FRANK RESTLEIndiana University, Bloomington, Indiana 47401

Instructions and the magnitude of an illusion:Cognitive factors in the frame of reference*t

Ss judged the length of a horizontal line having vertical lines at the ends and a verticalline crossing at the middle. As has often been shown, judgments of the horizontal linevaried inversely with the length of the vertical segments. One group of Ss were told to usethe end lines as frame of reference and ignore the center line, and the estimated weightsof end and center line were .22 and .02. The other group were told to ignore the end linesand use the center line as frame of reference. The weights of end and center line for thisgroup were .06 and .22. It was concluded that the Helson AI. equations are valid, but thatthe weights of parts of the field are partly under voluntary control and are not simply afunction of the visual field.

The magnitude of an illusion is greaterwhen S adopts a "whole perceiving"attitude than when he uses a "partisolating" a t t i tu de (Woodworth &Schlosberg, 1954). This might be because Scan correct his responses so as tocompensate for the illusion withoutchanging the appearance of the stimuli, orit might be because S call voluntarilychange his probabilities of sampling variouselernents of the field, and thereby affecthis frame of reference.

Several recent papers (Restle &Merryman, 1968, 1969; Merryman &Restle, 1970; Restle, 1970; Restle &Greeno, \970) have used a mathematicalmodel (Helson, 1964) of the frame ofreference to explain contrast illusions andthe moon illusion. The two equations ofthis theory are as follows: The judgement,Jx , of a stimulus of physical value. X. isgiven by

stimulus, SI The magnitude of the illusiondepends upon the weight WI given S" theillusion-inducing stimulus

If the weights of the elements of theframe of reference are determined by thevisual array interacting with receptors, theninstructions should not affect them, andthe effect of instructions must be throughresponse compensation. If, on thecontrary, the weights are partly undercontrol of the S, then it should be possibleto influence them through instructions.

In the present experiment Ss judged ahorizontal line of length L having verticallines of length E at the ends, and cross-lineof length C One group of Ss were told touse E and ignore C, the other were told touse C and Ignore E. II' the weights areunder voluntary control, these two groupsshould show different illusions, eachplacing more weight on the stimulus towhich aucnuon was directed.

as 10 contrast but little with the wallbehind.

ProcedureOn each trial S was shown a slide and he

then made a judgment of the length of thehorizontal line (I.) by pressing one of a rowof six buttons, the leftmost correspondingto "quite short," the rightmost to "quitelong," and the other four to "intermediatelengths."

Group I Ss were told to "Try todisregard the center vertical line thatcrosses right through the test line. Payattention to the vertical lines at the ends ofthe test line and use them as a frame ofreference to help you in your judgments."The instructions were given verbatim asabove and then paraphrased again after Sswere told about the responses. Group 2 Sswere told to "T ry to disregard the verticallines at the ends of the test line. Payattention to the center vertical line thatcrosses right through the test line and use itas a frame of reference to help you in yourjudgments."

When a stimulus was presented, anamber light on S's response panel was lit.That amber light went off when theresponse was made. Whenever all Ssresponded. the slide went off and a newslide was searched for. The maximum timeallowed was 6 sec to respond, and therewas a 5-sec wait between slides. The 27slides were shown seven times in sevenrandom permutations to each group of Ss.and responses to the last five trials arereported. All programming of stimuli,presentation of slides, and data collectionwere done by an IBM IROO on-linecomputer.

where A is the average level of the frame ofreference. If the stimuli in the field are ofmagnitudes SI, S2' "', Sn, then A is aweighted geometric mean

The response is taken to be a linearfunction of lx. provided the S uses a ratingscale with the usual instructions.

An illusion arises when a given stimulusis observed in two different frames ofreference differing with respect to some

where c and e arc the weights or the crossline and end lines, respectively, and K isthe unknown resultant of all constant orrandom factors in the experiment. Takinglogaruhms.

RESULTSThe first step of analysis is to reduce the

data to parameter estimates. Eqs. I and 2imply that

= log L + constant. (3)

Ir the raw responses are taken as thejudgments. calling the leftmost button I.etc .. then Eq.3 is not satisfied since theslope or log J I vs log L is not unity. Foreach S. a constant Z was found so that hisresponse, R, ' satisfied the equation

=logL c logC c log l: (l·ce)logK.

