Visual-geometric illusions: unisex phenomena

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1 Perception, 1979, volume 8, pages Visual-geometric illusions: unisex phenomena Clare Porac Department of Psychology, University of Victoria, Victoria, British Columbia, V8W 2Y2 Canada Stanley Coren Department of Psychology, University of British Columbia, Vancouver, British Columbia V6T 1W5, Canada Joan S Girgus Department of Psychology, Princeton University, Princeton, New Jersey 08540, USA Mickey Verde Department of Psychology, University of Victoria, Victoria, British Columbia V8W 2Y2, Canada Received 4 September 1978, in revised form 19 January 1979 Abstract. The possibility of sex differences in responses to visual-geometric illusions was investigated with the use of forty-five illusion variants and a sample of 221 observers. No difference in illusion magnitude as a function of sex was found. A second experiment measured illusion decrement and transfer of decrement to other illusion configurations. Again there were no significant differences between male and female observers. 1 Introduction Over the past decade it has become clear that a single process cannot account for visual-geometric illusions. Rather, they seem to be the result of several mechanisms associated with the structure of the visual system as well as with higher-level cognitive strategies. For instance, the optical system of the eye seems to produce predictable distortions in figures with converging line elements (Chiang 1968; Coren 1969) while lateral inhibitory effects on the retina (von Bekesy 1967; Ganz 1966; Coren 1970) or in the visual cortex (Burns and Pritchard 1971) seem to account for some other distortions. Numerous cognitive-judgmental mechanisms have also been implicated in illusion formation, including habits associated with picture perception (Coren and Girgus 1975; Day 1972; Gillam 1973; Gregory 1963, 1968), comparative judgment of elements in an array (Restle 1971; Restle and Merryman 1968; Massaro and Anderson 1971; Girgus et al 1972), local or global averaging of extents (Pressey 1967, 1971), or confusion of test and accessory lines (Erlebacher and Sekuler 1969; Coren and Girgus 1973). Although one mechanism may predominate in any one configuration (Coren et al 1976), several different mechanisms may be active in a single distortion (Coren and Girgus 1974; Girgus et al 1975). Recent evidence has suggested that there may be sex-related differences in some of the factors which affect illusion formation, for instance, at the structural level, McGuinness (1976a, 1976b) reports visual acuity differences for males and for females. Optical factors, such as image blur, have been shown to affect illusion magnitude in some configurations (Coren 1969; Coren et al 1978; Ward and Coren 1976); therefore, one might expect differences in illusion strength between males and females in those figures, such as the Poggendorff and Muller-Lyer, where image blur may play a role in illusion formation. In a similar vein, Girgus et al (1977) have shown that the amount of pigmentation in the crystalline lens is greater for males. Pollack (1969) and Sjostrom and Pollack (1971) have provided evidence which suggests that lens pigmentation may affect illusion response. Again such a structural difference might lead one to expect sex-related differences in illusion response.

