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Gender Differences in Illusion Response: The Influence of Spatial Strategy and Sex Ratio - Statistical Data Included
R. J. MillerR. J. Miller [1]
Two experiments explored factors related to gender differences in Ponzo illusion susceptibility. In Experiment 1, 54 male and 54 female (predominantly white, middle class) undergraduates were administered Witkin's Embedded Figures Test (EFT) and, on 2 separate occasions, a form of the Ponzo illusion. Results showed the Ponzo to be quite reliable over several days. Females were significantly more field dependent (as shown by slower responses to the EFT), and significantly more susceptible to the Ponzo illusion, than males. Furthermore, EFT performance correlated significantly with Ponzo susceptibility for females, but not for males, suggesting that the difference between males and females in Ponzo response may be due not to differences in field independence per se, but rather to differences in the strategies used to solve the illusion task. In Experiment 2, 111 male and 148 female (predominantly white, middle class) undergraduates were administered the Ponzo illusion twice, the 2 administrations separated by a bout 90 mm. Again, the illusion task showed good reliability, and females were significantly more susceptible to the illusion. Furthermore, the magnitude of the difference between males and females was systematically related to the sex ratio (the ratio of the number of males to the number of females) of the particular session in which each subject happened to be participating. It is suggested that social factors such as sex ratio might affect the strategies participants use when doing illusion tasks, and perhaps other spatial skills tasks as well.
Several recent investigations are concerned with the impact of pictorial depth and flatness cues on size constancy (Miller, 1997, 1998, 1999). Much of this research has incorporated the Ponzo illusion, two forms of which are illustrated in Fig. 1. A consistent observation has been that females are, on average, significantly more susceptible than males to the complex Ponzo. That is, females overestimate the length of the top line to a significantly greater extent than do males. This finding was unexpected when it first appeared, as several previous studies had shown no gender differences in Ponzo response (e.g., Brislin & Keating, 1976; Porac, Coren, Girgus, & Verde, 1979; Quina & Pollack, 1972). The apparent discrepancy was resolved by a set of experiments showing that although the gender differences found in the complex form of the illusion are reliable, there are in fact no gender differences to be found using the simple Ponzo, the form used by those other investigators (Miller, 1999).
To explain these findings, one must begin with a consideration of why anyone, male or female, would be fooled by the Ponzo stimulus. Various theories have been advanced, including those based on low-pass filtering (Ginsburg, 1984), assimilation (e.g., Pressey & Epp, 1992), relative size comparisons (Kunnapas, 1955), and tilt constancy (Prinzmetal, Shimamura, & Mikolinski, 2001), among others. One of the most frequently discussed explanations is that the illusion results, at least in part, from depth information contained in the illusion array (e.g., Coren & Girgus, 1978; Gillam, 1980; Leibowitz, Brislin, Perlmutter, & Hennessy, 1969; Miller, 1997; Ward, Porac, Coren, & Girgus, 1977). The best known modern form of this explanation is the inappropriate constancy scaling theory of Gregory (e.g., 1967), a variant of earlier conceptions described by Thiery (1896) and Tausch (1954). The radiating lines are assumed to provide linear perspective, so the top horizontal line is perceived (although not necessarily consc iously) as more distant than the bottom line. The result is an overestimation of the length of the top ("far") line relative to the bottom ("near") line due to misapplication of size constancy. Following this logic, one would assume that the greater the amount of depth information present in the array, the higher the susceptibility observers would show to the illusion. This assumption has been confirmed by several experiments (e.g., Miller, 1997, 1999).
One potential explanation for gender differences in Ponzo susceptibility is that females process depth information differently from males (Miller, 1999). In the simple Ponzo, where there is relatively little depth information to process (i.e., only two radiating lines), males and females do not differ. However, in the complex Ponzo, where there are more radiating lines (and thus more depth information), the difference between males and females in the influence of depth cues emerges, resulting in gender differences in illusion susceptibility.
