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 is capable of accounting for results from a variety of models of reaction time distributions and it makes novel predictions. It provides a unified 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. We show that 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 many families of distributions that have been proposed to account for {RT}s, indicating our theory provides a significantly better account of the data across tasks and modalities. In addition, a new methodology for analyzing {RT} data is derived from the theory, and we illustrate how it can be used to disentagle top-down and bottom-up effects in an experiment. Finally, we show how the theory links to neurobiological models of response latencies.