Weber laws, the Weber law, and psychophysical analysis

Abstract

In failing to define the units in which the stimulus is to be measured, the Weber law might seem to make no definite assertion, and indeed, it is shown that any single empirical function, supposed to relate a given stimulus intensity with that intensity which is just noticeably greater, can be put into the Weber form by a suitable change of scale in which the stimulus intensity is to be measured. Nevertheless, it turns out that if different individuals have different Weber functions, when the intensities are measured on a given scale, then it is by no means always possible to transform the scale so that all of the functions can take on the Weber form. Some necessary conditions are given for the possibility of such a transformation when there is at hand a finite number of functions, and when the functions depend upon a single parameter the necessary and sufficient condition is easily derived. The same discussion leads to a generalization of Thurstone's psychophysical scale and shows that such a scale is always possible.