Abstract
This study examined the responses of 40 undergraduate women and 40 men to two Poggendorff figures, a traditional figure with the right oblique line omitted and a modified variant with the left vertical line and the right oblique line absent. Participants placed a dot on the right vertical line where the oblique line, if extended, would intersect the right vertical line. The results showed that women displayed larger illusions than men on both figures, consistent with past findings. Finding a sex difference with the modified variant did not support the suggestion that the intersection between the oblique and vertical lines is responsible for such differences. The effects of spatial separation and size of acute angle were similar for both versions of the illusion. The effects of spatial separation were inconsistent with an explanation of the illusion based on depth cues and it was suggested that an explanation of the Poggendorff illusion should focus on processing between the vertical lines.
The traditional Poggendorff illusion consists of an apparent misalignment of a transversal interrupted by two vertical lines. As shown in Fig. 1A, the two portions of the transversal appear misaligned, although they are objectively collinear. Recently, Declerck and De Brabander (2002) and Ling, Hamilton, and Heffernan (2006) investigated sex differences in the magnitude of the illusion. In both studies, women exhibited a larger illusion than men with the traditional figure. Ling, et al., however, did not find sex differences in a figure which consisted of only the transversal and suggested that the intersection between the transversal and vertical line was responsible for the difference in perception by sex. In the present study, the role of an intersection in generating sex differences was investigated by comparing responses to a variant of the Poggendorff figure (Fig. 1B) without the intersection with responses to a variant containing the intersection (Fig. 1C). Pressey and Sweeney (1969) found that this variant induced the traditional illusion and that the degree of illusion from this variant and the traditional figure was highly correlated (r = .47 and r = .77 for Groups I and IV, respectively). Their findings suggest that similar processes or mechanisms underlie the illusion in both forms. If the intersection of the transversal and the vertical line is responsible for sex differences in the size of the illusion, sex differences should be found with the figure containing the intersection but not in the one without the intersection.
Traditional and modified Poggendorff figures
In the traditional figure, as the spatial separation between the vertical lines increases the degree of illusion as measured in angular distortion (Pressey & Sweeney, 1969) increases. In a more recent study by Jones-Buxton and Wall (2001) two experiments were conducted assessing the effects of varying the distance between the vertical lines on the magnitude of the illusion. In the first experiment, 10 Poggendorff figures (one of the original figures and nine variants of the figure) were presented to 19 participants. The distance between the transverse lines of the figure were held at a constant 4 cm apart. In the original Poggendorff figure, the vertical parallel lines were 4 cm apart, but on four figures, the vertical lines were moved progressively closer to each other, and for five figures, the vertical lines were progressively placed farther apart from the position of the vertical lines of the original figure. The results indicated that as the distance decreased from the original Poggendorff figure, the illusion disappeared, and as distance increased from the original Poggendorff figure, the illusion was still observed, but it decreased significantly. In a second experiment the same 10 Poggendorff figures and an additional three figures were constructed so that the distance between the parallel lines was extended beyond the transversals. Results were consistent with those of the first experiment, and for the three additional Poggendorff figures the illusion was eliminated, except for the position of the largest difference. In general, those results indicated that the largest illusion will be induced if the adjacent ends of the transversal make contact with the vertical line.
Jones-Buxton and Wall (2001) suggested that the findings were consistent with a depth processing theory. According to this theory (Gillam, 1971), the transversals are processed as though they are receding in depth and as a consequence appear misaligned. Jones-Buxton and Wall suggested that separating the end points of the transversals from the vertical lines would diminish the likelihood that the lines would be processed as receding in depth and thus result in a smaller illusion. From this viewpoint, one would predict that as spatial separation increased the amount of angular distortion should remain constant in the traditional Poggendorff variant in comparison to the traditional figure and that in the modified Poggendorff variant the magnitude of the illusion should decrease. The present study tested their prediction.
Method
Participants
Forty men and 40 women undergraduate introductory psychology students (age 18 to 44 yr., M = 21.15, SD = 4.76) were recruited to participate in a study investigating sex differences in the Poggendorff illusion via a bulletin board advertisement in the Psychology Department of the University of New Brunswick, Saint John. All participants received extra credit for their classes, and were informed that the purpose of the study was to examine the perception of perceived direction. The study was approved by the Research Ethics Board at the University of New Brunswick.
Materials
Figures consisted of black lines drawn on 28 × 27.1 cm sheets of white paper. For testing purposes the original figures were photocopied. The traditional figure consisted of two vertical lines and one transverse line (Fig. 1C), and the second figure consisted of only one vertical line and one transverse line. For the traditional figure, the vertical lines were 15 cm long and the transverse line on the left was 3 cm long. The size of the acute angle between the transverse and vertical lines was 20°, 30°, or 40°. The angle was varied to change the location of veridical locations of responses to minimize the likelihood that participants would make their judgments on the basis of remembering the location of their past responses. The distance between the two vertical lines was 10, 20, or 40 mm. The dimensions of the Poggendorff variant were identical to that of the traditional figure with the exception that the left vertical line was omitted. During testing a figure was placed in the center of a wooden target holder, and a chinrest was positioned in front of the holder to keep a constant 55 cm distance between the participant and the figure.
Procedure
Participants were tested individually on two randomized sequences of the 18 test figures. They were instructed to draw a small dot on the right vertical line where the transverse line, if extended, would appear to intersect the right vertical line. They were told that their responses should be based on their visual judgment and they were not allowed to tilt their head or use their hands to align their responses.