An alternative explanation is anchored on the idea that the Ponzo illusion is in part a spatial task, and its perception is a reflection of one or more spatial skills. One such skill is field independence, the ability to attend to, unembed, or otherwise perceptually separate simple visual forms that are embedded in a perceptually compelling, more complex visual field. Among the most frequently used measures of field independence are embedded figures tests. Such tests consist of complex geometric figures in which are camouflaged simpler figures. An example of the sort of figure included in such tests is shown in Fig. 2. The participant's task is to ignore the perceptually more demanding complex array and find the simple figure as quickly as possible. The more quickly the participant can find the simple figure, the more field independent he/she is said to be.
The Ponzo illusion also can be viewed as a task requiring the ability to unembed forms from their background. That is, to judge accurately the relative lengths of the two horizontal lines one must ignore the effects of the radiating lines. It is possible, then, that susceptibility to the Ponzo illusion is at least partly related to field independence in general, and to performance on embedded figures tests specifically. If that is true, one would expect a correlation between embedded figures test performance and Ponzo response, such that participants who are more field dependent also would be more susceptible to the Ponzo illusion, especially in the case of the complex Ponzo. That is, the simple Ponzo presents very little visual field in which the two horizontal lines can become embedded, and field independence probably is of little importance. However, the complex Ponzo has a more detailed embedding visual field than the simple Ponzo, and one might expect field independence to be more important as an influe nce on illusion susceptibility.
It is possible that spatial skills are more important for females than for males when solving the Ponzo illusion, and males are relatively less affected by the embedding characteristics of the Ponzo field. For the simple Ponzo, field independence effects should be minimal because there are only two radiating lines, and little need for spatial skills. In this case, females' spatial skills are essentially irrelevant, and a gender difference in illusion susceptibility does not exist. In the complex form of the illusion, however, there is a stronger perceptual field from which the horizontal lines must be unembedded. Here, females' spatial skills come into play, causing them on average to be more susceptible to the illusion than males because females are relying more heavily on these skills to do the task. If this interpretation is correct, one would expect Ponzo susceptibility to be correlated with embedded figures test scores for females, but less so or not at all for males.
If one assumes the rationale of the previous paragraph, the implication is that females are not more susceptible to the Ponzo illusion simply because they are more field dependent than males. Indeed, evidence of gender differences on embedded figures tests seems to be highly inconsistent (e.g., Halpern, 1989, 1992; Voyer, Voyer, & Bryden, 1995). Rather, such a rationale suggests that females rely more on field independence than do males when attempting to solve the Ponzo illusion. In other words, field independence has more of an influence on Ponzo response for females than for males. Such a possibility places gender differences in spatial skills in a somewhat different perspective than generally has been the case. In most previous discussions, the implication has been that both males and females rely on essentially the same spatial skills to solve spatial tasks, but they differ in the extent to which they possess such skills (e.g., Beatty & Duncan, 1990; Blough & Slavin, 1987; Caplan, MacPherson, & Tobin, 19 85; Halpern, 1992; Loring-Meier & Halpern, 1999; McGee, 1979; Voyer et al., 1995). It is possible, however, that a key difference between males and females may not be actual differences in spatial skills per se, but rather differences in the extent to which certain spatial skills are relied upon. It may be that the real gender differences of importance are not so much differences in skill, but rather differences in strategy, differences in the particular spatial skills that are applied to particular tasks.
The idea that gender differences in spatial tasks might be attributed at least in part to differences in strategies is not without some precedent (e.g., Bryden, 1980). As a recent example, there is widespread agreement that males perform consistently better than females in visual-spatial navigation tasks, tasks that require navigation through (often unfamiliar) environments (e.g., Astur, Ortiz, & Sutherland, 1998; Gron, Wunderlich, Spitzer, Tomczak, & Riepe, 2000; Moffat, Hampson, & Hatzipantelis, 1998). It has been shown that these gender differences can reflect differences in strategies, such that females rely more on landmark cues, whereas males use a combination of landmark and geometric cues (e.g., Sandstrom, Kaufman, & Huettel, 1998). There is some indication that these strategic differences may be traced to sex differences in specific brain areas used in performing such tasks (e.g., Gron et al., 2000), perhaps reflecting sex differences in hormone levels during development (e.g., Geary, 1989; Kimura, 1 992).