2 402 C Porac, S Coren, J S Girgus, M Verde At the level of cognitive-judgmental strategies there are also sex-related differences which could affect illusion magnitude. Maccoby and Jacklin (1974) have summarized evidence which suggests that males and females are very similar in their use of visual information when the tasks involve simple form matching or reproduction. However, males seem to perform with greater speed and accuracy on tasks which require more complex visual analyses. For example, adult males appear to be more efficient on the embedded-figures test where observers are asked to detect a simple figure which is hidden within a complex background (Bieri et al 1958; Goldstein and Chance 1965; Schwartz and Carp 1967). Also, performance on the rod-and-frame test, where observers are required to set a line to the bodily vertical when it is surrounded by a tilted frame, indicates that the settings made by females are more influenced by the direction of the tilted frame than those made by males (Bogo et al 1970; Gross 1959; Kato 1965; Morf et al 1971; Silverman et al 1973; Vaught 1965). Performance on both of these tests suggests that females have more difficulty with separating a judged element from its surrounding context than do males. Presently it is a contentious issue as to whether these differences in disembedding and other spatial abilities (such as the ability mentally to rotate forms into various orientations) are based upon differences in learned perceptual strategies or are rooted in biochemical variations between the sexes (Garron 1970; Maccoby and Jacklin 1974; Sherman 1967; Waber 1976, 1977); however, regardless of the point of view which is taken, these sex-related performance asymmetries may have important consequences for the perception of visual illusions. One of the oldest theories of illusions, dating back to Miiller-Lyer (1889), suggests that some illusory distortions may be caused by a confusion between test and inducing elements. It is argued that such confusion leads the observer to ascribe some of the properties of the accessory elements in the configuration to the test element which is being judged. Erlebacher and Sekuler (1969) have shown how such confusion tendencies may contribute to the Muller-Lyer illusion and Pressey (1967, 1971) has incorporated a variant of this same notion into his assimilation theory of illusions. Coren and Girgus (1973) provided direct evidence for the contribution of the confusion of test and accessory lines to illusion strength by demonstrating that as the test element becomes more discriminable from the inducing elements the magnitude of the obtained illusory distortion is reduced. Thus, when it is easier to separate the test element from the context, illusion magnitude is reduced. To the extent that confusion or assimilation of test and context elements is one factor in the formation of illusions, individual differences in viewing strategies or abilities to isolate the test element could alter the magnitude of the illusions. If males and females employ different viewing strategies or display different ability levels when attempting to isolate figural components from a context, then one might expect sex differences in illusion magnitude. Although sex differences have been found in the perception of illusory arrays which require three-dimensional reorganizations, such as Necker cube reversals (Immergluck and Mearini 1969), the studies which have concentrated on twodimensional static geometric illusions have tended to report a lack of sex differences (Fraisse and Vautrey 1956; Hartmann et al 1972; Pressey and Wilson 1978; Spitz et al 1970). However, these studies have utilized rather small samples and only a narrow range of illusion configurations. This could be a factor in their negative findings. In order to detect small but systematic differences a large sample should be employed. In addition, the investigation of a wide variety of illusion configurations would allow one to isolate the class of distortions associated with sex differences if any response asymmetries between males and females were uncovered. Such a comprehensive investigation could provide important insights both for the study of visual-geometric illusions and for the study of mechanisms which maintain sex-related

3 Visual-geometric illusions: unisex phenomena 403 differences and similarities in complex, visual-cognitive tasks. For these reasons, the experiments reported below were conducted. 2 Experiment 1 The first experiment attempted to assess whether there were sex differences in initial illusion magnitude using a full spectrum of forty-five geometric illusion variants. 2.1 Method Subjects. The sample was composed of 107 females and 114 males. All were undergraduate volunteers Stimuli. The stimuli were twelve of the most common illusion configurations. These are shown in figure 1: Poggendorff (figure la), Wundt (figure lb), Zollner (figure lc), Delboeuf (figure Id), Ebbinghaus (figure le), Ponzo (figure If), Jastrow (figure lg), Baldwin (figure lh), horizontal-vertical (figure li), Oppel-Kundt (figure lj), divided-line (figure Ik), and Sander parallelogram (figure 11). In addition, eleven variants of the Miiller-Lyer were included (figure 2). All of the illusions, except the Poggendorff, contain an overestimation and an underestimation distortion, and these were measured separately. Each illusion stimulus was drawn on a separate page (21 cm x 27-5 cm). In the lower left-hand quadrant of the page, there was a horizontal line on which the observer was asked to mark the apparent linear extent of the test dimension of the figure. The test extents which were measured in each figure were between 2 and 8 cm in length while the measurement line was always 15-5 cm. Thus, there was enough latitude to assess both overestimation and underestimation illusions. Coren and Girgus (1972a) have shown that this technique provides results that are comparable to those obtained by the method of adjustment, and Coren et al (1976) have demonstrated that this technique can be used to measure illusions of shape as well as extent. A small block of instructions, and an illustrative diagram in the upper right-hand corner of each page indicated which portion of each figure was to be judged Procedure. The illusion stimuli were assembled into booklets. Subjects received two such booklets, each of which contained the forty-five illusion configurations in different mixed orders. Each subject made two independent judgments on each illusion. These two judgments were averaged for the purpose of statistical analysis. Observers were tested in groups and response rate was self-paced, although subjects were urged to indicate their first impressions and not to linger over any of the arrays. 2.2 Results and discussion The mean illusion magnitude for each configuration was separately computed for males and for females. The absolute size of the illusory effect as a function of sex is shown for the twelve classical illusion variants in table 1. Table 2 shows the absolute illusion magnitude, as a function of sex, for the eleven variants of the Miiller-Lyer figure. For convenience, those segments which are usually overestimated in the various illusion configurations are indicated by a +, and those which were usually underestimated were indicated by a - placed next to the illusion name. A series of t tests was conducted to see if the differences between males and females was significant for any single configuration. This analysis revealed only three significant differences out of the forty-five illusion variants tested. These were for the Poggendorff, for the overestimated portion of the Baldwin illusion, and for the underestimated portion of the circle variation of the Muller-Lyer illusion; however, on the basis of chance alone, one would expect between two and three comparisons

