A generalization of Pie´ ron’s law to include background intensity and latency distribution
Resource
Journal of Mathematical Psychology 49, 450–463
Journal
Journal of Mathematical Psychology
Pages
-
Date Issued
2005
Date
2005
Author(s)
DOI
246246/2006111501275434
Abstract
Pie’ ron’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 t i-b C; in which R, b & C are positive parameters, is of much interest in the simple reaction time literature. In particular, consistent estimates of b 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 detectability of the signal, is not considered in Pie’ ron’s law. In this paper, we generalize Pie’ ron’s law based on the above comments. That is, we assume that both b & C are functions of the background intensity & of the percentile rank. We then investigate from a theoretical viewpoint some possible functional forms of b & C, with a special emphasis on the dependency of b on the background intensity. It is shown that the so-called ‘‘Fechner–Thurstone-type representation’’ forces b & C to be ‘‘separable.’’ If we further assume a near-miss to Weber’s law-type representation, then the functional form of b can be determined.
Subjects
Reaction time
Pie´ ron’s law
Functional equations
Near-miss to Weber’s law
Fechner–Thurstone-type representation
Publisher
Taipei:National Taiwan University Dept Phys
Type
other
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