(Editor:   Maureen McCarthy)


The Müller-Lyer illusion is a classic optical illusion first popularized by Franz Carl Müller-Lyer in the late 1800's (Kazdin, 2000). The classic presentation of the illusion is depicted in Figure 1. In this presentation, two lines of identical length (represented in red) are presented with what might be described as fins or wings attached to either end of the lines. The fins (or wings) on one line are oriented out, and on the other they are oriented in. (In the figure below, the fins-out line is on the left, and fins-in line is on the right.) The presence of the fins makes the two red lines appear to be different in length, with the fins-in arrangement causing the red line to look shorter and the fins-out arrangement causing it to look longer. Müller-Lyer coined the term "confluxion" to describe this illusion. The exact nature of this effect has been studied extensively without consensus (c.f., Dewar, 1967; Lewis, 1909; Presey & Martin, 1990; Restle & Decker, 1977) about which perceptual principles account for the illusion.

An example of lines with fins
Figure 1

The study contained in this collection is a variation of the original Müller-Lyer illusion, one which enables investigators to study the effect of changes in fin angle on the apparent length of lines. Participants in the study are presented with two lines, as in the standard Müller-Lyer presentation, but one of the lines has fins and one does not. Moreover the red lines are initially different in length. The participant's task is to adjust the plain line (without fins) to make the lengths the same. The adjustment is made using a slider (blue arrow in Figure 2 below) that can be dragged using the computer mouse. As the slider is moved up and down the scale, the adjustable red line changes in length. .

An image of lines used in the Muller-Lyer experiment
Figure 2


The independent variable is fin angle, which varies from 15 degrees to 165 degrees in 15 degree steps (i.e., 15, 30, 45, 60, 75, 90, 105, 120, 135, 150, 165). There are, then, 11 levels to the independent variable. Angles from 15 to 75 degrees are used to create "fins in" stimuli. Angles from 105 to 165 degrees are used to create "fins out" stimuli. The figures below illustrate.

Two sets of 11 trials are conducted. In each set, the angle used on any one trial is chosen at random from the set of 11, but once the angle has been used, it does not reappear until the next set of trials. The total number of trials, therefore, is 22 with each angle being used twice.

The dependent variable is the difference in length between the two lines. Lengths are measured in pixels. The red line with fins attached--call it the "illusory" stimulus--has a random length of between 100 and 150 pixels on the 640 x 480 pixel screen that is used at OPL. The adjustable line is randomly set to either 90 or 160 pixels at the start of each trial. Thus sometimes the adjustable line must be made longer and sometimes shorter in order to create a perceptual match with the illusory line. To compute the difference, the length of the adjustable line following adjustment is subtracted from the length of the illusory stimulus. A positive difference indicates that the illusory stimulus appears shorter than it in fact is; a negative difference indicates that the illusory stimulus appears longer than it in fact is. Because non-zero differences represent errors in judging the length of lines, the dependent variable in this experiment is a measure of adjustment error.

Example Data Analyses

Adjustment errors can be graphed to judge the effect of fin angle on adjustment error. Figure 3 is a plot of data points that represent how the average adjustment error changed as a function of fin angle for one small set of participants. Adding a regression line to the plot shows the general linear trend.

A graph of adjustment errors
Figure 3

For datasets that are reasonable large, it will be interesting to do separate plots for males and females. Some data indicate that females are more susceptible to this and other illusions than males are (e.g., Dewar, 1967; Porac et al., 1979). A steeper regression line for females than males would provide confirmation of this observation. Also, one could sum the absolute values of errors for males and females and compare the average errors.

Another thing to consider in the data is whether the 90 degree condition tended to produce accurate perception or whether it produced consistent adjustment errors. To address this issue statistically, a one-sample t-test could be use to compare the observed error (which was approximately -5 pixels in the dataset shown in Figure 3) to the expected difference of 0 (no error).

Data Download and Format

Data are downloadable in three formats (XML, Excel spreadsheet format, and comma delimited for statistical software packages like SPSS). The five columns provide classification data (participant ID number, gender, the class ID number, age, and date of participation)

A picture of muller-lyer data
Figure 4

Experimental data are recorded in columns 7- 17, reflecting the 11 different angles or levels of the IV presented in the experiment. Each value recorded in the respective column is a mean that represents a bias value that was derived by averaging the four trials.

Applications and Extensions

Although research on the Mueller-Lyer illusion began over a century ago (Judd, 1899), there is still no definitive theoretical explanation for why people experience the illusion. Students can be challenged to propose their own theories and then come up with the design of a novel experiment that would test their theory. Alternatively, they could search the literature for existing theories and then see how these theories have been tested to provide either confirming or disconfirming evidence.

Students wishing to use the OPL database to address a novel question might want to determine whether the the effect of fin angle on adjustment error is best described as linear or curvilinear.  For example, does the change from 105 to 120 degrees increase the adjustment error by the same amount as the increase from 150 to 165?  Does the angle increase from 75 to 60 degrees produce the same increase in error as the angle increase from 30 to 15 degrees? If the effect of fin angle is linear, the increase in error should be constant across these 15 degree increments.  Once students have resolved this issue empirically by using a very large dataset drawn from the cumulative OPL data archive, they could ask whether their findings have any relevance for judging the merit of existing theories.


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