4 404 C Porac, S Coren, J S Girgus, M Verde out of the forty-five to reach significance. Although females showed a greater illusion magnitude on 60% of the illusion configurations, once again this proportion was not a significant deviation from chance (z = 1 34). (a) (b) 7, If // / (c) K (d) (e) (0 D U (g) (h) (i) I - (j) (k) Figure 1. Variants of the classical illusions used in the stimulus set: (a) Poggendorff; (b)wundt; (c) Zollner; (d) Delboeuf; (e) Ebbinghaus; (f) Ponzo; (g) Jastrow; (h) Baldwin; (i) horizontalvertical; (j) Oppel-Kundt; (k) divided-line; (1) Sander parallelogram. (1)

5 Visual-geometric illusions: unisex phenomena 405 The only illusion configuration which showed a highly significant sex effect was the Poggendorff configuration. Here the illusion magnitude was 3 0 mm greater for males than for females. This difference is difficult to interpret, although it is consistent with a previous investigation of this pattern (Pressey and Sweeney 1970). A possible factor is based upon a consideration of the mechanism of the illusion. Gillam (1971) has suggested that this distortion arises because of pictorial depth cues implicitly present in the array. Females have been shown to differ from males in tasks involving three-dimensional responses to two-dimensional configurations, such as Necker cube reversals (Immergluck and Mearini 1969), and mental rotations (Tapley and Bryden 1977; Wilson et al 1975). Males seem to respond more readily to three-dimensional cues in such arrays. This might make them more responsive to implicit depth cues in the Poggendorff, resulting in greater illusion magnitude. Unfortunately, similar implied-depth arguments have been offered for the Miiller- Lyer illusion (Gregory 1968) and the horizontal-vertical illusion (Girgus and Coren 1975) and yet no sex differences emerge for these configurations. Thus, although a > < < - > (a) S \ (b) > < < > - = - (c) (d) ) C e^ 3 CEr-^ (e) (0 o oe-e iz (g) 00 (0 0) oo.... Figure 2. Variants of the Muller-Lyer illusion used in the stimulus set: (a) standard; (b) exploded; (c) no-shaft; (d) Piaget; (e) curve; (f) box; (g) circle; (h) lozenge; (i) Sanford; (j) minimal; (k) Coren dot.

6 406 C Porac, S Coren, J S Girgus, M Verde Table 1. Mean illusion magnitude for males and females on twelve classical illusion figures. Illusion Mean illusion magnitude (mm) Poggendorff Wundt+ a Wundt - b Zollner + Zollner - Delboeuf 4- Delboeuf- Ebbinghaus + Ebbinghaus - Ponzo + Ponzo - Jastrow + Jastrow - Baldwin + Baldwin - Horizontal-vertical + Horizontal-vertical - Oppel-Kundt + Oppel-Kundt- Divided line + Divided line - Sander parallelogram + Sander parallelogram - females males difference (females-males) (TV = 107) (7V=114) * * o overestimated segment; b - underestimated segment; * p < 005; ** p < POOL -o Table 2. Variant Mean illusion magnitude for males and females on eleven variants of the Muller-Lyer figure. Mean illusion magnitude (mm) Standard + a Standard - b Exploded + Exploded No shaft + No shaft - Piaget + Piaget Curved + Curved - Box + Box- Circle + Circle - Lozenge + Lozenge - Sanford + Sanford - Minimal + Minimal - Coren + Coren females (N = 107) males (TV = 114) difference (females--males) * overestimated segment; b - underestimated segment; *p<005.

