Weber's law orthogonal to the psychometric function



Psychometric function plots the percentage of the correct responses among an entire pool of responses (cumulative probability) in a psychophysical task versus the amount of change in an independent variable. These changes in the independent variable are made with reference to a constant initial value. If this initial value is altered, the psychometric function will change according to Weber’s law. In other words, in a task such as the detection of the luminance increment, the psychometric function is stretched to the right for greater initial stimulus intensities and is compressed to left for smaller initial intensities. All of this behavior can be plotted in a 3-D coordinate system. The amount of change in the stimulus intensity, the initial reference intensity, and the above-described probability would be plotted on the X, Y, and Z axes respectively. The formula would be: [Z=1/(1+exp((KY-X)/aKY))]. The intersection of the plot of this formula with any plane parallel to the XY plane would be a line plotting the Weber’s law, and that with any plane parallel to the XZ plane, would be a line plotting the psychometric function. That is why these two functions are called orthogonal in this article. K in the above formula is the same as appears in Weber’s law for just noticeable difference (JND). The coefficient “a” has an arbitrary value that should be at most equal to 0.34 to set the probability of change detection at 5 percents or less when veridically there is absolutely no change in the stimulus intensity. Further implications have been discussed.