Weber's Law of
Just Noticeable Differences

USD Internet Sensation & Perception Laboratory

## Introduction

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: 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

Objective

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). 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.]

Results

• Once you have completed judging all of the stimulus pairings, the results will be automatically displayed.  These results summarize the percent of the time your judgment was correct as a function of the difference in line length (for each of the four ranges of line length examined).  Save a copy of this data in your lab notebook.

• To find your difference threshold for the four ranges of line length examined, you must first plot the psychometric function obtained for each level of standard stimulus line size (30, 90, 150 and 210 pixels).  This is accomplished by plotting the "percent correct judgment" on the y-axis as a function of the "difference in line size" (delta I) on the x-axis.  Once plotted, interpolate the "difference in line size" value that yields 75% correct performance.  This point is the difference threshold.

• Once each difference threshold (delta I) has been interpolated convert it to the Weber fraction equivalent (delta I/I).

• Plot the Weber fractions obtained at each of the four ranges of line length and determine whether Weber's Law holds true for just noticeable differences in line length.

Notice
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.