University of Essex

Department of Psychology

Research Methods in Psychology (PS114-4-FY)

Laboratory Report

Timeslot 3pm

“Actual and perceived midpoints in relation to visual perspective and confusion theories”.

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Date: 23/02/12Word Count: 1,728

“Actual and perceived midpoints in relation to visual perspective and confusion theories”.

Abstract

This study was conducted into the theories surrounding visual perspective and confusion for the

purpose of assessing whether adding to an existing study would obtain similar results, for the

purpose of assessing the accuracy of both the perception and confusion theory. The three original

figures from the Muller-Lyer (1889) illusion were used and modified to include right-angled figures

and participants marked their perceived midpoints on these figures, recording percentage errors for

analysis. It was found that this study supported the local confusion theory as midpoint shift occurred

even when only one wing was present on the figure and also without depth cues in right-angled

figures. Therefore, it was concluded that it is likely that the Muller-Lyer illusion is produced locally

rather than globally.

Introduction

The famous Muller-Lyer (1889) illusion is a geometrical visual illusion that alters the way in

which a shape’s geometry is viewed at face value. The illusion consists of two parallel horizontal lines

of identical length with an arrow-shaped “wing” or “fin” at the end of each line, identical to the wing

at the opposite end. The difference between these two lines is that one set of wings point away from

the midpoint of the line at an acute angle of 45 degrees and the other set face inwards at an obtuse

angle of 135 degrees. The effect of this illusion is that the obtuse-winged line appears to be longer

than the acute-winged line, despite both lines being of exactly the same mathematical length. The

theories behind the cause of this distortion in perception are what render the Muller-Lyer illusion

intriguing. The first theory being investigated is the confusion theory that predicts local midpoint

shift based around the positioning of the wings around it. Obtuse wings have the effect of

“stretching” the line so that the end points appear further apart than that of the acute winged-line

that has the apparent effect of moving the end points inwards. In short, the midpoints are distorted

due to the end points of the lines being affected by the positioning of the wings at either end. The

second theory under investigation is the global perspective theory, described in detail by Gregory

(1998). This theory dictates that the faulty interpretation of the midpoints is due to the relation the

observer makes between the line and wings and an existing object such as a corner. The obtuse-

angled line appears to be a concave corner viewed from the outside, whereas the acute-angled line

appears similar to a convex corner viewed from the inside and therefore, the obtuse line appears

longer due to the perception of the line as further away and does therefore not predict midpoint

shift. Other similar studies such as Predebon (2000) requested that participants mark midpoints.

However, Predebon then requested participants to further bisect these two halves and found

midpoint distortion was more prominent when closer to the wings. This experiment will analyse the

effect on the estimated midpoint, based on wing placement. It is assumed that participants will

locate the end points of each line before bisecting this in order to estimate the midpoint. The judged

midpoint should shift in the same direction as the apparent end point would shift if the local

confusion effect is observed. The same local effect if observed at both ends of a line should either

increase the distance between actual and perceived midpoints or minimise the difference to very

little. Additionally, if the confusion theory is accurate, the right angled figures without depth cues

used in this study should not initiate midpoint distortions.

Method

Participants

This study was conducted using an opportunity sample of 63 undergraduate psychology

students as a component of their course.

Apparatus

Apple iMacs and eMacs were used to present stimuli and record responses for the estimated

midpoint of the three standard Muller-Lyer and three right angled figures. The relevant files for

participation were loaded prior to the experiment.

Materials

The stimuli presented to the participants displayed the original standard Muller-Lyer figures for

the first three conditions (obtuse wing at one end; acute wing at one end and arrow wings at both

ends). The figures are horizontal lines with either obtuse-angled wings facing outwards, acute-angles

wings facing inwards or one wing pointing inwards and one pointing outwards. Right angled figures

were utilised in the last three conditions without depth cues (wing extends outwards; wing extends

inwards and wings at both ends). However, instead of using “arrow” shaped wings, wings were

altered to resemble incomplete squares as opposed to triangles. Each condition was presented four

times in random order on a plain background and every line was at the consistent length of 26cm. A

diagram of the conditions is shown in the following table.

Design

The design of this experiment was within-subjects (repeated measures), as each participant

completed each condition twice to ensure reliability. The three conditions of the independent

variable were the number of wings, wing orientation and wing shape. The dependent variable was

the measured distance between the actual midpoint and the perceived midpoint of the participants

and there were two trials of six scores recorded for each participant for the purpose of reliability.

