Signal detection theory and Crozier's law: Derivation of a new sensory scaling procedure

Abstract

The relation between sensory thresholds and the “sensory scale” is examined in the light of the threshold model given by signal detection theory. The problem is seen as that of determining the function relating E, the central effect of a stimulus serving as the decision axis when threshold judgments are made, and I, the physical intensity of the stimulus. Consideration of the model shows that when deviations from Weber's law occur they may be accompanied by departures from Crozier's law and that the occurrence and extent of the latter depend on the relation between E and I and can be used to define it. The argument is applied to some of the data on visual brightness discrimination in the literature. The results suggest that E may be related to I by a power function with an exponent of the order of 1.0. The disparity between this function and the psychophysical laws given by classical scaling procedures is discussed, and it is suggested that it may prove useful to hypothecate a distinction between central discriminal and metric processes.