Weber's Law of
Just Noticeable Differences

USD Internet Sensation & Perception Laboratory


The Difference Threshold (or "Just Noticeable Difference") is the minimum amount by which stimulus intensity must be changed in order to produce a noticeable variation in sensory experience.

Ernst Weber (pronouned vay-ber), a 19th century experimental psychologist, observed that the size of the difference threshold appeared to be lawfully related to initial stimulus magnitude.   This relationship, known since as Weber's Law, can be expressed as:

WebersLaw.gif (3874 bytes)

Weber's Law, more simply stated, says that the size of the just noticeable difference (i.e., delta I) is a constant proportion of the original stimulus value.  For example: Suppose that you presented two spots of light each with an intensity of 100 units to an observer.  Then you asked the observer to increase the intensity of one of the spots until it was just noticeably brighter than the other.  If the brightness needed to yield the just noticeable difference was 110 then the observer's difference threshold would be 10 units (i.e., delta I =110 - 100 = 10).  The Weber fraction equivalent for this difference threshold would be 0.1 (delta I/I = 10/100 = 0.1).  Using Weber's Law, one could now predict the size of the observer's difference threshold for a light spot of any other intensity value (so long as it was not extremely dim or extremely bright).  That is, if the Weber fraction for discriminating changes in stimulus brightness is a constant proportion equal to 0.1 then the size of the just noticeable difference for a spot having an intensity of 1000 would be 100 (i.e., delta I = 0.1 X 1000 = 100).

Weber's Law can be applied to variety of sensory modalities (brightness, loudness, mass, line length, etc.).  The size of the Weber fraction varies across modalities but in most cases tends to be a constant within a specific task modality.

Instructions for the Laboratory Experiments

This lab will allow the participant to measure their just noticeable difference thresholds for the discrimination of line length using a psychophysical procedure known as the Method of Constant Stimuli.

Method of Constant Stimuli Experiment


Choose the longer of the two line segment stimuli presented on the screen (for a given trial).  You will be asked to enter approximately 240 judgments (60 each at four different levels of standard line size).

mocs.gif (2654 bytes)

Sample Method of Constant Stimuli Screen

Explanation of the Stimulus Screen

The bottom of the stimulus screen displays the controls that you will be using for this experiment.  You can indicate which of the lines you judge to be longer by using the mouse and "clicking" the appropriately labeled button.  By doing so, the computer will  lock-in your judgment and automatically display the next pair of line stimuli. [Keyboard Shortcut: You can also indicate which line segment appears longer by using the RIGHT-ARROW and LEFT-ARROW keys.  If these keys appear unresponsive at first, try again after using the mouse once or twice.]


Completion of this experiment requires approximately 200 responses (so both patience and effortful attention are required).

Lab Report Format

  1. What was the independent variable?
  2. What was the dependent variable?
  3. Draw the psychometric function for each of the "standard stimulus" lengths explored.
  4. Graphically interpolate a difference threshold from each of these psychometric functions.
  5. Calculate and plot the Weber fractions as a function of Standard Stimulus line length.
  6. Did Weber's Law hold true?  Explain the basis for your conclusion.

End of Weber's Law of Just Noticeable Differences.