This report describes two experiments. The major goal of Experiment 1 was to determine the relation, if any, between field independence and susceptibility to the complex Ponzo illusion. A secondary goal of this experiment was to gather some information regarding the reliability of the Ponzo illusion. Most research with this illusion has involved either a single measure of illusion susceptibility or several measures given consecutively in a single testing session. Brislin and Keating (1976) reported a test-retest reliability coefficient of .75 for participants whose testing sessions were at least 2 months apart, but this finding applied to only 12 participants, and the form of the illusion was a very unusual one. Although Experiment 1 did not involve such long time periods, it did provide the opportunity to evaluate the reliability of a traditional form of the illusion for a large number of participants.
Experiment 2 relates to an aspect of gender differences that is not generally applied to spatial perception, namely sex ratios (Deaux, 1985). Several investigators have noted that the ratio of males to females in a group can influence how one or both sexes behave in that group. Studies have shown sex ratio to be important in workplace behavior and corporate organization, in the tendency of females to assume traditional wife/mother roles, in the likelihood of sexual libertarianism, and the expression of feminist ideology, etc. (e.g., Gutek & Morasch, 1982; Guttentag & Secord, 1983; Kanter, 1977; Secord, 1982, 1983).
The fact that sex ratios seem to be important modifiers of behavior leads in the present context to the question of whether such ratios can influence the application of spatial strategies. If it is true that gender differences in spatial task performance are due to differences in strategies, then it might also be true that a variety of factors, including sex ratio, can influence the extent to which males and females rely on different spatial strategies. In other words, varying sex ratios may lead to changes in the extent to which male and female strategies differ, in turn leading to increases or decreases in gender differences on spatial skills, including, possibly, the Ponzo illusion. Experiment 2 provided the opportunity to observe the effect of sex ratio on Ponzo illusion response.
EXPERIMENT 1
Method
Participants
The original sample consisted of 61 male and 59 female (predominantly white, middle class) undergraduate students, who gave their informed consent to participate. All were enrolled in introductory psychology classes and were reimbursed for their participation by the awarding of credits in their courses. Participants who needed corrective lenses for normal vision were required to wear them. For reasons described herein, 7 males and 5 females were excluded from analysis, leaving 54 males and 54 females in the final sample.
Procedure
First Session. For the first session, each participant reported to a laboratory where he/she was tested individually. The Ponzo illusion was administered using a series of 35-mm slides on which were reproduced variations of the complex Ponzo shown in Fig. 1. There were 25 slides, on which the radiating lines and bottom horizontal line remained constant in length (24 cm for the bottom line) and position. The top horizontal line varied in length from slide to slide in approximately equal steps from 9.5 to 27.4 cm. The 25 slides were presented to the participant in random order using a Kodak Carousel projector. The lines of the projected illusion images had a luminance of approximately 5 cd/[m.sup.2], whereas the white background was about 103 cd/[m.sup.2].
The participant was seated 5 m from the screen, beside the projector, with room lights extinguished. He/she was asked to record on a response sheet which of the two horizontal lines was longer for each slide. Instructions emphasized an objective, analytic approach. That is, they were not told to indicate which line "seemed" longer or "appeared" longer, but rather to "select the line that, if you were actually to measure the two lines on the screen with a ruler, would be the longer of the two."
The response sheets were scored by first arranging each participant's responses in order, ranging from the response to the shortest top line through the response to the longest top line. The point of subjective equality was determined by interpolating a value halfway between the point where the participant stopped responding to the bottom line as longer and the point where he/she started responding to the top line as longer. In cases where there were several transition points, the point of subjective equality was found by interpolating a value halfway between the first and last transitions. If a response was surrounded on each side by three or more opposite responses, that response was treated as the opposite response and not considered a transition point, although this adjustment was rarely needed. Many years of experience with this procedure has shown that if a participant's range of uncertainty is more than five responses wide, he/she is using an inconsistent criterion for responding. Such inconsistency ca n result from an unclear understanding of the task, wandering attention, sleepiness, or any of a variety of other influences, including simple carelessness. Twelve participants showed ranges of uncertainty greater than five responses wide and their data were excluded. The final interpolated value was converted to a percent illusion score by expressing the difference between the bottom line and the subjectively equal top line as a percentage of the bottom line.