Procedure

Participants were assigned to small cubicles to minimise interference during the experiment and

were shown a computer presentation with a plain background in which they were instructed to click

the midpoint of the displayed figure as soon as it was located in order to obtain a measure of their

immediate perception using the pointer. Each of the six conditions was presented four times (two

out of four of which were left-right reversed for variation purposes), culminating in a total of twenty-

four figures displayed in random order. Each figure was displayed only for the amount of time taken

for participants to locate and select the midpoint and there was a two second gap between selecting

to continue and the next figure appearing. At the end of the slides, participants recorded the six

displayed results for each condition and repeated the experiment to obtain a more reliable

measurement of their percentage errors. Scores were then passed directly to the researchers for

analysis.

The formula used to calculate percentage error for each condition is as follows:

% error: actual midpoint (perceived midpoint / line length)

Results

Participants obtained twelve scores each, two for each condition. The means of these two sets

of scores were calculated to produce a single result for each participant. The conditions were as

follows for the standard Muller-Lyer figures: 1 (obtuse wing on one end), 2 (acute wing on one end),

3 (wings at both ends – arrows) and the right angled figures were as follows: 4 (wing extends

outwards), 5 (wing extends inwards) and 6 (wings at both ends). Six means and standard deviations

for these conditions were calculated for the 63 participants in total.

Descriptive Statistics to summarise data: Mean and Standard Deviation of Independent Variables

Mean Estimation Standard Deviation Standard Muller-Lyer figures

1 (obtuse wing on one end) 1.33 1.272 (acute wing on one end) -2.41 1.453 (wings at both ends - arrows) -4.51 1.17 Right-angled figures4 (wing extends outwards) 0.57 1.155 (wing extends inwards) 0.17 1.356 (wings at both ends) -0.599 1.2

The means calculated show that the condition with the highest average percentage error in the

three standard figures was condition three ( -4.51)and the lowest was condition one (1.33). In the

set of three right-angled figures, condition six was the figure with the highest percentage error with

a mean of -0.599 and condition five was the lowest (0.17). This displays that those conditions with

higher mean percentage errors obtained the highest levels of midpoint distortion (condition 3 at -

4.51) and those with the lowest percentages obtained the lowest scores for midpoint distortion

(condition 6 at -0.599). In both the standard and right-angled trials, wings at both ends of the line

obtained the highest percentage errors. The standard deviations for all six conditions all range from

1.15 to 1.45, representing consistency across the results obtained and shows there was little

variance in percentage errors. As expected, condition one obtained a midpoint distortion of 1.33 in

the direction of the obtuse wing and condition two obtained a midpoint shift of -2.41 in the direction

of the acute wing. Also, the difference between actual and perceived midpoint was larger in

condition three with two wings at a mean percentage error of -4.51. It is important to additionally

recognise that conditions four, five and six obtained scores of 0.57, 0.17 and -0.599 which are

significantly less in terms of effectiveness at distorting midpoints than the standard Muller-Lyer

figures.

One-sample t-tests were carried out for each condition. From the results, it is clear that

condition three obtained the largest value at t(62) = -30.68, p <.001 and so had the largest overall

effect on midpoint distortion. The t-value for conditions one to three grew gradually larger (from

t(62) = 8.30, p <.001 to t(62) = 30.68, p <.001). However, this was untrue for the right-angled figures,

as condition five was the only condition rendered significantly insignificant by its p-value, hence t(62)

= 0.97, p 0.334. This suggests that right-angled figures are not as distorting as acute and obtuse-

angled figures with obvious depth cues.

Discussion

Prior to the study, it was hypothesised that the local confusion effect would be observed in lines

with a wing at one end towards the direction of the wing and that wings at both ends would increase

distance between actual and perceived midpoints or serve to cancel each other out. The data

collected in this investigation supports the confusion theory as opposed to the perspective theory,

considering that the perspective theory would predict that there were no midpoint shifts due to the

lack of depth cues in the right-angled figures. This is consistent with the research findings of

Predebon (2000), whose research also produced evidence of local confusion. This study compared

the confusion and perspective theory for the first time and although the data collected seems

supportive of local confusion, it may be beneficial to extend this experiment further and perhaps

divide participants into groups such as male and female, or age-oriented to compare these theories

further. This may be necessary as it has previously been suggested that there are significant

differences in male and female spatial recognition performance.

References

Gregory, R. L. (1998). Eye and Brain (5th Ed.) Oxford University Press. Ch 10.

Gregory, R. L. (2009). Seeing through illusions. Oxford University Press.

Martin, G.N., Carlson, N.R. & Buskist, W. (2009). Psychology. (4th ed.). Harlow, Essex: Pearson Education.

Muller-Lyer F. C. (1889). Optical illusions of judgement. Archives of Physiology Suppl, 263-270.

Predebon, J. (2000). Length illusions in conventional and single-wing Muller-Lyer stimuli. Perception & Psychophysics, 62, 1086-1098.