Recasting (the near-miss to) Weber's law.

Abstract

The authors argue mathematically that a common, power-function model of the just-noticeable difference in stimulus intensities is logically inconsistent with an exponent other than 1 in those frequent situations in which a particular averaging over experimental conditions has taken place. The authors show that an alternative power-law model, one which does not share this logical inconsistency, provides a good fit to many well-known, psychoacoustic intensity discrimination data. They also show that the exponent in this alternative model must be nonconstant with the discrimination criterion in experiments implementing this averaging of data.

Analytical methods in the theory of psychophysical discrimination I: Inequalities, convexity and integration of just noticeable differences

“…(16) in particular) is a very strong and useful constraint. For example, the model xðxÞ ¼ x þ kx b is incompatible with the group property (16); see Falmagne (1985) and Doble, Falmagne, and Berg (2003) for a detailed discussion of this fact.…”

The history of dipper functions

“…2AFC) constrain the possible relationships between and € ΔI JND . A recent discussion of these constraints can be found in Doble, Falmagne, and Berg (2003) and Iverson (2006aIverson ( , 2006b). All are satisfied by Weber's Law.…”

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

“…A similar assumption has been proposed by Falmagne and his colleagues in the study of discriminability (Doble et al, 2003;Falmagne, 1994). The relevant experimental work on the intensity discrimination of pure tones was recently reported by Doble, Falmagne, and Berg (2004), where they clearly showed that the exponent in the homogeneity equation is not a constant but a function of the discrimination criterion.…”

“…Accordingly, a more general formulation, which states that D p is homogeneous of degree r (r40), has been proposed, to which the name ''nearmiss to Weber's law'' is attached (for more discussion, see Doble et al, 2003;Falmagne, 1985Falmagne, , 1994.…”

“…The aim of this work is to determine theoretically the dependence of the parameters b and C on the background intensity in the generalized Pie´ron's law under two additional assumptions, one closely related to the near-miss to Weber's law (see Doble, Falmagne, & Berg, 2003;Falmagne, 1994) and the other closely related to the generalized Fechner-Thurstonetype representability considered in Falmagne (1985Falmagne ( , 1994. In particular, we show that under a near-miss to Weber's law-type assumption for RTs and a Fechner-Thurstone-type representation, the functional form of b in the generalized Pie´ron's law can be determined.…”