Counting processes in human timing

A subject reproducing a long duration, t, may time out either a single interval of duration t or a succession of n intervals, each of duration t/n. It is shown that a class of timing models obeying Weber’s law predicts the variance of reproductions of t to be a decreasing function of the number of subdivisions, n. In contrast, a second class of proportional variance models, which includes Creelman’s pulse counter model (1962), predicts no change in the variance as a function of n. Data are presented from a duration reproduction experiment in which subjects counted silently at a specified rate up to a given number and then responded. Several statistics involving the variance of the reproduced durations are shown to be predicted significantly better by the Weber’s law class of models than by the proportional variance class of models.