7 Visual-geometric illusions: unisex phenomena 407 strong sex-related effect emerges for one illusion response, the source of the difference remains unclear. When we consider the overall pattern of results, given the sample size and the number of illusion configurations tested, the data suggest that sex-related asymmetries probably do not exist for responses to two-dimensional visual-geometric illusion arrays. 3 Experiment 2 As early as 1902, Judd observed that the magnitude of the perceptual distortion found in the Muller-Lyer illusion diminished with free inspection. This illusion decrement has been repeatedly confirmed for the Muller-Lyer (Coren and Girgus 1972b, 1974; Day 1962; Dewar 1968; Festinger et al 1968; Girgus et al 1973) and has also been shown to occur in other illusory configurations including the Poggendorff, the Zollner, the Wundt-Hering, and the Oppel-Kundt (Coren and Girgus 1972b; Coren and Hoenig 1972). A great deal of evidence seems to suggest that this decrement in illusion strength involves some form of perceptual learning. For instance, Burnham (1968), Coren and Hoenig (1972), Day (1962), and Festinger et al (1968) have shown that if the eyes are free to explore the configurations with saccadic movements, this results in a larger reduction in illusion magnitude. These investigators argue that erroneously long or erroneously short saccades allow observers to learn the direction and extent of the illusion, and are the information feedback upon which the recalibration of the illusory percept is based. There is other evidence which suggests that decrement of illusion magnitude involves a learning process. To begin with, the rate of decrement responds to traditional learning variables such as the spacing of trials (Dewar 1968; Mountjoy 1958). Furthermore, the total amount of illusion reduction is cumulative over periods of days or weeks (Girgus et al 1975; Judd 1902). Finally, the illusion decrement transfers from one configuration to another, and the magnitude of this transfer depends upon the perceived, rather than the structural, similarity between configurations (Coren and Girgus 1974). All of these lines of evidence seem to indicate that illusion decrement involves some form of perceptual learning. The data of experiment 1 gave no evidence for differences in illusion susceptibility as a function of sex. However, such differences could appear in the perceptual learning phenomena associated with visual-geometric illusions. This expectation is based upon reports which indicate that, while males are somewhat more proficient at spatial tasks than are females, females manifest superior performance in some perceptual learning or visual discrimination tasks (Laughlin and McGlynn 1967; Pishkin et al 1967; Stevenson et al 1968). If males and females differ with respect to the type of visual-perceptual learning involved in illusion decrement, one might expect significant variations between the sexes in the rate and/or the amount of illusion decrease over time and in the magnitude of the transfer of the decrement training. In order to test this hypothesis, a second experiment was conducted. 3.1 Method Subjects. Twenty male and twenty female volunteers participated in this study Stimuli. Three variants of the Muller-Lyer illusion were selected from the Coren and Girgus (1974) transfer experiment. The stimulus used for decrement training was the standard Muller-Lyer configuration which is shown as figure 2a. Two variants were used to test transfer of decrement. They were the exploded form (figure 2b), which has been scaled as highly similar to the standard form by Coren and Girgus (1974), and the Piaget form (figure 2d), which has been scaled as very dissimilar to the standard form.

