A Theory of Reaction Time Distributions

Abstract

We develop a general theory of reaction time (RT) distributions in psychological experiments, deriving from the distribution of the quotient of two normal random variables, that of the task difficulty (top-down information), and that of the external evidence that becomes available to solve it (bottom-up information). The theory provides a unied account of known changes in the shape of the distributions depending on properties of the task and of the participants, and it predicts additional changes that should be observed. A number of known properties of RT distributions are homogeneously accounted for by variations in the value of two easily interpretable parameters: the coefficients of variation of the two normal variables. The predictions of the theory are compared with those of multiple families of distributions that have been proposed to account for RTs, indicating our theory provides a significantly better account of experimental data. For this purpose, we provide comparisons with four large datasets across tasks and modalitities. Finally, we show how the theory links to neurobiological models of response latencies.