Weber’s Law
Clifford Philogene Fordham University
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Weber’s Law
Abstract
Weber’s Law is a perceptual law that states that for two stimuli to be perceived as having
different intensities, the second must differ from the first in a constant proportion. In this study, we took data from college students who were asked to determine whether there were differences of saturation in pairs of circles that either had the same or different saturation. I hypothesized that there would be a positive relationship between the percent correct at same intensity at low saturation and percent correct at same intensity at high saturation. Our results, inferential and descriptive statistics, proved our hypothesis true based on the mean, standard deviation, correlational value, and p-value. This study was used to better conceptualize Weber’s Law for real life application.
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Weber’s Law
Weber’s Law
Psychologist Ernst Weber conducted the first systematic studies of sensory thresholds. His experiments were designed to determine sensory thresholds, of which there are two types – absolute threshold and different threshold. The absolute threshold is the minimum intensity of a stimulus one can detect. Weber said an absolute threshold was the intensity of a stimulus at which we detect at least 50% of the time that it is there. A practical exam of the absolute threshold can be seen in a simple hearing test in which one presses a button when he or she hears a tone. The intensity at which he can hear or not hear the tone is his absolute threshold for the tone. The difference threshold, however, is defined as how much change there must be in the stimulus for a subject to detect the change. It is commonly referred to as the Just Noticeable Difference (JND). Weber’s law is a description of the “just noticeable difference” that can be perceived by an individual (Britt, 1975). Salary, as one of many
variables, depicts Weber’s Law with a real life application. For ex ample, at the lower end of the scale two jobs of just noticeable difference in difficulty might have salaries of $100 and $120 a month respectively. At a higher level two jobs of just noticeable difference in difficulty might be paid $1000 and $1200 respectively, but certainly not $1000 and $1020 (Hay, 1950). Another example can be visualized in Dr. Mete Sirvanci’s study “An Empirical Study of Price Thresholds and Price Sen sitivity.” In this particular experiment,
Dr. Sirvanci hypothesized that the price (stimulus) of a given product is the main factor which determines the magnitude of the response (Sirvanci, 2011). As such, the law can be applied in the form of a mathematical ratio
Weber’s Law
where K is the constant ratio; I is the stimulus; and delta I is the JND, or change in stimulus. In other words, Weber’s Law concerns the minimal differences that can be
detected among stimuli, usually designated as the “differential threshold” or JND (Britt, 1975).
An article regarding stars and brightness claims that “the eyes sense brightness approximately logarithmically over a moderate range and stellar magnitude is measured on a logarithmic scale” (Bhatia, 2001). The article goes on and uses a practical application of the brightness of stars and the relationship of Weber’s Law. Modern researchers have attempted to incorporate such perceptual effects into mathematical models of vision.
In this paper, the relationship between the d ifference in saturation and student’s
percent correctness is studied. More specifically, this study is to determine how differences in saturation effect one’s perception of the change. We hypothesized, based
on 40%, 50%, and 60% differences in low saturation, that as the difference in saturation became greater, the accuracy of participant’s responses would also be greater. In this
case, as we moved away from the just noticeable difference, participants should be able to perceive a change more easily. Our independent variable was the difference in saturation, and our dependent variable was the accuracy of the participant’s responses in
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Weber’s Law
respect to change. All of the individuals who participated in this study were part of the experiment group, as no control was needed.
Methods Participants
469 male and female college students were the participants for our study. The equipment used was a computer with a designed program and a calculator. Participants were to sit in front of a computer screen that displayed two circles, next to one another. The circles varied in range of saturation differences from 10% to 100%. The intensities within the circles varied as well, differing from high saturation to low saturation. Participants were asked to determine if there was a difference between the two circles, or if they were identical. On the screen, buttons corresponding to the two answers were displayed and used to collect the data. Data was then distributed into inferential and descriptive statistics.