8 408 C Porac, S Coren, J S Girgus, M Verde All figures were comprised of 1 mm lines. In the standard and exploded forms the shafts were 8 cm, the wings were 2 cm, and the angle between the wings and the horizontal was 45. In the exploded form, the gap between the wings and the shaft was 2 mm. For the Piaget form, the center shafts were 8 cm. For the apparently shorter segments the outside bars were 5 cm, while those of the apparently longer were 11 cm. The apparently longer segment of each illusion figure was made adjustable via a tongue-and-groove apparatus. The configuration was viewed at a distance of 40 cm from the observer. The black lines had a reflectance of 4 6% and the background had a reflectance of 74-7% Procedure. Each sex group was divided in half, with ten observers tested for transfer on the similar (exploded) form and ten tested for transfer on the dissimilar (Piaget) form of the illusion. Each observer made two initial settings of apparent equality on the transfer stimulus to which he or she was assigned. The settings were balanced as to starting position, with one half of them starting with the adjustable shaft clearly longer than the comparison length while the other half started with it clearly shorter. Following this, all observers inspected the standard form of the Muller-Lyer figure (figure 2a) for 5 min, moving their eyes sequentially from a%gle vertex to angle vertex. Settings to apparent equality were taken at 1 min intervals. Other investigators have shown that this procedure leads to sizeable reductions in illusion magnitude (Coren and Girgus 1972b; Girgus et al 1973). Following the inspection period, all observers made two additional settings to apparent equality on the initially tested illusion variant (either the Piaget or the exploded form). The rate of illusion decrement is given by the change in illusion magnitude during inspection. The amount of transfer is given by the difference between the initial (preinspection) and final (post inspection) measures on the nonpracticed figure. 3.2 Results and discussion The time course of illusion decrement is shown in figure 3. Since all of the observers inspected the standard form of the Muller-Lyer for 5 min, one may assess differences between the sexes in the rate of decrement by collapsing the practice data for males and for females across the specific transfer conditions. An analysis of variance indicated that significant reduction in illusion magnitude occurred over the inspection period (Fs >190 = 5-86; p < 0 001). There was no difference in the rate of decrement as a function of sex CF 138 = 1 13), nor was there a significant interaction between sex and time CF Sjl90 = 0-88). However, figure 3 gives some suggestion that illusion magnitude in the male group is decreasing at a slower rate than in the female group. Since the analysis of variance measure of interaction is not particularly females Illusion (mm) O en X^^ No o o 5 ' Time (min) Figure 3. The magnitude of the Muller-Lyer illusion as a function of inspection time both for males and for females.

9 Visual-geometric illusions: unisex phenomena 409 sensitive to small slope differences, a more powerful test for possible rate disparities was used. This was done by fitting a least-squares regression line through each individual observer's data. When this is done, the slope of each regression line is based upon six scores and provides a stable estimate of each observer's rate of decrement. For females the mean slope was -1-05, while for males it was 0-53 (indicating a rate of illusion decrease in mm min" 1 ). However, this difference is not statistically significant (7 38 = 1-39). Thus, there is no evidence for sex-related differences in illusion decrement. Coren and Girgus (1974) demonstrated that decrement of the Muller-Lyer transfers to other variants of this illusion as a function of the judged similarity between inspection and test configurations. Thus, one would expect that inspection of the standard form of the Muller-Lyer would bring about large amounts of transfer of the reduction in illusion magnitude to the similar (exploded, figure 2b) variant. On the other hand, very little transfer to the dissimilar (Piaget, figure 2d) variant would be expected. Table 3 presents the results from the present experiment which used this paradigm. The third column under each illusion variant heading represents the mean difference in illusion magnitude between the pretest and the posttest. As can be seen, there is very little pretest-posttest reduction in the Piaget form of the illusion both for males and for females. In fact, females tend to show a negative transfer in that they have a higher mean illusion magnitude after 5 min of inspection of the standard form than they had before inspection. Such results might be expected if individuals are fluctuating around a mean transfer value of zero with some observers showing a positive effect of the decrement training and others showing a negative effect. On the other hand, both males and females show positive transfer to the similar or exploded form. This reduction is on the order of 17% of the original illusion magnitude for the male observers and 25% for the female observers. When an analysis of variance was performed upon these pretest-posttest difference scores, it was found that the transfer effect as a function of the similarity of the variant to the standard figure was highly significant (F i>36 = 7-71; p < 0-01). These data, then, replicate the findings of Coren and Girgus (1974). However, when one looks at the effect of sex, there was no difference between males and females CFi ;36 = 1-36); also, there was no significant interaction between sex and form CF 1;36 = 2-53). Thus, there was no evidence for sex-related differences in either the rate or the magnitude of illusion decrement or the pattern of decrement transfer to other configurations. Table 3. Mean illusion magnitude (mm) on variants of the Muller-Lyer illusion used in the transfer task (total number of observers = 40; number of observers in each cell = 10). Similar (exploded Muller-Lyer) Dissimilar (Piaget Muller-Lyer) pretest posttest difference pretest posttest difference Males mean S.D Females mean a S.D a This rather large negative transfer effect was influenced by the atypical scores of one observer. When her responses were excluded the mean became and the standard deviation was Neither this new value nor the value reported in the table was significantly different from 0 when tested.

