procedure of muller lyer experiment

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How the Müller-Lyer Illusions Works

• The Illusion
• Explanations
• Does Everyone See It?
• Similar Optical Illusions

The Müller-Lyer illusion is an optical illusion where two lines of the same length appear to be of different lengths. 

A German  psychologist  named Franz Carl Müller-Lyer created the illusion in 1889. In the original version, he asked people to mark where they thought the midpoint of the line was to gauge if they perceived the lines as being different lengths.

What Do You See?

In the top half of the image above, which line looks like it’s the longest? 

For most people, the line with the fins of the arrow protruding outward (the center line) appears to be the longest. The line with the arrow fins pointing inward appears to be shorter. 

While your eyes might tell you that the line in the middle is the longest, the shafts of both lines are exactly the same length—which you can see in the bottom half of the image.

Like other  optical illusions , the Müller-Lyer illusion has had psychological researchers scratching their heads to try to come up with an explanation. Here are a few theories they’ve come up with. 

How the Müller-Lyer Illusion Works

Optical illusions aren’t just fun, they also serve as an important tool for researchers. By looking at how we perceive illusions, we can learn more about how our brains and  perceptual processes  work. 

That said, experts do not always agree on what causes optical illusions—and the Müller-Lyer illusion is a great example.

Müller-Lyer: Real Life Example

If you've ever tried to dress a certain way to make your legs look longer, then you've used the Müller-Lyer in real life.

One study actually put this piece of fashion wisdom to the test and found that when looking at a drawing of a woman wearing a high-cut swimsuit, people thought her legs were much longer compared to when she was dressed in calf-length tights.

The Size Constancy Explanation

According to psychologist Richard Gregory, the Müller-Lyer illusion happens because of a misapplication of size constancy scaling. 

In most cases, size constancy lets us perceive objects in a stable way by taking distance into account. In the three-dimensional world we live in, this principle allows us to perceive a tall person as being tall whether they are standing next to us or off in the distance. When we apply this same principle to two-dimensional objects, Gregory suggests that errors can crop up.

Other researchers say that Gregory's explanation does not sufficiently explain the illusion. For example, other versions of the Müller-Lyer illusion use two circles at the end of the shaft. In this case, there are no depth cues but the illusion still occurs. It has also been shown that the illusion can occur when viewing three-dimensional objects.

The Depth Cue Explanation

Depth plays an important role in our ability to judge distance.  One explanation of the Müller-Lyer illusion is that our brains perceive the depths of the two shafts based on depth cues.

When the fins are pointing inward toward the shaft of the line, we see it as sloping away like the corner of a building. This depth cue leads us to see the line as being further away and therefore shorter.

When the fins are pointing outward away from the line, it looks more like the corner of a room sloping toward us. This depth cue leads us to believe that the line is closer and therefore longer.

The Conflicting Cues Explanation

An alternative explanation proposed by R. H. Day suggests that the Müller-Lyer illusion occurs because of conflicting cues.

Our ability to perceive the length of the lines depends on the actual length of the line and the overall length of the figure. Since the total length of one figure is longer than the length of the lines themselves, it causes us to see the line with the outward-facing fins as longer.

Researchers from the University of London suggest that the illusion demonstrates how the brain reflexively judges information about length and size before anything else.

Dr. Michael Proulx explained that "many visual illusions might be so effective because they tap into how the human brain reflexively processes information. If an illusion can capture attention in this way, then this suggests that the brain processes these visual clues rapidly and unconsciously. This also suggests that perhaps optical illusions represent what our brains like to see.”

Mental Math

Some researchers have even applied complex mathematical concepts like probability to explain how the Müller-Lyer illusion works.

Does Everyone See the Müller-Lyer Illusion?

One of the interesting things about optical illusions, including the Müller-Lyer illusion, is that not everyone sees them the same way. 

Research has shown that people from different cultures have different perceptions of the Müller-Lyer illusion—and some people don’t seem to “fall” for it at all.  For example, in the early 20 th century, researchers discovered that indigenous people from the Murray Islands in Australia were less likely to see the lines as being different lengths than Europeans.

In the 1960s, researchers looking at how culture influences perception used the Müller-Lyer to show that people who live in places with more rectangular structures might be more susceptible to the illusion than people living in places that have fewer edges and straight lines.

Later studies that looked at people living in rural vs. more urban areas supported the idea that seeing a lot of these rectangular structures might affect how they perceived the Müller-Lyer illusion.

Other researchers challenged these ideas and showed that people living in cultures of all shapes and sizes responded to the illusion the same way. Instead, they thought that how much pigment people have in their eyes might play a role in how they perceive illusions.

And another cool thing? In 2021, Professor Susan Goldin-Meadow from the University of Chicago did a study using the Müller-Lyer illusion. The participants included English speakers and American Sign Language users, and they were asked to consider the illusion in different contexts—by just looking at it, by planning to describe it to someone else, or by gesturing like they were going to pick up the lines.

They found that people were more likely to see the illusion when they were only looking at it and less likely to “fall for it” when they were thinking about how to describe it or gesturing. 

When describing the study in a press release for the university, Goldin-Meadow said “the Müller-Lyer illusion has always fascinated me. And using it struck me as an ideal way to ask this question about where gestures come from. I thought they were tied to language because gestures and speech are so well integrated. But now we have evidence that gestures may also stem from action.” 

So, not only was the study a fascinating look at the illusion itself but it’s also a great example of how these tricks played on our eyes can help us learn more about our brains. 

Illusions Like Müller-Lyer

There are a few other optical illusions psychologists have studied that are similar to the Müller-Lyer illusion:

• Vertical-horizontal illusion. This illusion has participants judge the lengths of horizontal (side to side) and vertical (up and down) lines. The vertical line and horizontal line are connected, with the vertical line going up from the center of the horizontal line. Participants usually over or underestimate the length of the bisecting line—even when they’ve been told that the lines are exactly the same length!
• Ponzo Illusion: This illusion has two lines placed over a drawing of a railroad track. Participants are asked which line is longer, but the truth? They’re the same length! How is that so? It’s all about perspective—in this case, linear perspective. The line that appears to be farther away on the track looks longer, while the one that’s closer looks shorter.

Wolfram Demonstrations Project. Müller-Lyer Illusion .