Next, the participant was administered the Embedded Figures Test (EFT; Witkin, 1971). The EFT involves a series of 12 complex geometric forms in which are camouflaged simpler forms (similar, but not identical, to Fig. 2). Instructions and the administration procedure were taken directly from the test manual (Witkin, Oltman, Raskin, & Karp, 1971). For each of the 12 complex forms, the participant was first shown the complex form for 15 s, and was asked to describe it. Then, for 10 s, he/she was shown the simple form that was hidden in the complex form. Finally, he/she was shown the complex form again and timing began. The participant indicated when he/she had located the hidden simple form by first announcing that he/she had found it, and then tracing it lightly with a stylus. The simple and complex figures never were simultaneously visible to him/her. The score was the mean amount of time required (in seconds) to find the simple forms in each of the 12 complex figures. Thus, lower scores represent greater fie ld independence. There are two forms of the test; Form A was used in this experiment.
Second Session. The participant returned for the second session a minimum of 5 days (mean 9.87 days, SD = 5.11) after completing the first session. He/she was again tested with the Ponzo illusion, the administration and scoring procedures for which were the same as in the first session.
Results
The above procedure yielded a total 108 data sets (54 males and 54 females), each participant having provided a value for the first Ponzo administration (Ponzo 1), one for the second Ponzo administration (Ponzo 2), a composite Ponzo score that represented the mean of Ponzo 1 and Ponzo 2, and a score for the EFT. Descriptive statistics for all these measures, as well as effect sizes for the male versus female comparisons expressed as Cohen's (1988) d, are shown in Table I. The difference between males and females on the EFT was statistically significant, t(106) = 2.17, p = .032. The Pearson r values for comparisons of Ponzo 1 with Ponzo 2 were .751 for all participants combined, .668 for males, and .798 for females, all significant at p [less than] .001.
A 2 x 2 (sex x Ponzo administration) ANOVA was conducted, with the two levels of sex being male and female, the two levels of Ponzo administration being Ponzo 1 and Ponzo 2, and the dependent variable being Ponzo scores (percent illusion). The effect of sex was significant, F(1, 106) = 7.06, p = .009, as was the difference between Ponzo 1 and Ponzo 2, F(1, 106) = 4.35, p = .039. The interaction was not statistically significant.
The relation between EFT scores and Ponzo 1, Ponzo 2, and composite Ponzo values for males and females was examined. The resulting Pearson product-moment correlation coefficients are shown in Table II. As can be seen in this table, all three r values were statistically significant for females, whereas none were significant for males.
Discussion
With respect to Ponzo illusion reliability, the correlations between Ponzo 1 and Ponzo 2 were substantial, indicating that there was a considerable degree of consistency in how participants responded to the task over time. The fact that there were statistically significant differences between the two administrations, however, shows that the passage of several days between assessments did have some effect on participant response, although as can be seen in Table I this difference was small in absolute terms.
Several interesting findings emerged regarding gender differences. The fact that females were more susceptible than males to both administrations of the Ponzo illusion was no surprise, and confirms previous findings (e.g., Miller, 1997, 1999). The fact that females scored, on average, higher than males on the EFT (i.e., more in the direction of field dependence) is not entirely surprising either, as such a difference has been reported by other investigators, although many investigations have shown no difference (see, e.g., Voyer et al., 1995). All the effect sizes indicated in Table I were "medium" according to Cohen's (1988) guidelines. What is novel, however, is the possibility that gender differences on the Ponzo illusion are related to field independence. The simple explanation would be that field independence predicts Ponzo susceptibility, and females are more susceptible, on average, to the Ponzo illusion because they are, on average, more field dependent than males. However, the explanation expressed i n this simple form would imply that males who score high on the EFT would be more susceptible to the Ponzo illusion than other males whose EFT scores are lower. The fact that there was no significant correlation between EFT and Ponzo performance for males belies this implication. In contrast, the correlations between EFT and Ponzo performance for females were much higher, and were statistically significant.
