Fixed and optional stopping models for two-choice discrimination times

Several current models for choice- or discrimination-time experiments represent the stimulus as a sequence of independent and identically distributed observations. This paper develops and compares models based on two different stopping rules that a subject might use to terminate his sampling process and convert his perceptual evidence into an observable response. The fixed and optional stopping rules yield different predicted forms for the speed/accuracy tradeoff function and for the relation between mean and variance of response times. These predictions are developed in the general case and then specialized for certain conditions of symmetry, so that the expressions are easier to apply and to compare between models. A later section considers how changes in stopping criteria (either between or within experimental trials) affect predictions about mean response times for correct responses and errors, and then uses these ideas to relate the optional stopping rule for the Random Walk models to those of the Accumulator models. A final section considers specialized models for stimulus detection and intensity discrimination that assume Poisson-distributed sensory input, and relates these models to the present fixed stopping model.