Ninio J. Geometrical illusions are not always where you think they are: a review of some classical and less classical illusions, and ways to describe them .  Front Hum Neurosci . 2014;8:856. doi:10.3389/fnhum.2014.00856

Morikawa K. An application of the Müller-Lyer illusion .  Perception . 2003;32(1):121-123. doi:10.1068/p3437

Gregory RL.  Eye and Brain - the Psychology of Seeing, Fifth Edition . Princeton University Press; 2015.

McGraw KO, Stanford J. The apparent distance of interior and exterior corners: a test of Gregory's misapplied size constancy explanation for the Mueller-Lyer illusion .  J Gen Psychol . 1994;121(1):19-26. doi:10.1080/00221309.1994.9711169

M Woloszyn. Contrasting three popular explanations for the Muller-Lyer illusion . Current Research in Psychology . 2010;1(2):102-107. doi:10.3844/crpsp.2010.102.107

Vickers D, Smith PL.  Human Information Processing: Measures, Mechanisms, and Models . Amsterdam: North-Holland; 1989.

Proulx MJ, Green M. Does apparent size capture attention in visual search? Evidence from the Muller-Lyer illusion .  Journal of Vision . 2011;11(13):21-21. doi:10.1167/11.13.21.

Howe CQ, Purves D. The Müller-Lyer illusion explained by the statistics of image–source relationships .  Proceedings of the National Academy of Sciences of the United States of America . 2005;102(4):1234-1239. doi:10.1073/pnas.0409314102

Rivers 1901:  The measurement of visual illusion   Rep. Brit. Ass., p. 818

Segall, M. H., Campbell, D. T., & Herskovits, M. J. (1966).  The influence of culture on visual perception .  Bobbs-Merrill.

Ahluwalia A. An intra-cultural investigation of susceptibility to 'perspective' and 'non-perspective' spatial illusions .  Br J Psychol . 1978;69(2):233-241. doi:10.1111/j.2044-8295.1978.tb01653.x

Jahoda G. Retinal pigmentation, illusion susceptibility and space perception .  International Journal of Psychology . 1971;6(3):199-207. doi:https://doi.org/10.1080/00207597108246683

University of Chicago. What size is an object? Your description might depend on your intentions .

Prinzmetal W, Gettleman L. Vertical-horizontal illusion: one eye is better than two .  Percept Psychophys . 1993;53(1):81-88. doi:10.3758/bf03211717

APA Dictionary of Psychology. Ponzo illusion .

By Kendra Cherry, MSEd Kendra Cherry, MS, is a psychosocial rehabilitation specialist, psychology educator, and author of the "Everything Psychology Book."

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Müller-Lyer illusion

Learn about this topic in these articles:, description.

The Müller-Lyer illusion is based on the Gestalt principles of convergence and divergence: the lines at the sides seem to lead the eye either inward or outward to create a false impression of length. The Poggendorff illusion depends on the steepness of the intersecting lines. As…

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Müller-Lyer illusion: Cognitive style, attentional and temperamental determinants data

While the cognitive predictors of visual illusions have been widely researched, thus far, the temperamental ones have not been studied. The dataset provides data on cognitive and temperamental determinants of the Müller-Lyer illusion recorded in a group of 170 participants aged 20–33. The cognitive predictors included: the field dependent-independent cognitive style and the efficacy of attention networks: alerting, orienting, and executive control. The dataset is related to the research findings in the paper ‘Cognitive and temperamental determinants of susceptibility to the Müller-Lyer illusion’ published in Personality and Individual Differences.

Specifications Table

Value of the Data

• • The data allow broader understanding of determinants of the Müller-Lyer illusion, which is one of the most frequently analysed visual illusions in cognitive science.
• • The dataset fills a lack of data on susceptibility to illusions that depend on the resistant/non-resistant and stimulated/unstimulated temperament types, which take into account the importance of rhythmicity for each of these types.
• • The data provide information on susceptibility to visual illusions that concern several professions such as pilots, drone operators, laparoscopy surgeons, dentists, and doctors operating USG equipment and CT scanners. Broader understanding of cognitive and temperamental determinants of illusions may allow the design of appropriate cognitive training for those particularly likely to experience illusions.

1. Data Description

The dataset contains information about participants (id number and sex: 1 = female, 2 = male) and results obtained in four tasks: Visual Illusion Simulation (VIS), Embedded Figure Test (EFT), Attention Network Test (ANT), The Formal Characteristics of Behavior-Temperament Inventory (FCB-TI).

List of variables in the dataset:

• VIS_ML_reference_line-length (in inches) of the reference line (top component) in the Müller-Lyer illusory figure.
• VIS_ML_time 1–15-number of milliseconds participant took to estimate the line length in the Müller-Lyer illusory figure in each trial.
• VIS_ML_under 1–15-the participant's underestimation of the bottom line length in the Müller-Lyer illusory figure in each trial.
• VIS_ML_over 1–15-the participant's overestimation of the bottom line length in the Müller-Lyer illusory figure in each trial.
• VIS_ML_error 1–15-the participant's estimation of the bottom line length in the Müller-Lyer illusory figure in each trial. The estimation was converted into percentage of error in the database.
• VIS_ML_error_total-the participant's mean percentage of error of one trial in estimation of the line length in the Müller-Lyer illusory figure across 15 trials.
• VIS_ML_time_total-the participant's mean reaction time (in milliseconds) of one trial in estimation of the line length in the Müller-Lyer illusory figure across 15 trials.
• EFT_Witkin-total number of seconds participant took to find the simple figure in the complex figure in all 12 tasks.
• ANT_no_cue-participant's mean reaction time (in milliseconds) of the no cue condition (measure of tonic alertness).
• ANT_double_cue - participant's mean reaction time (in milliseconds) of the double cue condition (measure of phasic alertness).
• ANT_center_cue-participant's mean reaction time (in milliseconds) of the center cue condition.
• ANT_spatial_cue-participant's mean reaction time (in milliseconds) of the center cue condition.
• ANT_congruent-participant's mean reaction time of all congruent flanking conditions.
• ANT_incongruent-participant's mean reaction time of all incongruent flanking conditions.
• ANT_alerting-participant's mean reaction time of the double cue condition subtracted from the mean reaction time of the no cue condition.
• ANT_orienting-participant's mean reaction time of the spatial cue condition subtracted from the mean reaction time of the center cue condition.
• ANT_executive-participant's mean reaction time of all congruent flanking conditions subtracted from the mean reaction time of incongruent flanking conditions.
• FCBTI_Briskness-total number of participant's points on the Briskness temperament trait scale.
• FCBTI_Perseverance-total number of participant's points on the Perseverance temperament trait scale.
• FCBTI_Rhythmicity - total number of participant's points on the Rhythmicity temperament trait scale.
• FCBTI_Sensory_Sensitivity-total number of participant's points on the Sensory Sensitivity temperament trait scale.
• FCBTI_Endurance-total number of participant's points on the Endurance temperament trait scale.
• FCBTI_Emotional_Reactivity-total number of participant's points on the Emotional Reactivity temperament trait scale.
• FCBTI_Activity-total number of participant's points on the Activity temperament trait scale.