Materials
Procedure
Results
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Weber’s Law
The two variables were moderately, positively correlated, r (444) = .29, p < .05. The percent chance of correctly perceiving two circles were the same under high saturation was moderately/positively correlated to the chance of perceiving two circles as identical were the same under low saturation. Our p-value, which is a measure of significance, or the probability that the null hypothesis is correct, also sup ported our hypothesis.
Correlations PercentCorrect_ PercentCorrect_ Same_LowSat Pearson Correlation PercentCorrect_Same_Low Sat
Sig. (2-tailed)
Pearson Correlation Sat
**
.291
.000
N PercentCorrect_Same_High
1
Same_HighSat
454
446
**
1
.291
Sig. (2-tailed)
.000
N
446
453
**. Correlation is significant at the 0.01 level (2-tailed).
Discussion
Weber’s Law denotes the constant proportion, or the ratio of change in intensity
required to produce a just noticeable difference compared to the previous intensity of stimulus. Since Weber’s law is a perceptual law that measures the just noticeab le
difference, it is clear why our hypothesis was valid. As our data showed, larger differences in saturation produced a greater accuracy of percent correctness in determining the difference between the two circles. These findings are consistent with previous theories, such as marketing and salaries analogies described in the introduction section.
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Weber’s Law
Using our experiment, it simplifies Weber’s Law to almost common sense. If
there is a bigger change between two stimuli, the probability of noticing the difference becomes greater. If there were, for instance, a black circle and white circle next to one another, a person should be able to tell that they are two distinct circles. However, if there is only a 10% difference between saturation of two grey circles, that probability becomes slimmer. Our results were consistent with our hypothesis and previous theories on Weber’s Law, which deepens the true understanding of the law itself.
There are no limitations with this experiment. However, it is always crucial to include a large sample size. Though our results were conclusive, a greater population of participants would yield even more conclusive results. This was a simple study that involved no biases, no problematic measures, and did not take much effort for individuals to participate.
Statistics Gender N
Valid
Age
Handed
469
469
469
0
0
0
Mean
.37
.33
.09
Median
.00
.00
.00
0
0
0
Std. Deviation
.521
.813
.292
Variance
.271
.661
.085
Missing
Mode
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Weber’s Law
Gender Cumulative Frequency Valid
Percent
Valid Percent
Percent
Female
306
65.2
65.2
65.2
Male
154
32.8
32.8
98.1
9
1.9
1.9
100.0
469
100.0
100.0
2 Total
Age Cumulative Frequency Valid
Percent
Valid Percent
Percent
15-25
386
82.3
82.3
82.3
26-35
35
7.5
7.5
89.8
36-45
32
6.8
6.8
96.6
46-55
11
2.3
2.3
98.9
56-65
3
.6
.6
99.6
66-76
2
.4
.4
100.0
469
100.0
100.0
Total
Handed Cumulative Frequency Valid
Right Handed Left Handed Total
Percent
Valid Percent
Percent
425
90.6
90.6
90.6
44
9.4
9.4
100.0
469
100.0
100.0
Correlations
Correct_SameSat_LowSat
Pearson Correlation
Correct_SameS
Correct_SameS
at_LowSat
at_HighSat 1
**
.291
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Weber’s Law
Sig. (2-tailed) N Correct_SameSat_HighSat
Pearson Correlation
.000 454
446
**
1
.291
Sig. (2-tailed)
.000
N
446
**. Correlation is significant at the 0.01 level (2-tailed).
453
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Weber’s Law
References Bhatia, V.B. “Astronomy and astrophysics with elements of cosmology.” C RC Press. p
20. 2001. Britt, Henderson. “How Can Weber’s Law Can Be Applied to Marketing.” Business Horizons. Feburary 1975. Hay, Edward. “The Application of Weber’s Law to Job Evaluation Estimates.” Hay and
Associates, Philadelphia, PA. 1950. Sirvanci, Mete. “An Empirical Study of Price Thresholds and Price Sensitivity.” Journal of Applied Business Research. Vol 9, Num 2. 2011.
