Limitations of first-order approximations for calculations using intensity jnd’s

Abstract

The way in which the noninfinitesimal size of the intensity jnd affects calculations using power functions for pure-tone loudness and neural count is examined. The results of the commonly used first-order differential for representing the change in the power functions due to a jnd in intensity are compared with the second-order approximation and the exact formula. Examples are taken from a variety of psychophysical studies dealing with loudness and intensity discrimination. The second-order and exact formulas are shown to be more consistent with experimental data than the first-order differential.