This research was conducted as part of the Practical course in the Department of Psychology, University of Dhaka. This study was conducted by Durjoy Pramanik Dipto, under supervision of Farjana Begum (Assistant Professor), Department of Psychology, University of Dhaka.
Estimation of Müller-Lyer Illusion by the Method of Average Error
Abstract
The title of this experiment is Estimation of Müller-Lyer Illusion by the Method of Average Error. It aimed to examine whether the line with feather ends is perceived as longer than the one with arrow ends. The hypothesis stated that even if both lines are of equal length, the feather-shaped line would appear longer than the arrow-shaped one. A single-subject design was used, and the experiment involved only one participant. The structure followed an ABBA format with four phases: pull, push, push, and pull. Two conditions—left and right—were used. Each phase included four trials, and the condition changed in each trial. Specifically, trials 1 and 4 were under the left condition, while trials 2 and 3 followed the right condition. After all trials were completed, the constant error (CE) was calculated. The CE was -1.910 cm, meaning the feather-ended line was perceived as 1.91 cm longer. This result supports and confirms the hypothesis.
Introduction
Psychology
is defined as "the scientific study of behavior and mental processes of
all organisms," including both humans and animals. Feldman (2010)
says psychology is the scientific study of how people behave and how their
minds work. Crider and his colleagues (1993) also said that psychology is a
science that studies both behavior and mental processes. Today, psychology has
many different branches, like cognitive psychology, experimental psychology,
clinical psychology, industrial and organizational psychology, abnormal
psychology, educational psychology, and more.
The main
goals of psychology are to describe, explain, predict, and change or control
human behavior and mental processes. Psychologists use scientific methods like
experiments and studies that look at how things are related (correlational
studies). Some important topics in psychology are how we sense things, how we
perceive them, how we learn, and how we think about the world around us.
Sensation
means our sense organs are activated by physical energy, such as light or
sound. Perception is how our brain sorts, interprets, and understands the
things we sense (Feldman, 2010).
There are
three main types of perceptual instanses. These are delusions, hallucinations,
and illusions. A delusion is a strong false belief that someone holds even if
there’s proof it’s wrong. Hallucination means seeing, hearing, tasting,
smelling, or feeling something that isn’t really there.
Crider et
al. (1993) defined illusion as a situation where what we see or sense doesn't
match the actual object. Loren and Gingús (1978) said illusions can happen for
two reasons: one is because of a real distortion in what we’re sensing, and the
other is because our brain interprets the information incorrectly. Illusions
can happen with any of our five senses.
Illusions
are mistakes our brain makes when understanding real things around us. There
are different types of illusions, such as geometric, movement, physical, moon,
and physiological illusions. A moon illusion is when the moon looks bigger on
the horizon than it does high in the sky. Physical illusions are caused by the
environment, like when a stick in water looks bent. A movement illusion happens
when you are riding fast in a vehicle and think the trees beside the road are
moving.
Physiological illusions are caused by too much stimulation to the brain. Geometric illusions are visual errors where shapes or lines look different than they are. The Müller-Lyer illusion is a famous geometric illusion studied using special illusion cards.
Literature
Review
The
Müller-Lyer illusion was first introduced by Franz Carl Müller-Lyer in 1889 and
later published in 1896. He showed that when two lines are the same in length,
the one with arrow tails (facing outward) looks shorter, while the one with
feather tails (facing inward) looks longer. Müller-Lyer believed that our brain
doesn’t only focus on the line itself but also includes the visual space around
the ends. These "arrows" at the ends give us misleading distance
cues, which changes how we perceive the length of the line. His work became a
foundation for studying perceptual errors and illusions in psychology.
In 1896,
Gérard Heymans conducted a similar experiment and discovered that individuals
who had previously encountered the illusion were less influenced by it. He
concluded that familiarity and learning can diminish the impact of the
illusion. This reinforces the notion that experience and exposure significantly
influence our interpretation of visual stimuli.