2. Experimental Design, Materials and Methods

2.1. participants.

The participants were 170 healthy persons aged 20–33 ( M  = 24.75, SD = 3.29), composed of 93 females ( M  = 24.97; SD = 3.46) and 77 males ( M  = 24.48; SD = 3.06) who were right-handed and without self-reported vision defects. Recruitment advertisements were posted on social media and the websites of SWPS University as well as websites contracted by SWPS University.

2.2. Procedure

The research took place in the university laboratory and took about two hours that included two short breaks. Participants performed the three-part procedure in the following order: (1) a computer version of EFT on an NVIDIA SHIELD 16 GB 8 inches tablet, (2) VIS and ANT tasks on a desktop computer with Java, E-prime, and a 21.5 inches LCD monitor / TFT active matrix (model HP S2231), and (3) FCB-TI(R) in a paper and pencil version. There were 10 min rest and refreshment breaks between individual parts.

3. Materials

3.1. visual illusion simulation.

Susceptibility to the Müller-Lyer illusion was diagnosed using a computer version of the Visual Illusion Simulation, prepared by H. Bednarek and P. Sobecki in 2016. The task was displayed on a 21.5-inch screen and participants were seated about 50 cm from the monitor. The participants' task was to adjust the length of the bottom line to appear equally long as the upper one. The line lengths were set using the arrows keys and confirmed with enter (15 trials). Participants had no time limit to complete the VIS task.

The illusory figure was black and was presented on a white background. Both reference and adjusted lines were placed above each other. Spacing between the top and bottom lines was 3 inches. The reference line length (top component) was presented with inward-pointing arrows and its length was 300 px (about 3.08 inches). The adjusted line (bottom component) was presented with outward-pointing arrows and its starting length varied randomly between 250 and 350 px. The update speed (change of the length of stimuli for 1px) was 60 msec. Arrows angles were 40° and thickness of the lines was 2 px. Resolution of the screen was 1920 × 1080. The refresh rate was 60 Hz. An illustration of the stimuli is presented in Fig. 1 .

Visualization of the Müller-Lyer illusion in VIS task.

The size of error was expressed in inches. Susceptibility to the illusion was determined as an overestimation or underestimation of the length of the bottom line. A higher score meant a larger error and indicated susceptibility to the illusion. The raw data was transformed into percentage of error for each participant and trial as proposed by Grzeczkowski and co-workers [1] : the value of the reference line length was subtracted from the adjusted line length and then the difference was divided by the value of the reference line length and multiplied by 100. Positive results were achieved by subjects who overestimated the length of the adjusted line (bottom component), while negative results were achieved by participants who underestimated the bottom line length.

3.2. Embedded figure test

Field-dependent/independent cognitive style was diagnosed using a computer version of the Embedded Figure Test (EFT) [2] , prepared by H. Bednarek and W. Uliajnow in 2016. The task was performed on a NVIDIA SHIELD 16 GB 8-inch tablet with the NVIDIA SHIELD Direct Stylus 2 pen provided and used to trace the simple figure.

The task was to find and outline a simple geometric figure concealed in a complex figure. Example of one simple and complex figure is presented in Fig. 2 . The test comprised a training stage and the proper test that contained 12 tasks. The complex figure was displayed for 5 s, then the simple figure was revealed for 10 s, and, finally, the complex figure appeared on the screen again. The time limit for finding the simple figure hidden in the complex one was 180 s. The participant was able to return to the view of the simple figure five times during one task (five attempts counted to the time limit). After that time, if the participant did not find the simple figure, another card with a complex figure was displayed.

Example of a simple geometric figure and a complex figure in EFT task.

The performance indicator was the total time needed to solve all 12 tasks.

3.3. Attention network test

The Attention Network Test (ANT) was used to assess the participants’ alerting, orienting, and executive function systems [3] . Participants were seated 50 cm from a computer screen. The test was administered using E-Prime® software. The test consisted of 24 practice trials with full feedback that included a summary of feedback for speed and accuracy with 3 blocks of 96 trials each (2 repetitions × 4 cue conditions × 3 flanker conditions × 2 target positions × 2 target directions) that gave no feedback. There was a short break between blocks.

The stimulus appeared above or below the point of fixation and consisted of a central arrow and surrounding arrows that pointed in the same direction as the middle one (congruent condition) or in the opposite direction (incongruent condition). The participants’ task was to press the appropriate key-either (<) or (>) -on the keyboard as quickly as possible to specify whether the middle arrow was pointing to the left or right.

The central arrow occurred in one of three conditions: (a) neutral – no flankers (e.g., →), (b) congruent – flanked by pairs of arrows pointing in the same direction (e.g., →→→→→), or (c) incongruent – flanked by pairs of arrows pointing in opposite directions (e.g., →→←→→). There were four cueing conditions: (a) no cue (fixations cross only)-a temporally uninformative condition, (b) center cue (black asterisk at the fixation cross)-temporally informative, (c) double cue (one black asterisk above and one below the fixation cross)-temporally informative, and (d) spatial cue (single black asterisk above or below the fixation cross)-temporally and spatially informative as it indicated the upcoming location of the subsequent target.

The efficacy of alerting system function was calculated by subtracting the mean reaction time of the double cue condition (measure of phasic alertness) from the mean reaction time of the no cue condition (measure of tonic alertness). The orienting system efficacy was calculated by subtracting the mean RT of the spatial cue condition from the mean RT of the center cue one. The conflict (executive control) effect was calculated by subtracting the mean RT of all congruent flanking conditions from the mean RT of incongruent flanking conditions.

