Discrimination of numerical proportions: A comparison of binomial and Gaussian models

Abstract

Observers discriminated the numerical proportion of two sets of elements (N = 9, 13, 33, and 65) that differed either by color or orientation. According to the standard Thurstonian approach, the accuracy of proportion discrimination is determined by irreducible noise in the nervous system that stochastically transforms the number of presented visual elements onto a continuum of psychological states representing numerosity. As an alternative to this customary approach, we propose a Thurstonian-binomial model, which assumes discrete perceptual states, each of which is associated with a certain visual element. It is shown that the probability β with which each visual element can be noticed and registered by the perceptual system can explain data of numerical proportion discrimination at least as well as the continuous Thurstonian–Gaussian model, and better, if the greater parsimony of the Thurstonian-binomial model is taken into account using AIC model selection. We conclude that Gaussian and binomial models represent two different fundamental principles—internal noise vs. using only a fraction of available information—which are both plausible descriptions of visual perception.