Estimation of Separable Representations in Psychophysical Experiments

Studying how individuals compare two given quantitative stimuli, say d1 and d2, is a fundamental problem. One very common way to address it is through ratio magnitude estimation, that is to ask individuals not to give values to d1 and d2 but rather to give their estimates of the ratio p = d1/d2. Several psychophysical theories (the most known being Stevens’ power-law) claim that this ratio cannot be known directly and that there are cognitive distortions on the apprehension of the different quantities. These theories result in the socalled separable representations (which include Stevens’ model). In this paper, we propose a general statistical framework that allows for testing in a rigorous way whether the separable representation theory is grounded or not. We conclude in favour of it, but strongly reject Stevens’ model. As a byproduct, we provide estimates of the psychometric functions of interest.