lyerillusion decreased with an increase intarget size. The results of the presentstudy show that it is the outgoingillusion which produces the decrease.

The assimilation theory ofgeometrie illusions (Pressey, 1971)provides a relatively simpleexplanation of the interaction betweenforms of the Mueller-Lyer illusion andtarget size. This theory states that theMueller-Lyer illusion is due to theassimilation of the standard line toeither the shorter or Ionger magnitudesenclosed by the obliques. Moreover, itstates that the effectiveness of acontext decreases as the distance fromthe center of the field increases(Pressey , Butchard, & Scrivner, inpress). Operationally, the center of afield is defined by determining themost extreme elements to be judged(as set by instructions) and calculatingthe midpoint of these elements.

60

- VertlCal -Horizontal----Ou'going Müller-Lyer

-Ingoing Muller-L~r

35

TARGET-SIZE (in mm.l

10

allowed. Moreover, responses were tobe made only after a signal was given.

Each 0 received all combinations oftype and size of target. The stimuliwere presented in four consecutiveblocks of 12 targets in each block. Theorder of targets was randomizedwithin blocks, between blocks, andbetween Os.

A mernory drum, set at 5 sec,controlled viewing time. It was startedas soon as the target was placed on thestand, and a loud dick signalad 0 tomake his response. The sheet was thenremoved and a new trial began whenthe next target was placed on thestand. The illuminance of the stimuli,at the face of the holder, was 10 fc.

RESULTSReproductions of length were

measured by a transparent millimeterscale , and these measurements wereaccurate to within 0.5 nun. In the firstanalysis, the control scores weresubjected to an analysis of variance.Only target size had a significanteffect. Pigmentation had no effect onthe control scores and, even whenGroups 1 and 2 were compared withGroups 4 and 5, no discernible trendswere present.

Magnitude of illusion was calculatedby subtracting the mean control scorefrom the mean illusion score for eachof the nine targets. These scores werethen divided by the standard distanceto obtain a "percent illusion." Ananalysis of variance, in which the maineffects were type of illusion, targetsize , and fundus density, was carriedout. The F value for type of illusionwas 41.96 (df =2/138; p < .01) andfor target size it was 5.30 (df = 2/138;P < .01). The F value for the Type ofIllusion by Size interaction was 3.57(df =4/276; P < .05). None of theremairring F values was significant atthe .05 level.

In a se'cond analysis, the scores forthe vertical-horizontal illusion wereremoved and an analysis of variancewas again performed. The F value fortarget size was 9.83 (df =2/138;P < .01) and for Type of Illusion bySi z e interaction i t was 6.11(df = 2/138; p < .01). None of theremairring F values was significant atthe .05 level.

It is clear from these analyses thatfundus density had no effect on them a g n i t ud e of either of theMueller-Lyer illusions or thevertical-horizontal illusion. Once again,the extreme fundus density groupswere blocked, and, as with the controlscores, no systernatic trends wereevident.

The relationship of illusion to targetsize is shown in Fig.1. Theoutstanding feature of these results isthat the ingoing Mueller-Lyer and thevertical-horizontal illusions do not

78 Psy chon. Sei., 1972, Vol. 26 (2)

Now, when a very small o utgoingMueller-Lyer illusion is employed, theobliq ues are located near the center ofthe field and will contribute a greatdeal to the judgment of the standarddistance. However, as target sizeincreases, the tips of the obliquesmove further and further from thecenter of the field and hence becomef airly ineffective in altering thepercept. In other words, in a very largetarget, it becomes relatively easy to"gate " out the context by the simpleprocedure of not directing eyemovements to the obliques. It shouldbe noted that, according to thisanalysis, increasing target size hasroughly the same effect as decreasingthe length of the outgoing obliques,and therefore, the illusion shoulddecline with an increase in target size.

The ingoing Mueller-Lyer illusion,on the other hand, should not changeas a function of target size. Theingoing obliques are always orientedtowards the center o] the [ield . Nomatter how large the target, if the 0 isto judge its length he must process

Psychon. Sei., 1972. Vol. 26 (2)

information from one extreme edge tothe other extreme edge of the standarddistance. As he does so, the ingoingobliques fall in the same relativeposition to the center of the field andhence remain of constanteffectiveness.

The final point worth mentioningabout the data is that, in the very largetargets, the ingoing illusion is largerthan the outgoing illusion. Manyinvestigators have reported that it isthe outgoing illusion which produces alarger effect. As argued in an earlierpaper (Butchard & Pressey, 1971), theproper conclusion appears to be thatthe form of illusion which is largerdepends upon stimulus variables suchas length of obliques, angle ofobliques.f and target size.

REFERENCESBEGELMAN. D., & STEINFELD. G. An

investigation of several parameters of theh oriz orrtal-vertical illusion. Perception &Psvchophysfcs, 1967, 2.539-543.

BINET, A. La mesures des Illusions visuellesehez les enfants. Revue Phrlosophique,1895, 40, 11-25.

BUTCHARD. N .. & PRESSEY. A. w. Thccffects 0 f closing lines on the two formso f the Mulle r-Lver illusion. Psv chonornicScience, 1971, 23, 257-258.

HEYMANS. G. QuantitaetiveUntersuchungen ueber das "optischeParadoxon." Zeitschrift f ur Psychologieund Physiologie der Sinnesorgane, 1896,9, 221-255.

PlAGET, J. The mechanisms of perception.Trans. G. N. Seagri m , London: Routledge& Kegan Paul, 1969.

POLLACK, R. H., & SILVAR, S. Magnitudeof the Mueller-Lyer illusion in children asa function of pigmentation of the Fundusoculi, Psvchono mic Science, 1967, 8.83-84.

PRESSEY. A. W. An extension ofassimilation theory to illusions of siz e,a r e a , and direction. Perception &Psv cho phvsics, 1971.9, 172-176.

PRESSEY, A. W., BUTCHARD, N., &SCRIVNER, L. Assimilation theory andthe Ponzo illusion: Quantitativep r e d i c t i o n s , Canadian Journal o fPsvchologv, in press.

NOTES1. We are indcbted to David Brver, O.D.,

and E. M. Finkleman, O.D., for theirassistance. Dr. Brver performed the fundusratings. We are also indebted to Drs, F.Shivelv and L. Shewehuk for their critiealevaluation o f the thesis.

2. Unpublished data bv C. A. Bayer andA. W. Pressey , entitled "Analysis of twoforms o f the Müller-Lv er illusion."

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