A generalization of Pieron's law to include background intensity and latency distribution

摘要

Pieron's law, which formulates the effect of the signal intensity i on the mean or the median reaction time (MRT) as a power function, MRT = R + i(-beta)C, in which R, beta and C are positive parameters, is of much interest in the simple reaction time literature. In particular, consistent estimates of beta are obtained. However, this law offers no information regarding the effect of the signal intensity on other aspects of the reaction time distribution. In addition, the background intensity, which also has some impact on the delectability of the signal, is not considered in Pieron's law. In this paper, we generalize Pieron's law based on the above comments. That is, we assume that both beta and C are functions of the background intensity and of the percentile rank. We then investigate from a theoretical viewpoint some possible functional forms of beta and C, with a special emphasis on the dependency of beta on the background intensity. It is shown that the so-called "Fechner-Thurstone-type representation" forces beta and C to be "separable." If we further assume a near-miss to Weber's law-type representation, then the functional form of beta can be determined. (c) 2005 Elsevier Inc. All rights reserved.