In 1966,
psychologist Richard Gregory proposed that this illusion occurs because our
brain employs size constancy—a cognitive trick we use to perceive size in
relation to distance. For instance, an object that is far away appears smaller,
but our brain understands that it actually isn’t. Gregory suggested that the
lines with feather tails resemble the inner corners of a room, while those with
arrow tails resemble the outer corners. Consequently, our brain perceives them
as being at different distances, even though they are not (Gregory, 1966).
In the same
year, Segall, Campbell, and Herskovits (1966) did a cross-cultural study and
found that culture affects perception. People who lived in “carpentered
environments” like cities (with straight walls and corners) were more likely to
fall for the illusion than those in non-industrial, rural African communities.
This suggests that cultural exposure to angles and lines affects how we
interpret them.
Coren and
Girgus (1972) carried out multiple experiments and discovered that the
Müller-Lyer illusion remains effective even when the visual context is
eliminated or made simpler. This indicates that fundamental visual processing
systems in the brain are involved. They also observed that the illusion
remained potent even after participants were cautioned about it, implying that
it functions at an automatic, unconscious level.
More
recently, Ninio (2014) reviewed different types of geometric illusions and
explained how the visual system's reaction to lines, angles, and contrast can
create strong distortions. He showed that the illusion doesn’t only happen with
arrow or feather shapes—it also occurs in different forms like circles, curves,
and zigzags, proving that the illusion is part of a broader group of geometric
misperceptions.
In 2020, Zeman, Brooks, and Biederman explored how illusions like Müller-Lyer can help us understand 3D perception in the brain. They found that the illusion tricks our brain because it uses depth cues, similar to how we view 3D scenes. Their study used neuroimaging and eye-tracking, and it showed that illusions can be useful tools in understanding how the brain creates a sense of space and distance from flat images.
Problem
The problem
of this study was to find out Muller-Lyer illusion by the method of average error.
Hypothesis
The
hypothesis of the experiment was although two lines were of the same length,
one with the feathers shaped will be perceived longer than the other with arrow
shaped.
Variables
There are two types of variables (independent and dependent variable) in this experiment. The independent variable of the experiment was the shape of the line, and the dependent variable was the degree of illusion.
Rationale
The
Müller-Lyer illusion is important both theoretically and practically. From a
theoretical perspective, this illusion helps psychologists understand
perception. It reveals the complexities of cognitive processing, such as how we
judge size, distance, and shape based on visual cues. Researchers can use this
to assess individual differences in perception, and even attention. It offers
insight into the mechanisms behind visual misinterpretations, which can be
useful in psychological testing and cognitive studies.
From a
practical standpoint, the Müller-Lyer illusion has valuable applications in
creative and design-related fields. Artists can use the illusion to add depth
and uniqueness to their artworks. Interior designers can manipulate room
layouts. In fashion, designers may apply this illusion to clothing to create
the appearance of added volume or dimension, enhancing the overall aesthetic
and function of their creations.
Method
Participant
An adult, 20
years old male was selected for this experiment. His visionary and auditory
system were all good and he was fit for this study.
Apparatus
Here are the
following apparatus those were used in this experiment:
- Muller-Lyer illusion card
- Paper
- Pencil
- Black Screen
- Calculator
Design
A
single-subject design was employed in this study, specifically using a repeated-measures
approach. The experiment involved only one participant, and no control
condition was included. The push and pull conditions, along with the left-right
combinations, were arranged in an ABBA sequence. The mean was intended to be
calculated based on each trial or time.
|
No of Phases No
of Series |
Left(A) |
Right(B) |
Right(B) |
Left(A) |
Mean(X) |
|
Pull |
- |
- |
- |
- |
- |
|
Push |
- |
- |
- |
- |
- |
|
Pull |
- |
- |
- |
- |
- |
|
Push |
- |
- |
- |
- |
- |
Procedure
We selected one male participant for the experiment. First, we gave him a warm
welcome and then provided both written and spoken instructions about the task.