10 410 C Porac, S Coren, J S Girgus, M Verde 4 General discussion This pair of experiments attempted to investigate the possibility that sex differences exist in the perception of visual-geometric illusions. The first experiment tested for differences in static illusion magnitude across forty-five illusion variants. Despite the fact that a large sample of illusions was used and a large sample of observers, only one illusion configuration (the Poggendorff) produced a difference between male and female observers. The second experiment looked for differences in the dynamic properties of responses to visual-geometric illusions as manifested in illusion decrement and transfer of decrement between configuration variants. Once again, no reliable sex differences were found in either class of perceptual responses to the illusory arrays. Thus the results of the two experiments are quite consistent. In some respects, these results are surprising given the evidence which indicates that males and females may differ in certain structural characteristics of the eye. It is more surprising given that males and females respond differentially on spatial disembedding, visual discrimination, and visual tasks which require three-dimensional reorganizations. To the extent that such tasks indicate a particular cognitive or perceptual information processing bias, one might have expected sex differences to emerge in the magnitude of visual-geometric illusions and illusion-related phenomena. A recent study by Tapley and Bryden (1977) may provide an explanation for this inconsistency. In a systematic exploration of sex differences in the ability to perform mental rotations of objects (thought to be a type of visual-spatial ability), these investigators found that other tests of spatial ability may not be correlated with an observer's performance in the mental rotation task. Thus, it seems that nonverbal cognitive and visual-analytic skills may manifest themselves in specific situations with little or no transfer from one type of task to another. Thus, the sex-related response patterns which are seen in embedded-figure, rod-and-frame, visual-discrimination, and mental-rotation tasks may represent situation-specific behaviors which do not generalize to the type of visual analysis needed to produce greater or lesser degrees of illusion susceptibility. Acknowledgements. This research was supported in part by grants A0293 and A9783 from the Natural Sciences and Engineering Research Council of Canada and from the National Science Foundation ( ). Experiment 2 was submitted in partial fulfillment of the Bachelor of Arts Degree (Honours) at the University of Victoria by M Verde. References Bekesey G von, 1967 Sensory Inhibition (Princeton, NJ: Princeton University Press) Bieri J, Bradburn W, Galinsky N, 1958 "Sex differences in perceptual behavior" Journal of Personality Bogo N, Winget C, Gleser G C, 1970 "Ego defensive and perceptual style" Perceptual and Motor Skills Burnham C A, 1968 "Decrement in the Muller-Lyer illusion with saccadic and tracking eye movements" Perception and Psychophysics Burns B D, Pritchard R, 1971 "Geometrical illusions and the response of neurons in the cat's visual cortex to angle patterns" Journal of Physiology (London) Chiang C, 1968 "A new theory to explain geometrical illusions produced by crossing lines" Perception and Psychophysics Coren S, 1969 "The influence of optical aberrations on the magnitude of the Poggendorff illusion" Perception and Psychophysics Coren S, 1970 "Lateral inhibition and geometric illusions" Quarterly Journal of Experimental Psychology Coren S, Girgus J S, 1972a "A comparison of five methods of illusion measurement" Behavior Research Methods and Instrumentation Coren S, Girgus J S, 1972b "Illusion decrement in intersecting line figures" Psychonomic Science

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