How much time does it take to discriminate two sets by their numbers of elements?

Abstract

The ability to evaluate the number of elements in a set-numerosity-without symbolic representation is a form of primitive perceptual intelligence. A simple binomial model was proposed to explain how observers discriminate the numerical proportion between two sets of elements distinct in color or orientation (Raidvee et al., 2017, Attention Perception & Psychophysics, 79[1], 267-282). The binomial model's only parameter β is the probability with which each visual element can be noticed and registered by the perceptual system. Here we analyzed the response times (RT) which were ignored in the previous report since there were no instructions concerning response speed. The relationship between the mean RT and the absolute difference |ΔN| between numbers of elements in two sets was described by a linear regression, the slope of which became flatter as the total number of elements N increased. Because the coefficients of regression between the mean RT and |ΔN| were more directly related to the binomial probability β rather than to the standard deviation of the best fitting cumulative normal distribution, it was regarded as evidence that the binomial model with a single parameter - probability β - is a viable alternative to the customary Thurstonian-Gaussian model.