A random walk model of digit comparison

Abstract

To choose the greater of two digits, information in memory about the digit values must be compared. Like comparisons of values on perceptual dimensions, the response time and the probability of an error for digit comparisons increase as the difference in the digit values decreases. A random walk model of the comparison process explains these distance effects. Six subjects participated in three experiments to test the model. When model parameters were estimated from comparison data for all digit pairs, the estimated internal magnitude of the digit one was far from all other digits, implying that comparisons with the digit one generally require only a single step in the random walk. When comparisons with the digit one were excluded, the estimated internal magnitudes of the remaining digits were nearly linear. The model accounted for general features of the relationship between speed, accuracy, and the digit values, as well as the effects of response time deadlines. Modifications to the model are considered to account for the observed dependence of response biases on stimulus values.