Each trial began with presentation of a fixation cross for a variable duration (400–1600 ms). A cue was then presented for 100 ms in the cue conditions or the fixation cross remained unchanged for the same duration in the no cue condition. After another short fixation period lasting 400 ms, the target with or without flankers (neutral versus congruent/incongruent conditions, respectively) was presented until the participant responded or 1700 ms elapsed. The post-target fixation period then appeared for a duration equal to 3500 ms minus the duration of the initial fixation and reaction time. A single session lasted approximately 20 min.

3.4. The formal characteristics of Behavior-Temperament Inventory

To diagnose temperament types, the participants completed The Formal Characteristics of Behavior-Temperament Inventory in the revised version (FCB–TI(R)) [4] which measures seven temperamental traits that refer to the formal aspects of behavior. They are manifested in the energetic level meaning intensity of reactions (traits: Briskness, Perseverance, and Rhythmicity) and temporal features referring to time characteristics of reactions (Sensory Sensitivity, Endurance, Emotional Reactivity, and Activity) [5] .

The FCB-TI(R) consists of 100 items and is rated on a 4-point scale: 1-I strongly disagree, 2-I disagree, 3-I agree, and 4-I definitely agree. The results of each scale are calculated by totalling the number of points accorded by the answer key. Higher test results on each scale equals a greater intensity of a temperament trait.

Ethics Statement

The work was approved by the local Ethical Commission at the University of Social Science and Humanities (permission no 11/2016, registered as 12/04/2016). It fulfilled the stipulations of the Declaration of Helsinki: Medical Research Involving Human Subjects. All participants provided their written informed consent prior to the study.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships which have or could be perceived to have influenced the work reported in this article.

Acknowledgments

This work was funded by the Polish National Science Center (Narodowe Centrum Nauki) grant NCN OPUS 9 2015/17/B/HS6/04183 “The influence of training of cognitive functions on susceptibility of visual illusions”, under the supervision of Hanna Bednarek.

The Müller-Lyer illusion through mental imagery

• Open access
• Published: 16 November 2022
• Volume 42 , pages 29316–29324, ( 2023 )

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• María José Pérez-Fabello   ORCID: orcid.org/0000-0003-2856-4038 1 &
• Alfredo Campos 2  

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Previous studies have pointed to a link between visual perception and mental imagery. The present experiment focuses on one of the best-known illusions, the Müller-Lyer illusion, now reproduced under conditions of real perception and by means of imagery. To that purpose, a tailored ad-hoc set of combined figures was presented to a total of 161 fine art students ( M age = 20,34, SD  = 1,75) who individually worked with two different variations of the Müller-Lyer figures which consisted of a 10 mm long shaft and two fins set at an angle of 30º, being 15 mm long in one instance and 45 mm long in the other. In small groups, participants also completed an image control questionnaire. Results yielded that the longer the oblique lines, the larger the magnitude of the illusion both in the situation of real perception and in the imaginary situation. Also, the magnitude of the illusion augmented in the situation of perception in contrast to the imaginary situation, both with 15 mm long fins and with those of 45 mm. However, no significant differences were found in the magnitude of the illusion between high and low individuals in image control, although interactions between image control and other variables were indeed significant. The consistency of the outcome is a step forward in the study of illusions through mental images and opens the door to new lines of research that could involve innovative methods of analysis, different versions of the illusion and wider groups of participants.

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Introduction

The classic Müller-Lyer illusion ( 1889 ) is one of the best known and non-contested experiments on visual perception: a line of a given length looks subjectively longer or shorter according to the direction its fins are pointing to, inward (> <) or outward (< >). This inward/outward-pointing fins (Dragoi & Lockhead, 1999 ) have also been termed wings-out/wings-in (Greist-Bousquet & Schiffman, 1981 ; Porac, 1994 ) tail fins or arrowheads (Wang et al., 1998 ).

Many aspects of the Müller-Lyer illusion have already been studied. As stimuli definers, researchers have considered geometric and physical parameters (Cretenoud et al., 2020 ; DeLucia, 1993 ; Dragoi & Lockhead, 1999 ; Saccone & Chouinard, 2019 ; Schwarz & Reike, 2020 ; Zhang et al., 2020 ), neurophysiological factors (de Brouwer et al., 2015 ; Qiu et al., 2008 ; Tabei et al., 2015 ; Weidner et al., 2010 ; Zhang et al., 2013 ), the magnitude of the illusion as a function of age (Bondarko & Semenov, 2009 ; Brosvic et al., 2002 ), the influence of sociocultural backgrounds (McCauley & Henrich, 2006 ; Phillips, 2019 ), the influence of the illusion on interpersonal distance (Brunce et al., 2021 ), the illusion as related to personality traits (Zhang et al., 2017 ) and clinical disorders (Chouinard et al., 2013 ; Costa et al., 2021 ). Furthermore, there is a copious number of recent studies that deal with the experience of the illusion in a wide variety of animals (Costa et al., 2021 ; Santacà & Agrillo, 2020 ; Santacà et al., 2020 ; Schwarz & Reike, 2020 ).

Inaugural studies on the Müller-Lyer illusion induced by means of images were carried out during the decade of the 1980´s (Berbaum & Chung, 1981 ; Ohkuma, 1986 ; Watters & Scott, 1989 ) tried to demonstrate similitudes between perceptive processes and imagination by replicating the Müller-Lyer illusion through mental images. For this purpose, they shaped the figures by adding dots at line ends. Then they asked participants to imagine the oblique lines that formed the fins both towards the inner dots and towards the outer dots. Final results were akin to those of a situation of actual perception, so the authors concluded that imagination and perception shared similar processes and brain areas. In fact, it has been recently shown that when perception and mental imagery are externally triggered, similar neural codes get activated in sensory as well as in high-level brain areas (for reviews, see Dijkstra et al., 2019 ; Pearson, 2019 ). Current studies have also supported that the way our brain processes external inputs during perception is affected by mental imagery (Dijkstra et al., 2021 ; Ohkuma, 1986 ) compared the magnitude and nature of the image-induced Müller-Lyer illusion to those of the perceptive illusion. In order to do so, he presented three scenarios: the first with complete figures, perceptive situation; the second with wingless figures (similar to those used by Berbaum & Chung,  1981 ), imaginary situation; and the third with the figures of the imaginary situation but with no instructions so as to stimulate imagination, control condition. Once again, the fact that mental imagery has semi-perceptual features is confirmed. In all these three conditions, when figures are presented outwards (> <), the straight line turned out to be estimated longer than in the case of inward figures (< >). In the condition of perception, the outward figures rendered a significantly higher illusion than in the imaginary condition, whereas no differences were found in the imaginary condition and the control condition. In the case of inward figures, there was no significant difference between the condition of perception and the imaginary condition, and conversely, there was a significant difference between the imaginary condition and the control situation. Watters and Scott ( 1989 ) compared three imaginary conditions using drawings of partial lines and providing instructions to imagine the missing parts in order to generate the Müller-Lyer illusion. The three conditions rendered different illusion sizes, just in the same way as in the full perception situation.