What these findings suggest is that females are not more susceptible to the Ponzo illusion simply because they are more field dependent than males. Rather, they suggest that females rely more on field independence than do males when attempting to solve the Ponzo illusion. In other words, field independence has a significant influence on Ponzo response for females, but not for males. This possibility suggests that a key difference between males and females may not be actual differences in spatial skills per se, but rather differences in the extent to which certain spatial skills are relied upon. It may be that the real gender differences of importance are not so much differences in skill, but rather differences in strategy, differences in the specific spatial skills males and females apply to particular tasks.
EXPERIMENT 2
Experiment 2 was originally intended as a study of several perceptual and personality variables, including the Ponzo illusion and hypnotic susceptibility. With respect to the Ponzo illusion the goal of the experiment was to provide an additional examination of gender differences and Ponzo reliability. However, as described herein, it provided an unexpected opportunity to examine the relation between sex ratio and Ponzo response.
Method
Participants
The original sample for Experiment 2 consisted of 120 male and 148 female (predominantly white, middle class) undergraduate students, who gave their informed consent to participate. All were enrolled in introductory psychology classes and were reimbursed by the awarding of credits in their courses. Participants who needed corrective lenses for normal vision were required to wear them. For the same reasons indicated for Experiment 1, 9 males and 19 females were excluded from analysis, leaving 111 males and 129 females in the final sample.
Procedure
Four sign-up sheets were posted for this study, one for each of four consecutive evenings (Monday--Thursday). The scheduled time period for each evening's session was 7:30-9:30. No attempt was made to control the numbers of males and females signing up for any session--each student selected whichever of the four evenings he/she found most convenient. Thus, the proportion of males to females for each session was essentially randomly determined.
All four sessions were conducted in the same classroom by the same experimenter. After the participants for a given session were seated in the classroom, the first of two Ponzo illusion assessments occurred. The Ponzo task was administered following essentially the same procedure as in Experiment 1, using the same slides and response sheets, the same instructions, and the same scoring procedure. In the case of Experiment 2, however, the slides were projected onto a large screen in the front of the room. The projected images provided essentially the same contrast as in Experiment 1, but in Experiment 2 all image dimensions were greater by a factor of three.
Following the first Ponzo administration, participants engaged in a group hypnotic susceptibility task. This task was part of an unrelated experiment, and will not be further described, except to point out that it was a standard group screening procedure (Shor & Orne, 1962) that required about 75 min to complete. This task was followed by a 10-15 mm break, which was in turn followed by a second administration of the Ponzo task, using the same stimuli and instructions as the first Ponzo administration.
Results
The above procedure yielded a total of 240 data sets (111 males and 129 females). Table III shows descriptive statistics for the first Ponzo administration (Ponzo 1), the second Ponzo administration (Ponzo 2), and the composite Ponzo, as well as effect sizes for the male versus female comparisons. The Pearson r values for comparisons of Ponzo 1 with Ponzo 2 were .755 for all participants combined, .770 for males, and .684 for females, all significant at p [less than] .001.
A 2 x 2 (sex x Ponzo administration) ANOVA was conducted, with the two levels of sex being male and female, the two levels of Ponzo administration being Ponzo 1 and Ponzo 2, and the dependent variable being Ponzo score (percent illusion). The effect due to sex was significant, F(l, 238) = 31.14, p [less than] .001, as was the difference between Ponzo 1 and Poazo 2, F(l, 238) = 17.45, p [less than] .001. The interaction was not statistically significant.