METHOD

Apparatus and MaterialsSumuli were slides of white lines on a

dark background. Each display consisted ofa horizontal line of length 1. = 8. 10, or12em; vertical lines at the ends of thehorizontal line of length E = 12, 14. or16 ern: and a vertical line bisecting thehorizontal line of length C = 6. R. or10 em. 'I he combinations of L, E, and Cproduced 3 x 3 x 3 = 27 displays. The 27slides were projected from a KodakRA·750 random-access slide projector ontoa screen 3 m from S. The screen was130 x 130 em and its edges were masked so

SubjectsTwenty-eight students enrolled in

introductory psychology courses at IndianaUniversity participated in the experimentto fulfill a course requirement. Ss were runIn groups of four. and each such group wasassigned to one of two conditions, resultingin 12 Ss in Group I and 17 Ss in Group 2.

( I)Jx =XiA

'This research IVa, supported by Public HealthService Gran t MH 16817. The author thanksJanice Carlson. who prepared the stimulusmaterials. and Ann Brown. who wrote theprograms for analy-» of data,

'Requests for reprints should he sent to I rankRestlc, Department of Psychology. IndianaUniversity. Psychology Building. B'loolllington.Indiana 47401.

Perception & Psychophysics, 1971, Vol. 9 (1A) Copvright /97/, Psvchonomic Journals.Lnc., Austill. Texas 31

10g(RL + Z) =logh =log L + constant,

with h defined as above. The value of Zmay be interpreted as the "zero point" ofthe scale used by S. Determination of sucha zero point reduces individual differencesconsiderably and provides a closeagreement between model and data forevery S.

A standard linear multiple regression oflog J l on log C and log E was thenperformed for each S, and the parameters cand e estimated for each S.

The main experimental hypothesis wasthat Group I Ss, instructed to use E andignore C, would yield larger values of ethan of c. The mean values were .221 and.056, respectively. Group 2 Ss wereinstructed to ignore E and use C, henceshould yield smaller values of e than of c.Their mean values were .024 and .219,respectively. The difference betweengroups in e-c was statistically significant[t(27) =2.96, p < .01] .

DISCUSSIONSs can voluntarily change ,the relative

weights of various stimuli in their frame ofreference if instructed to do so. Theresulting difference in weight leads todifferent measured illusions in the visualfield.

This result supports the position takenby the author (Restle, 1970) with respect

to individual differences in the magnitudeof the moon illusion, that variousSs mightuse different frames of reference (themagnitude of objects on the horizon, thetotal extent of the visual field, or their ownnoses), employing different strategies, andfor that reason make consistently differentjudgments.

It might be objected that the presentresults are contaminated, because the visualfixation point was not controlled, and nodirect observations of the Ss' ocularorientations were made. However, oursampling theory of the frame of referenceholds that perceiving involves active search,and that the frame of reference dependsupon where the S centers his viewpoint. Inthis experiment, we have measured thejudgmental consequences of instructions.The final result is what is of interest here,though it would be interesting to learn theresults of studies of visual fixation in thistask. If fixation were controlled, then oureffect might be sharply attenuated, eventhough the effect is large under normalviewing conditions. If it were found thatocular orientation depends on instructions,in this task, then it would still be necessaryto show that those visual fixationsproduced the observed difference injudgment.

The notion of perceptual samplingemployed in this paper is similar to Piager's( 1961) except that Piaget says that the part

of the field centered by the S is therebymade larger, whereas in the present model,the part of the field centered is merelythereby made part of the frame ofreference. Since Ss were not judging theparts of the field emphasized byinstructions, Piaget's concept would notpredict any differences in performancebetween the groups of the presentexperiment.

REFERENCESHELSON, H. Adaptation-level theory. New

York: Harper & Row, 1964.MERRYMAN, C. T., & RESTLE, F. Perceptual

displacement of a test mark toward the largerof two visual objects. Journal of ExperimentalPsychology, 1970, in press.

PIAGET, J. l.es mechanisms perceptifs. Paris:Presses Universitaires de France, 1961.

RESTLE, F. Moon illusion explained on the basisof relative size. Science, 1970. 167,1092-1096.

RESTLE, F., & GREENO, J. G. Introduction tomathematical psychology. Reading, Mass:Addison-Wesley, 1970.

RESTLE, r., & MERRYMAN, C. T. Anadaptation-level theory account of arelative-size illusion. Psychonomic Science,1968, 12, 229-230.

RESTLE. F., & MERRYMAN, C. T. Distance andan illusion of length of line. Journal ofExperimental Psychology, 1969,81, 297-302.

WOODWORTH, R. S., & SCHLOSBERG, H.Experimental psychology. New York: Holt,Rinehart & Winston, 1954.

[Accepted for publicotion May 15. 1970.)

32 Perception & Psychophysics, 1971, Vol. 9 (IA)