Other illusions were also induced through mental imagery but led to contradictory data. Wallace ( 1984a ), for his part, examined the horizontal-vertical illusion by means of mental imagery using the VVIQ (Marks, 1973 ) to measure the subjects’ imaging ability. Those categorized as high in imaging ability experienced the illusion in the imaginary situation as much as in full figure perception. However, those low in this ability only experienced the illusion if elicited by physically present lines. The illusion of Ponzo, Hering and Wundt (Wallace, 1984b ) yielded identical results. Blanuša and Zdravković ( 2015 ) looked into the differences between perception and imagination with the help of the horizontal-vertical illusion. Conclusions confirmed that there was not a significant difference in the magnitude of the illusion between the two processes: the illusion was equally strong in both cases. Varying the size of the stimulus showed that there was a gender difference in the size of the mental image for medium and large stimuli, while there was no significant difference in the strength of the illusion. Thus, women tended to overestimate size in the image condition for medium and large stimuli. There are other studies that focus on finding differences between perception and image but did not succeed in inducing illusions through images. This is the case, for instance, of the Ponzo illusion (Giusberti et al.,  1998 , Reisberg & Morris,  1985 ) or the Ebbinghaus illusion (Giusberti et al.,  1998 ).

There is no recent review of the influence of wing length on the magnitude of the illusion in the Müller-Lyer illusion. It was only Dewar ( 1967 ) who studied this variable by randomly assigning to two experimental groups the task of valuing a figure a hundred times a day for five consecutive days. The fins formed an angle of 60º but were of different lengths for the two groups. The first group rated a figure with 1 cm fins while the second rated a figure with 3 cm fins. The author did not find any significant differences in the magnitude of the illusion as far as wing length is concerned. In the present work this variable is restudied after diverging results came out when varying stimulus sizes in the horizontal-vertical illusion (Blanuša & Zdravković, 2015 ).

Cretenoud et al. ( 2020 ) examined the Müller-Lyer illusion in different contexts (poor-context, moderate-context, rich-context) trying to prove the fact that the more real the context, the more intense the illusion. It is of note that the moderate and rich contexts had longer wings. Although the authors were dealing with different variables, it seems appropriate to accept that enlarged oblique lines generate richer contexts that can influence the magnitude of the illusion. In fact, Gregory’s inappropriate constancy scaling theory (Gregory, 1963 ) stresses the perception of depth as the main cause of the illusion, which would lead to relative scales of constancy of the lines sizes (Ward et al., 1977 ). Alternatively, and in agreement with Howe and Purves’ theory of probability in natural scenes (Howe & Purves, 2005 ), the Müller-Lyer illusion may well be due to a probabilistic strategy of visual processing given that visual perceptions are generated in such a way that reflects the statistic relation between retinal images and their sources in the tangible world (for more information, see Redding & Vinson, 2010 ).

Zhang et al. ( 2017 ) associated certain perception and personality traits to a counteraction to the Müller-Lyer illusion. All participants in this study are fine art students skilled in experiencing and resisting illusions, and in fact, they are considered to somehow embody what Pearson and Westbrook ( 2015 ) called phantom perception, which implies hallucinations, mental imagery, synaesthesia, perceptual filling-in and many illusions.

Amongst the specific attributes of fine art students is an object image processing style, that is, they focus on the literal appearance of objects and are highly skilled in visualising details such as colour, form, brightness, etc., (see Pérez-Fabello et al., 2016 , 2018 ). They are also good at envisioning, with image control as pivotal when it comes to work formalisation (Pérez-Fabello et al., 2014 ). Also, they tend to have dissociative experiences, especially those related to absorption, fantasy proneness and imagination (Pérez-Fabello & Campos, 2022 ). These types of experiences, essential to artistic work and creativity, are highly boosted throughout their undergraduate studies (Pérez-Fabello & Campos, 2022 ).

The present study

This research stems from pioneering works on the Müller-Lyer illusion induced through mental images (Berbaum & Chung, 1981 ; Ohkuma, 1986 ; Watters & Scott, 1989 ). Despite the abundance of recent work on the Müller-Lyer illusion (Costa et al., 2021 ; Cretenoud et al., 2020 ; Santacà & Agrillo, 2020 ; Santacà et al., 2020 ; Schwarz & Reike, 2020 ; Zhang et al., 2020 ), no studies are found on the induction of the illusion by mental imagery and few are concerned with the influence of the wings length on the magnitude of the illusion. Also, fine arts students are of the utmost interest because they have certain personality and perceptual traits that seem to be related to resistance to the Müller-Lyer illusion (see, Pérez-Fabello et al., 2016 , 2018 ; Pérez-Fabello & Campos, 2011a , b , c , 2022 ; Zhang et al., 2017 ). On account of this, the present study is designed to inquire into the efficacy of mental images in the said illusion as compared to the illusion provoked by a real situation. Our aim was also to estimate the influence of wing length on the illusion. To that end, we used either the Bentano version or a combined version of the Müller-Lyer illusion, both specifically tailored for the particular purpose of increasing results reliability. Besides, we used the term bias as the mean deviance from actual length (Kahneman et al., 2022 ) in order to measure the magnitude of the illusion. Therefore, our basic hypothesis was the following: Bias, i.e., the magnitude of the illusion, is affected by the situation (real and imaginary), the wings length of the Müller-Lyer figures (15 and 45 mm) and participants’ image control in their attempt to match the two horizontal lines of the shapes.

Materials and methods

Participants.

The first group of participants comprised 219 students of whom 58 were discarded: 40 because they were already familiar with the Müller-Lyer figures and 18 because they were not able to visualize the wings in the imaginary situation. Eventually after the discard phase, the total participants were 161 (118 women and 43 men), all fine art undergraduates from the University of Vigo. The mean age was 20.34 years, ( SD  = 1.75), range 18 to 26 years. All students freely volunteered to participate in the study.