In the course of analyzing the results, it became clear that chance had provided the opportunity to examine another variable, namely, sex ratio. It happened that the four sessions differed considerably in the relative numbers of males and females who participated, as follows: Monday (22 males, 39 females), Tuesday (31 males, 34 females), Wednesday (34 males, 25 females), Thursday (24 males, 31 females). Fig. 3 shows composite Ponzo values for males and females for each of the four sessions of the experiment, as well as the sex ratio (the proportion of males to females) for each session. A 2 x 4 (sex x session) ANOVA was conducted, showing significant results for sex, F(1, 232) = 33.56, p [less than] .001, and for session, F(3, 232) = 2.96, p = .03. However, there also was a significant interaction, F(3, 232) = 4.43, p = .005.
Because of this interaction, simple main effects analyses were conducted for males and females separately. For males, the simple main effect due to session was significant, F(3, 107) = 3.17, p = .03. It also was significant for females, F(3, 125) = 5.02, p = .003. Comparisons of males with females were made for each of the four sessions using Fisher's LSD tests. For Session 1 this comparison was not significant. These comparisons were significant, however, for Session 2, t(232) = 2.82, p [less than] .005; Session 3, t(232) = 5.86, p [less than] .001; and Session 4, t(232) = 2.05, p [less than] .025. All these tests were one-tailed.
The simple main effects of session were further probed using two-tailed Fisher's LSD tests. For females the differences between Sessions 1 and 4 and between Sessions 2 and 3 were not significant. The remaining comparisons were all significant: Sessions 1 and 2, t(125) = 2.95, p [less than] .01; Sessions 1 and 3, t(125) = 2.95, p [less than] .01; Sessions 2 and 4, t(125) = 2.44, p [less than] .02; and Sessions 3 and 4, t(125) = 2.49, p [less than] .02. For males, the comparisons between Sessions 1 and 2, Sessions 1 and 4, Sessions 2 and 4, and Sessions 3 and 4 were not significant. The remaining two comparisons were significant: Sessions 1 and 3, t(107) = 2.04, p [less than] .05; and Sessions 2 and 3, t(107) = 2.95, p [less than] .01.
Finally, the Pearson product--moment correlation between the magnitude of the difference between male and female Ponzo scores for each session, and the corresponding sex ratios, was calculated. The resulting r = .996.
Discussion
With regard to Ponzo illusion susceptibility in general, the results of Experiment 2 reinforced those of Experiment 1 and previous studies. Using this form of the illusion, females provided significantly higher illusion scores than males. As in Experiment 1, the effect sizes were "medium" according to Cohen's (1988) guidelines. The results regarding Ponzo consistency also were similar to those in Experiment 1. That is, the correlations between Ponzo 1 and Ponzo 2 were substantial, indicating that there was a considerable degree of consistency in how participants responded to the task over time (although, of course, the amount of time elapsing between administrations was considerably less in Experiment 2 than in Experiment 1). The fact that there were statistically significant differences between the two administrations, however, shows that repeated testing did have some effect on participant response, although as can be seen in Table III this difference was small in absolute terms. When using the administrati on procedures incorporated into these experiments, it is clear that the Ponzo illusion is quite reliable, with results that hold up well over significant periods of time.
The relation between sex ratio and Ponzo response is intriguing. It is clear that the difference in Ponzo response between males and females varied as a direct function of the ratio of males to females. As that ratio increased, so did the gender differences in Ponzo response. Furthermore, the change affected both genders. That is, as sex ratio increased, female Ponzo responses tended to increase in magnitude, and male Ponzo responses tended, albeit less consistently, to decrease in magnitude.
Certainly one must bear in mind that this was a serendipitous finding. Experiment 2 was not specifically designed for the manipulation of sex ratio as a variable, and this fact should temper one's interpretation. For example, it might be argued that the effect could be due to day of the week, not to sex ratio, because the four sessions were run on different weekdays. Perhaps there is something about Thursdays that leads to different Ponzo responses than, for example, Mondays. Such an eventuality seems extremely unlikely, but it cannot be eliminated without appropriate controls. For the moment, at least, the conservative approach would be to consider the relation between sex ratio and gender differences in Ponzo response as no more than correlational (and one based on only four data points).
