Bernasconi M., Seri R. (2016).

What are we estimating when we fit Stevens’ power law?. Journal Of Mathematical Psychology, vol. 75, pp. 137-149

Abstract:

Estimates of the Stevens’ power law model are often based on the averaging over individuals of experiments conducted at the individual level. In this paper we suppose that each individual generates responses to stimuli on the basis of a model proposed by Luce and Narens, sometimes called separable representation model, featuring two distinct perturbations, called psychophysical and subjective weighting function, that may differ across individuals. Exploiting the form of the estimator of the exponent of Stevens’ power law, we obtain an expression for this parameter as a function of the original two functions. The results presented in the paper help clarifying several well-known paradoxes arising with Stevens’ power laws, including the range effect, i.e. the fact that the estimated exponent seems to depend on the range of the stimuli, the location effect, i.e. the fact that it depends on the position of the standard within the range, and the averaging effect, i.e. the fact that power laws seem to fit better data aggregated over individuals. Theoretical results are illustrated using data from papers of R. Duncan Luce.