(Editor: Nancy Dess, Occidental College)

Introduction

Things are not always as they appear. In the figure below, the diagonal line segments do not appear to be segments of a discontinuous straight line (collinear) when in fact they are. This illusion is known as the Poggendorff illusion after its founder (Coren & Girgus, 1978). Several factors affect the degree of misperception experienced in this illusion. One such variable is the separation of the verticals: The greater the separation, the greater the illusion. In this experiment, separation of the verticals and the length of the diagonal segments are both manipulated. This experiment thus allows students to evaluate whether each variable affects the illusion and, more interestingly, whether the effect of vertical separation is strengthened or diminished depending on the length of the diagonal lines. This experiment also allows students to evaluate whether varying the separation of the verticals affects the illusion more or less than does varying the length of the diagonals.

Design

The experiment uses a 2 x 3 factorial design that crosses three levels of a separation variable (narrow, medium, and wide) with two levels of a length variable (long and short). Both variables are manipulated within participants. The order of trials is fixed, beginning with four Narrow-Long trials, followed by four Medium-Long trials, four Wide-Long trials, four Narrow-Short trials, four Medium-Short trials, and four Wide-Short trials. Order is fixed on the assumption that the illusion neither strengthens nor diminishes over trials.

On each trial participants drag the upper right diagonal to the position they perceive to be collinear with the fixed lower left diagonal. The initial position of the upper right diagonal is randomly set to be both above and below the true collinear position of the lower left diagonal. The dependent variable is the deviation in pixels between the height of the adjusted diagonal line segment (the right diagonal) and the height of a true collinear diagonal line segment. A negative value indicates that the right diagonal was placed too low, which is the placement that reflects the Poggendorff illusion.

The factorial design of the experiment invites an analysis to determine the relative impact of diagonal length versus vertical line separation on the magnitude of the Poggendorff illusion. The analysis can compare differences in the magnitude of the marginal means for Wide, Medium, and Narrow trials on the one hand and Long and Short diagonal trials on the other. Students who have experience with the analysis of variance can use a two-way repeated measures ANOVA to test the significance of the two possible main effects as well as the effect of the interaction of vertical separation and diagonal line length.

Data Analyses

Sample data appears below:

Figure 1 |

The first six columns are self-explanatory. The following six columns reflect data from the six conditions in the study. The error value is reported as the dependent variable measure. Error is calculated by subtracting the y-axis coordinate from a fixed x-axis coordinate for each of the two diagonal lines.

Note: Error is computed by subtracting the y-coordinates for the two diagonal lines for a fixed x-axis coordinate.

References

Coren, S., & Girgus, J. S. (1978).Seeing is deceiving: The psychology of visual illusions.Oxford, England: Lawrence Erlbaum.