The figures used for this study were either the Bentano version or a combined version of the Müller-Lyer figures. All of them were created in the 3D research laboratory at the faculty, redesigned in resin in a 3D printer and grouped in three sets. Two figures were similar to two of the Müller-Lyer figures created by Takei and Co. (Japan) and the third figure, consisting in only a horizontal line, kept the same size of the two previous ones (see Figs.  1 , 2 and 3 ). Our experiment involved generating the Müller-Lyer illusion in two different moments: one when participants used the complete sets of figures (real situation) and another when they used the figure with no oblique lines and had to imagine its fins or wings (imaginary situation). For the real situation two figures were used, one with 15 mm long fins at an angle of 30 degrees (see Fig.  1 ) and another with 45 mm long fins also at an angle of 30 degrees (see Fig.  2 ). For the imaginary situation, a version of the Müller-Lyer figures was designed but discarding all oblique lines (see Fig.  3 ). Participants were required to perform the same task as in the real situation, but in this case they were asked to imagine the wings of either 15 or 45 mm, as appropriate. All horizontal lines were 10 cm long and all figures consisted of a mobile part and a fixed part that contained the standard stimulus. Additionally, at the back side of the standard stimulus, there was a millimetre scale used to assess the magnitude of the illusion by determining the bias committed in the attempt to match the 10 cm shaft of the standard stimulus with that of the slider stimulus. Participants were required to manipulate the slider stimulus up to the point that it was just as long as the horizontal line of the standard stimulus. The bias was expressed in mm for every subject in perceiving each of the figures and it showed the magnitude of the Müller-Lyer illusion since a different perception of the shaft size is generated depending on the direction the wings are pointing to: inwards or outwards.

30º and 15 mm Müller-Lyer figure

30º and 45 mm Müller-Lyer figure

Figure used in the imaginary situation for the 30º and 15 mm figure and for the 30º and 45 mm figure

Participants were also instructed to complete an image control test, the Spanish version (Pérez-Fabello & Campos, 2004 ) of the Gordon Test of Visual Imagery Control (Gordon Test, Richardson,  1969 ). The Gordon Test measures the subject’s manipulation or control of mental images. The test consists of 12 items, each one with 3 options: No = 0 points, Unsure = 1 point or Yes = 2 points. Pérez-Fabello and Campos ( 2004 ) have reported a reliability of 0.69 for the Spanish version of the test.

This study has been carried out over three consecutive school years. First, students were asked to complete the Gordon Test in their respective classrooms and in small groups of approximately 20 students per group. After that, each participant was asked to adjust the line to match the length of the standard stimulus and that of the slider stimulus of the Müller-Lyer illusion. The standard stimulus was 10 cm long and participants were to make it equal to the slider stimulus by manipulating the mobile part of the figure (slider stimulus) in the following four experimental situations: real 15 mm, real 45 mm, imaginary 15 mm, and imaginary 45 mm. At no time were participants informed of their scores as they ignored that their performance was being evaluated.

We counterbalanced the presentation of the figures in the real situation, in the imaginary situation and in the figure that was first presented. The first participant started with a real situation (beginning with the 15 mm figure), the second participant started with an imaginary situation (beginning with the 45 mm figure) and so on and so forth, counterbalancing both figures and situations.

All participants reported having normal or corrected-to-normal vision. The bias committed in the attempt to match shafts was measured in the four tasks.

The experiment was approved by the ethics committee of the University of Vigo and was performed in accordance with the 2013 Declaration of Helsinki. Participants gave written informed consent.

Control of variables

All participants were presented the same figures, the same procedure and the following counterbalance: real and imaginary situation. Figures were to be at the same eye distance and with the same experimenters, lighting, and premises. All individuals who either knew the figures or achieved no image in the imaginary situation were disregarded.

Instructions

Real situation: “You will see two figures. Place them in such a way that they are perpendicular to your line of sight and keep your arms outstretched (indications are given). Now try to match the two horizontal lines in such a way that they are the same length. In order to do so, you will have to regulate length by adjusting the figures’ mobile part until you think you have got it right. The maximum time allotted for each figure is 15 seconds.” This instruction was given for the 15 mm figures as well as for the 45 mm figures.

Imaginary situation: A bare horizontal line is presented. “You will see a figure. Place it in such a way that it is perpendicular to your line of sight (indications are given). Now try to imagine its fins just like they are in this set (the 15 mm and 45 mm full figures are shown, as applicable). Then try to match the two horizontal lines so as they are the same length. In order to do so, you will have to regulate length by adjusting the figures’ mobile part until you think you have got it right. The maximum time allotted for each figure is 15 seconds.” This instruction was given for all imaginary situations either in the case of 15 mm wings or 45 mm wings.

Once the tests were over, participants were asked whether they were already familiar with the figures and whether they were able to imagine the wings. They were also asked to assess their own performance from 0 to 3 (being 0 = not able to imagine and 3 = perfectly able to imagine).

Data analysis

Statistical analysis was performed using the IBM SPSS Statistics, Version 25.0, statistical software (IBM Corporation, Armonk, NY, USA). The internal consistency of the tests was calculated by the Cronbach’s alpha.

Our purpose was to find out to what extent the situation (real or imaginary), the wings length (15 and 45 mm) and the subjects’ image control ability affected the bias committed in the attempt to match the horizontal lines in the Müller-Lyer figures. In order to do so, a mixed three-way ANOVA was. The independent variables were: 2 situation (real and imaginary) x 2 wing length (15 and 45 mm) x 2 image control (high and low) and the dependent variable corresponded to bias values when trying to match the horizontal line in the Müller-Lyer’s figure.

In order to divide the participants into high and low in the Control Test, the median score in each test was taken into account. Participants who scored above the group median were considered high in image control ability and participants who scored below the group median were considered low in image control ability.

We first evaluated the reliability of the Control Test (Richardson, 1969 ) reaching a Cronbach alpha of 0.71. Situation, wing length and image control were all subjected to a mixed three-way analysis of variance to find out whether they affected the bias committed in the attempt to match the horizontal lines in the Müller-Lyer figures (see means and standard deviations in Fig.  4 ). An intra-subject contrast test revealed that in the real situation, wing length affected bias, F (1, 150) = 621.36, p  < .001, η p 2  = 0.81, power = 1. In the case of the figure with 45 mm wings, participants obtained higher bias values than in the case of the 15 mm set. In the imaginary situation, bias was affected by wing length, F (1, 150) = 151.91, p  < .001, η p 2  = 0.50, power = 1. Whenever participants used the 45 mm Müller-Lyer figure, bias values were significantly higher than in the case of the 15 mm figure.