A within-subject design was used, which had four phases – pull, push, push,
pull – and two conditions – left and right.
The
experiment followed an ABBA format and was completed in one sitting without any
breaks. The participant was given a Muller-Lyer card that had two lines: one
was a fixed arrow-pointed line and the other was an adjustable feather-pointed
line.
In the first
phase, the feather-pointed line was made shorter. The participant was asked to
pull it (without backtracking) to make it the same length as the arrow-pointed
line. In the first trial, the card was placed in his left hand and he used his
right hand to pull the line. For the next three trials of this phase, the card
was placed in his right, right, and left hand, and he had to pull the line.
In the
second phase, the feather-pointed line was made longer, and the participant was
asked to push it so that it matched the arrow-pointed line. This phase also had
four trials with different conditions. The conditions were left, right, right,
and left hand, in order.
The third
phase was the same as the second one, and the fourth phase was the same as the
first one. Each phase had four trials, and the pattern of conditions stayed the
same. The first and fourth trials used the left-hand condition, and the second
and third trials used the right-hand condition. After each trial, the error was
recorded. After finishing all trials, we took a comment from the participant,
thanked him, and said goodbye. The ABBA format was used throughout the study.
Result
The result
of the experiment is illustrated here in the form of a table:
|
No of Phases No
of Series |
Left(A) |
Right(B) |
Right(B) |
Left(A) |
Mean(X) |
|
Pull |
8.00 |
8.50 |
8.50 |
8.00 |
8.25 |
|
Push |
8.00 |
8.50 |
8.00 |
8.50 |
8.25 |
|
Pull |
8.00 |
8.50 |
7.50 |
8.50 |
8.12 |
|
Push |
8.00 |
7.50 |
7.50 |
8.00 |
7.75 |
Here is the calculation:
Point of
subjective error (P.S.E) = (Mean of A+B+B+A)/4 = (8.25+8.25+8.12+7.75)/4 centimetres
= 8.09 centimetres
[std=
Standard value of the card = 10 cm ]
Constant error
(C.E) = PSE- Std = 8.09-10 centimetres = -1.91 centimetres
In this
study, the illusion card had a standard length of ±10 cm. The participant's
Point of Subjective Equality (PSE) was measured at 8.09 cm, indicating how they
perceived the line length. This resulted in a Constant Error (CE) of -1.91 cm.
Since CE reflects the difference from the true length, it tends to be negative
when the perceived length is shorter than the actual. Thus, the CE in this
experiment was -1.91 cm, showing a consistent underestimation.
This experiment, titled "Estimation of Müller-Lyer Illusion by the
Method of Average Error", explored whether the feather-ended line
looks longer than the arrow-ended line, even when they are the same length.
Based on the hypothesis, when both lines are equal in size, people tend to see
the feather-ended line as longer. A single-subject design was used, with just
one participant who was asked to adjust the feather-ended line so it matched
the length of the arrow-ended one. In some trials, the feather-ended line was
made longer or shorter than the arrow-ended line, and the participant had to make
them equal.
The results
showed a consistent perceptual error of 1.91 cm. The average error clearly
indicated a significant difference. One possible reason is eye movement or the
concept of size constancy. Eye movement might have been more in the
feather-ended line than the arrow-ended one. Since eye movement helps judge
depth, this likely affected how far the line appeared. This process is known as
a monocular depth cue.
Size
constancy also helps explain the illusion. Our brain may interpret the arrow-
and feather-ended lines as the inner and outer corners of a rectangle. Due to
this, the arrow-ended line is seen as closer and therefore appears shorter,
while the feather-ended line is seen as farther away and appears longer.
Since the average error in results clearly shows a strong Müller-Lyer illusion effect, the hypothesis of the study was confirmed.
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