Results
Size of illusion was measured with a protractor to calculate the magnitude of angular illusion on each figure. Illusion scores in the traditional direction were scored positively, while those in the opposite direction were scored negatively. Data from 40 men and 39 women were analyzed, with one woman's results being omitted due to a missing figure in the test package. The illusion scores were submitted initially to a 2 (sex) by 2 (trial) by 2 (variant) by 3 (angle) by 3 (spatial separation) split plot analysis of variance (ANOVA) using SPSS. Main effects for sex, variant, angle, and spatial separation were all statistically significant.
Sex differences
The mean illusion for men and women averaged across all conditions indicated significant sex differences in susceptibility to the illusion (F1,77 = 4.82, p = .03, partial η2 = 0.06). The mean illusion for men was 6.56° and the mean illusion for women was 8.54° (see Table 1). The interaction between sex and variant of illusion was not statistically significant. Two follow up ANOVAs on each variant of the illusion were conducted. The results, depicted in Table 1, indicated that women had a larger illusion than men for both variants of the figure. The ANOVAs indicated a significant effect of sex for the traditional figure (F1,77 = 4.82, p = .03, partial η2 = 0.06) and for the modified figure (F1,77 = 4.18, p = .04, partial η2 = 0.05).
Mean illusion for men and women on both Poggendorff variants
Variants, angle, and spatial separation
Table 2 shows the mean illusion for the different combinations of size of angle and magnitude of spatial separation for each variant of the illusion. Main effects and each of the interactions among the three variables were all statistically significant. The traditional figure induced a larger illusion than the modified version (F1,77 = 459.94, p < .001, η2 = 0.86), and size of illusion increased with increases in angle (F2,154 = 41.64, p<.001, η2 = 0.35) and larger spatial separation (F2,154 = 54.04, p<.001, η2 = 0.41). Examination of the data suggested that with the traditional figure, the mean illusion increased more as spatial separation increased than it did in the modified Poggendorff figure.
Mean illusion for Poggendorff variants, angles, and spatial separation
The interaction between Poggendorff variant and angle is more complex. For the traditional figure, the mean illusion increased more as the size of angle varied between 20° and 30° than between 30° and 40°, while for the modified figure the mean illusion increased less between 20° and 30° than between 30° and 40°. ANOVAs conducted on each Poggendorff variant indicated that spatial separation and angle were statistically significant for both variants at p < .001.
Discussion
The results are consistent with past research where women perceive a larger illusion than men (Declerk & DeBrabander, 2002; Ling, et al., 2006). Most importantly, however, is the finding that consistent sex differences occurred with both variants of the illusion and not only with the traditional figure. The modified version did not have the oblique line making contact with a vertical line and thus questions the explanation by Declerk and Debrander, 2002) if an actual intersection is responsible for sex differences. Their suggestion was based on comparing sex differences between a figure with only the oblique lines versus that of the traditional figure. Another interpretation of their results along with the present findings, would be that there are no sex differences in aligning two oblique lines but that the process or processes responsible for the Poggendorff illusion lead to sex differences. It is plausible that an intersection could enhance the sex differences. If the intersection increased the magnitude of sex differences in the magnitude of illusion then an interaction between sex and Poggendorff variant would be expected, however, the interaction was not statistically significant. The mean difference in the size of the illusion for the two variants was 6.60° for men and 7.76° for women. One might think that although not statistically significant the direction of the differences is in the predicted direction but the percentage of increase in illusion between the variant without an intersection with the variant with an actual intersection for men is 302% but only 267% for women.
To explain sex differences on the Poggendorff illusion, one might turn to the general finding that men tend to perform better on tasks of visual spatial ability than women. For example, in their meta-analysis of sex differences in spatial abilities, Voyer, Voyer, and Bryden (1995) reported large effect sizes for mental rotation tests (d = 0.67, Table 5) and rod and frame tests (d = 0.48, Table 5). Focusing on general factors leading to sex differences on a variety of tasks may be more fruitful in discovering general principles underlying sex differences than concentrating on specific components within the Poggendorff figure.
The effects of spatial separation on the magnitude of the illusion are consistent with studies which used the traditional figure (e.g., Pressey & Sweeney, 1972) and the current findings indicate that this effect also occurs with the modified figure. Similar results for both Poggendorff figures also occurred for the effects of varying size of angle. In both variants, size of illusion increased as size of angle increased. Basically, as with the finding of sex differences, the results indicate similar trends on the magnitude of illusion with both variants of the figure.
In the study by Jones-Buxton and Wall (2001), the distance between the oblique lines remained constant while the spatial separation between the vertical lines varied. They argued that when the vertical lines were positioned away from the oblique lines, cues to depth which would lead to the illusion were less pronounced and as a consequence would lead to a smaller illusion. The present findings of increased illusion with increased spatial separation with both variants of the figure call into question this explanation of their findings. From their analysis, as spatial separation increased, the magnitude of the illusion should decrease with the modified variant and remain constant with the traditional figure, not increase.
The findings of similar trends with both variants of the illusion suggest that an explanation of the illusion which focuses on either misjudgment of angles (e.g., Chiang, 1968) or misjudgment of distances formed between the oblique line and the vertical line which it intersects are insufficient as a complete explanation of the illusion. An explanation which includes processing between the vertical lines is needed such as those offered by Pressey (1971) or Day and Dickerson (1976). In Pressey's original explanation, he argued that during the Poggendorff task an observer projects a series of possible projections from an oblique line to the opposing vertical line and then selects one of projections. Later, Wilson and Pressey (1976) tested the suggestion that the selection was based on underestimation on the distance between the oblique lines, however, this suggestion was rejected because findings indicated that the distance was overestimated and not underestimated. It may be worthwhile to investigate other options which examine processing between the vertical lines.