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Application of Weber’s Law on Visual Perception

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Date of Experiment:                                                         Date of Submission:

     July 14, 2016                                                              August 4, 2016


Application of Weber’s Law on Visual Perception


        The experiment aims to determine if the Weber’s Law could be applied to judgment of sizes. In this case, the subjects were instructed to make 30 lines consisting of 10 lines with length 2-, 4-, and 6-inch in a short bond paper, each line randomly drawn that no two lines of the same length should be drawn consecutively. The mean 1 and 2 shows the average error of the subject for each length of line – mean 1 shows the average error regardless of the sign and mean 2 shows the average error of each by getting the mean of each considering the sign then divided by 32, 64 and 96 respectively. The results have showed that the subject had a mean of 0.018, 0.031 and 0.082 respectively for mean 1 and had a mean of       -5.63x10-4, -7.8x10-5 and 6.04x10-4 respectively for mean 2. This implies that in both of the means, the subject had lesser average error in the 2-inch line which means that the subject has lesser mistake in this line. And since the subject got the highest average error in the 6-inch line, it could be implied that the subject had most of these lines wrong. The signs in the mean 2 indicated the direction in which the subject had most of her mistakes.


        Ernst Heinrich Weber is a German anatomist and physiologist whose fundamental studies are about the sense of touch. In his study, he introduced the concept of just noticeable difference which talks about the smallest perceived difference between two stimuli. This made a great impact on the study of psychology and physiology (2016).

        Der Tastsinn und das Gemeingefuhl is the book published by Webers in 1851 which has a translation of “The Sense of Touch and the Common Sensibility” was considered by an English psychologist to be the “foundation stone of the experimental psychology.” Gustav Theodor Fechner was the one who expressed Weber’s empirical observations mathematically and later on formulated Weber’s Law (2016).

        According to Choo & Franconeri (2014), Weber’s Law “expresses a general relationship between a quantity or intensity of something and how much more needs to be added for us to be able to tell that something has been added.” If a viewer is 75% accurate at knowing the length difference between lines that are 5 and 5.5 cm in its length, a “proportionally larger difference” would be needed for the researchers to elicit the same level performance for the lines that would be 10 times higher than the former – 50 and 55 centimeters.



        To find out if the Weber’s Law applies to judgment of size


        Gustav Theodor Fechner coined the word psychophysics in his book Elemente der Psycophysyk. He discovered that by changing a physical stimulus slowly and noting the steps of judgment expressed, a relationship is established between physical and physiological series. Wilhelm Wundt adapted Fechner’s work which included sensory thresholds – methods of measurement of sensitivity and signal detection theory. Threshold or limit is the point of intensity in which the participant can detect the presence of or difference in a stimulus. Stimuli with intensities below the threshold are considered not detectable, and which stimuli close to the threshold will be observed or detected some of the time. Hence, a threshold is described as the point at which a stimulus or change in a stimulus is detected.

There are two kinds of threshold, namely;

  1. Absolute threshold – the level of intensity of a stimulus at which the subject is able to detect the presence of stimulus as often as 50% of the time.
  2. Difference threshold is the magnitude of difference between two stimuli intensities that the participants are able to detect as often as 50% of the time. It is also called as Just Noticeable Difference.

Ernest Weber, a 19th century experimental psychologist observed that the size of difference threshold appeared to be fully related to initial magnitude. This relationship leads to Weber’s Law, which state that the amount of change in stimulation needed to produce a noticeable difference is a constant proportion of the original stimulus. Weber’s Law can be expressed as

Where Δl (delta l) = K

Where Δl represents the difference threshold, l represents the initial stimulus intensity and K signifies that the proportion on the left side of the equation remains constant despite variations in the l term.

In other words, the more intense the stimulus, the more stimulus intensity has to increase before the subject notices a change. Practical example: if the subject is represented with two spot light with 100 intensity, to be able to detect that one light is brighter than the other using Weber’s Law, one could predict the observers difference threshold: 0.1 (Δl/1 = 10/100 = 0.1).

The Weber fraction for discriminating changes in the stimulus brightness is a constant proportion equal to 0.1.Then the size of the just noticeable difference having intensity of 1000 would be 100 (0.1 x 1000 = 100). Weber’s law can be applied to a variety of sensory modalities (brightness, loudness, mass, length of lines).


        Paper with 2-, 4-, and 6-inch lines beginning at different starting positions from the edge. There should be 10 lines of each length, arrange in random such that the same length does not appear successively. (Appendix B)


        Each student is his or her own S. Use a sheet of paper to mask the lines so that only one line is seen at a time. S examines each line and marks lightly with a ballpen what appears to be the midpoint. When all 30 midpoints have been “subjectively” marked, measure each line with a ruler to the nearest 1/16 inch and mark the actual midpoint. Record the amount of error for each of the lines and direction (before the midpoint, a “minus” error; beyond the midpoint, a “plus” error).



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