Psychometric functions for temporal discrimination: Duration or log duration?

Duration discrimination data collected with single-presentation tasks (e.g., bisection or temporal generalization tasks) or dual-presentation tasks (e.g., greater-less or same-different tasks) are usually analyzed by fitting psychometric functions. The independent variable in these functions is test duration measured in seconds or milliseconds. In contrast, the independent variable is log stimulus magnitude in psychometric functions for discrimination in other sensory modalities, most often because of the applicability of Weber's law. We report a study aimed at determining empirically whether duration discrimination data are best described by psychometric functions of duration or log duration. We first conducted a simulation study to identify the design (type of task, number of test durations, number of trials, etc.) with which the generating psychometric function (of duration or log duration) fit the data substantially better than the impostor function. Based on these results, we conducted an empirical study with the same-different task that adaptively administered 1,200 trials over 11 test durations around the standard duration. We collected 45 datasets and fitted both types of psychometric function in each case. By the loglikelihood-ratio statistic, psychometric functions of duration fitted the data better in only 7 of 45 cases (15.6%), in agreement with simulation results obtained when data were generated by psychometric functions of log duration. Analysis of data from 69 published papers (totaling 17,000+ psychometric functions) also indicated better fit of psychometric functions of log duration in the expected proportion given the typically small numbers of trials per function.