Means and standard deviations of bias according to the real and imaginary situation, the length of the oblique lines and image control

Interactions between variables were significant. The interaction between real situation and image control was significant, F (1, 150) = 9.38, p  < .01, η p 2  = 0.06, power = 0.86 (see Fig.  5 ).

Interaction between the length of the oblique lines and control test in bias in the real situation

The interaction between imaginary situation and image control was significant, F (1, 150) = 4.29, p  < .05, η p 2  = 0.03, power = 0.54 (see Fig.  6 ).

Interaction between the length of the oblique lines and control test in bias in the imaginary situation

Also significant was the interaction between real situation and imaginary situation, F (1, 150) = 5.88, p  < .05, η p 2  = 0.04, power = 0.67 (see Fig.  7 ). However, interaction between the three variables, situation, wing length and image control was not significant, F (1, 150) = 0.01, p  = .94, η p 2  = 0.01, power = 0.05. Results of the inter-subject test showed that image control did not have a significant influence on bias either, F (1, 150) = 2.24, p  = .14, η p 2  = 0.02, power = 0.32.

Interaction between the length of the oblique lines and real and imaginary situation in bias

The reliability of the Gordon Test in our study amounted to 0.71, which was similar to those previously found of 0.69 and 0.74 (Pérez-Fabello & Campos, 2004 , 2020 ). Although Ashton and White ( 1974 ) reported that the test did not have a simple factorial structure and that the consistency of this test was low (McKelvie, 1992 ; McKelvie & Gingras, 1974 ), the reliability achieved was, according to the criteria of George and Mallery ( 2003 ), acceptable. Wing length affected the magnitude of the illusion in the real situation, namely that of perception, as much as in the imaginary situation. Participants obtained higher bias values when lines were longer. Although Dewar ( 1967 ) did not find any differences in the magnitude of the illusion, the method used now was a different one. In addition, the specific characteristics of fine arts students may also have caused the difference in results. Alternatively, the conclusions driven by Cretenoud et al. ( 2020 ) seemed to suggest that richer contexts boost illusion, so therefore, we assume that longer oblique lines imply richer contexts, generate higher depth and, according to the perceptual constancy theory (Gregory, 1963 ; Ward et al., 1977 ), could have an influence on the magnitude of the illusion. In any case, this outcome needs to be confirmed by further studies.

There was a significant interaction between the real and the imaginary situation both in the case of 15 mm fins and 45 mm fins. The magnitude of the illusion was greater for the real situation. Berbaum and Chung ( 1981 ) did not find any significant differences between the perceptive and the imaginary conditions. For his part, Ohkuma ( 1986 ) found that the size of the illusion was greater in the perceptive than in the imaginary condition in the case of outward figures (in his study > <) but did not find any differences between both conditions in the case of inward figures (in his study < >). Watters and Scott ( 1989 ) found the same illusion magnitude in the situation of actual perception as well as in the imaginary situation.

Although our hypothesis anticipated that image control might affect the magnitude of the illusion, no significant differences were found between those high and low in image control. However, the interaction between the real and the imaginary situation was significant as did as well between the imaginary situation and image control. It is adventurous to assume an explanation for these results due to the lack of previous similar investigations. Inaugural studies on images had rendered contradictory data. Ohkuma ( 1986 ) did not find any significant differences in image ability between high and low scoring subjects either in the size of the illusion using the VVIQ (Marks, 1973 ) nor in image control using the Gordon Test (Gordon,  1949 ) both in the real and in the imaginary situation. Using other types of geometric illusion such as the horizontal-vertical illusion, the Ponzo illusion or the Hering and Wundt illusion, Wallace ( 1984a , b ) found that participants skilled on images (VVIQ; Marks 1973 ) experienced the illusion in the imaginary situation as much as in full perception of the lines, however, those with low scores only experienced the illusion when it was produced in the actual presence of the lines.

Despite inconsistent findings regarding the Müller-Lyer illusion, numerous work has highlighted the qualities of mental images and their similitudes with perception (Blackwell, 2019 ) contributing evidence on the activation of the same brain structures when perceiving or imagining (Dijkstra et al., 2019 , 2021 ; Pearson, 2019 ). Even so, perception is more powerful than imagination, so a combination of neuroimaging and conductual evidence has led to suggest that mental images may be considered a “weak” form of perception (Pearson et al., 2015 ). All this is consistent with our conclusion, namely that the magnitude of the illusion is greater in the situation of actual perception than in the imaginary situation. In fact, similar results have been obtained in both situations. Image control can be said to influence neither the real situation nor the imaginary situation, which is essentially the same conclusion as that reported by Ohkuma ( 1986 ). On the other hand, the influence of wing length was significant in the real situation and in the imaginary situation, as formerly indicated by Watters and Scott ( 1989 ). These results consolidate similitudes between the two cognitive processes, perception and imagination, but further work is required to arrive to a more accurate explanation.

The strength of this study relies on the fact that research on illusions through mental images is retaken with the inclusion of new methods, different illusion versions and a wider sample of subjects. We believe that designing combined sets of figures to elicit the illusion contributes reliability to the study. The weak point of this work is the use of a particular group of participants instead of a sample population that, together with gender difference, hinders results generalization. New studies will address other groups of population and will connect new figure factors, geometric as well as physical, with the magnitude of the illusion. We deem of great interest to keep researching on personality traits as related to resistance to the illusion.

With the help of an in-depth study of the Müller-Lyer illusion, this work sheds light on the differences and commonalities of visual perception and mental imagery. We obtained identical results for the situation of actual perception and for the imaginary situation, both rendering a higher illusion magnitude when the figures with longer fins were used. Consequently, the magnitude of the Müller-Lyer illusion is greater in the situation of actual perception than in the imaginary situation both in the case of the figures with 15 mm fins and with 45 mm fins.

Data availability

The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.

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Pérez-Fabello, M.J., Campos, A. The Müller-Lyer illusion through mental imagery. Curr Psychol 42 , 29316–29324 (2023). https://doi.org/10.1007/s12144-022-03979-y

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What size is an object? Your description might depend on your intentions

Gesturing reduces effect of a classic optical illusion, study finds.