Assuming the relation between sex ratio and Ponzo response is reliable, however, one is left with the need to account for it. At this point, any explanation must remain speculative. However, one possibility worth considering is an extension of the findings of Experiment 1. If one assumes that gender differences in the Ponzo illusion are due, at least in part, to gender differences in the cognitive strategies employed to do the task, it does not require a major additional leap to suggest that both males and females have some flexibility in the extent to which they rely on such strategies. It is entirely possible that the "decision" as to which strategy to rely upon, and to what degree, is a part of the social role being played by the observer at any given time. Part of that social role is, of course, the sex role. It is not unlikely that young college-age males and females shape many aspects of their sex role behavior to fit the sex ratio they encounter at any given moment, and such behavior could well include how they respond to the Ponzo illusion. If this is the case, of course, one wonders how many other spatial tasks are susceptible to the same influence, and how many reported sex differences in spatial abilities would be modified if the social context (e.g., sex ratio) were different. Such a possibility is certainly worth further investigation.
(1.) To whom correspondence should be addressed (until August 2001) at Department of Psychology, 209 Johnson Tower, Washington State University, P.O. Box 644820, Pullman, Washington 99164-4820; e-mail: rjmiller@mail.wsu.edu. After that date, correspondence should be addressed at Department of Psychology, 133 Holmes. SUNY College at Brockport, Brockport, New York 14420-2977.
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Table I. Descriptive Statistics and Effect Sizes for Embedded Figures
Test and Ponzo Illusion - Experiment 1
Males (n = 54) Females (n = 54)
Measure M SD M SD
EFT 34.42 17.00 41.77 18.13
Ponzo 1 18.49 7.06 22.08 7.24
Ponzo 2 17.62 6.00 20.86 8.21
Composite 18.05 5.97 21.47 7.33
Pozno
All participants Effect size (d)
Measure M SD (males vs. females)
EFT 38.09 17.87 0.42
Ponzo 1 20.28 7.34 0.50
Ponzo 2 19.24 7.34 0.46
Composite 19.76 6.87 0.51
Pozno
Note. EFT means expressed in seconds. Ponzo values represent percent
illusion. Compsoite Ponzo is mean of Ponzo 1 and Ponzo 2.
Table II. Pearson Product-Moment Correlation Coefficients for Relations
Between EFT and Ponzo Illusion - Experiment 1
Pearson r
Comparison Males (n = 54) Females (n = 54)
EFT with Ponzo 1 -.016 .286 *
EFT with Ponzo 2 .200 .466 **
EFT with Composite Ponzo .091 .403 **
(*)p [less than] .05
(**)p [less than] .01.
All tests one-tailed.
Table III. Descriptive Satistics and Effect Sizes for Ponzo Illusion -
Experiment 2
Males (n = 111) Females (n = 129)
Measure M SD M SD
Ponzo 1 22.97 8.09 27.95 7.64
Ponzo 2 21.14 8.32 26.66 7.30
Composite Ponzo 22.06 7.72 27.31 6.85
All participants Effect size (d)
Measure M SD (Males vs. females)
Ponzo 1 25.65 8.22 0.63
Ponzo 2 24.11 8.24 0.71
Composite Ponzo 24.88 7.71 0.72
Note. Ponzo values represent percent illusion. Composite Ponzo is mean
of Ponzo 1 and Ponzo 2.
Fig. 3. Variations in composite Ponzo values (percent illusion) for
males and females for each of the four sessions. The sex ratio (defined
as the number of males divided by the number of females) is indicated
for each session. Sessions are displayed in order of increasing sex
ratio. Error bars represent standard errors.
Monday (0.52)
Thursday (0.77)
Tuesday (0.83)
Wednesday (1.29)
Note: Table made from bar graph
COPYRIGHT 2001 Plenum Publishing Corporation
COPYRIGHT 2001 Gale Group