Imagine describing the precise dimensions of a common object—like a coin—for another person. Did you move your hand, pretending to pick one up to show its size? If so, you likely weren’t alone.

A new study led by a renowned University of Chicago psychologist suggests that under some circumstances, gesturing can improve the accuracy of people’s descriptions of object size relative to their estimations based on sight.

For the study, published in Psychological Science , Prof. Susan Goldin-Meadow and her colleagues asked participants to examine and reexamine a Müller-Lyer illusion—a set of lines or sticks whose lengths appear to vary due to stylized arrow marks.

The Müller-Lyer illusion is one of the most famous optical illusions in psychology. It consists of two sticks, one framed by closed fins and one framed by open fins. After seeing the illusion, viewers usually estimate that the stick with two open fins is longer, even though the sticks are actually the same length.

In the study, participants gauged the lengths of sticks placed in a frame exhibiting the illusion three times: once after looking at the sticks, once as they prepared to pick up them up and once more while using a hand gesture to describe an action involving the sticks for another person. Their accuracy varied in a predictable way—it increased equally in both of the latter two situations, where movements were involved.

That might be because the way people perceive objects depends in part on their intentions, according to Goldin-Meadow, the Beardsley Ruml Distinguished Service Professor in the Departments of Psychology and Comparative Human Development. If someone intends to act on an object in an optical illusion, they may gauge its length more accurately.

“When you look at the illusion, you are captured by it,” said Goldin-Meadow, a leading expert on non-verbal communication. “But if you begin to move as if to grab one of the objects, something different seems to happen between your hand and your mind: You’re no longer quite as susceptible to the illusion as you were. Our discovery is that your accuracy also improves when you gesture about the object while you talk, just as it does when you act.”

Co-authors of the study include UChicago graduate student Amanda Brown, Diane Brentari, the Mary K. Werkman Professor of Linguistics, and Wim Pouw at the Max Planck Institute of Psycholinguistics in the Netherlands. Together, the researchers wanted to better understand the relationship between action, gesture and estimation under the Müller-Lyer illusion.

The team wanted to shed light on the origin of gesture—which seems to be related to both action and speech—by evaluating the way people gauged the illusion in three contexts: estimating based on sight alone, preparing to act, and describing in speech with gesture.

Forty-five people participated in the study, including 32 English speakers—who gestured spontaneously while speaking—and 13 users of American Sign Language (ASL), who used conventional signs to articulate their perceptions of stick length.

People were most susceptible to the Müller-Lyer illusion when they tried to estimate stick lengths without thinking about an accompanying action. For both English speakers and ASL users, however, the magnitude of the illusion lessened equally when they prepared to act or described an action for someone else.

According to Goldin-Meadow, the fact that the illusion was less powerful when participants were describing objects with gestures suggests that the mechanisms responsible for producing gestures in speech and sign language might derive from the way we act on objects, rather than from language.

“The Müller-Lyer illusion has always fascinated me,” she said. “And using it struck me as an ideal way to ask this question about where gestures come from. I thought they were tied to language because gestures and speech are so well integrated. But now we have evidence that gestures may also stem from action.”

Citation: “ People Are Less Susceptible to Illusion When They Use Their Hands to Communicate Rather Than Estimate .” Brown et al.,  Psychological Science , July 9, 2021.

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The limits of our perception and perfection: the Muller-Lyer Illusion

Let’s try this fun Muller-Lyer Illu­sion — Which of the 2 cir­cles sur­round­ed by oth­er cir­cles is bigger?

Are you sure? Would you mind using a tape measure?

Here’s a link to a neu­ropsy­cho­log­i­cal expla­na­tion .

More brain teas­er games:

• Top 25 Brain Teasers, Games and Illusions
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The question that we all want an answer to is: What does the experiment show? Does it provide support for the linear perspective hypothesis? The answer is "Yes" but with a qualification. First, let's see why the researcher who designed the experiment would argue that the data does support the hypothesis. Here is a graph that shows the results of trials done with one group of subjects.

The illusion was calculated by finding the difference between matching size for experimental stimuli (arrow and fork junctions) and control stimuli (T junctions). According to the linear perspective hypothesis, the lines with arrow junctions should produce a negative illusion score (less than the control), while the lines with fork junctions should produce a positive score (greater than the control). And the prediction was that lines with asymmetrical junctions (rotated corners) should produce less illusion than lines with symmetrical junctions (unrotated corners). That is, lines with asymmetrical arrow junctions should have a less negative illusion score than lines with symmetrical arrow junctions, while lines with asymmetrical fork junctions should have a less positive illusion score than lines with symmetrical fork junctions. Did the prediction turn out to be accurate? . . . Well it certainly seems to be. The straight on corners, with the symmetrical fork and arrow junctions produced the greatest illusions. The rotated corners (asymmetrical) produced some illusion but not as much (just as the hypothesis predicted).

Does the data provide evidence that is consistent with the truth of the linear perspective hypothesis? Yes. It is what the theory predicts (within a reasonable degree of accuracy). Since the evidence is consistent with the theory, does that mean that the linear perspective hypothesis has been proven to be true? No . That is too strong a claim. The author of this experiment (Dr. Gordon Redding) claims that any difference in the illusion for stimuli depicting rotated and non-rotated virtual corners is due to the difference in virtual corners. Do you think he is right? Maybe he is. But we can't draw this conclusion with absolute certainty because there are other possible explanations for the data, as Dr. Redding himself is willing to admit. The experimental stimuli have been divided into two groups: those with rotated virtual corners and those with unrotated virtual corners. The two groups do vary with respect to the "degree of the rotated corner". But, they may also differ with respect to any number of other properties. And if they do, the explanation for the experimental results may turn out to depend primarily on this other property, rather than on the property identified by the linear perspective hypothesis (i.e., the degree of the rotated corner).

If there are two different properties (variables) that change in a parallel way, then the same experimental results will give equal support to two different hypotheses, each claiming that only one of the properties provides the proper explanation for the outcome of the experiment. A variable that co-varies (changes its level) with an independent variable is called a "confounded variable". Can you identify a confounded variable in our design that might explain the results?

For a more detailed discussion of what can (and cannot) be learned from the results of this experiment, see "Muller Lyer Experiment Debriefing"