Determination of optimal data placement for psychometric function estimation: A computer simulation

Abstract

Psychometric functions are used to relate the responses of a subject to physical stimuli in a variety of psychophysical tasks. However, it is time consuming to obtain data to determine a psychometric function if many stimulus levels and many trials are required. A computer simulation was conducted to determine the minimum number of data points needed for such a determination. The computer simulation also determined the optimal placements of the stimuli and the number of trials per datum point for psychometric function determinations. Results indicate that a 2-point sampling method with 30–50 trials per point at optimal locations can produce a psychometric function with accurate spread and threshold estimates in a yes–no paradigm. However, the 4-point sampling method yields statistically smaller variances of the estimates. For the 2-alternative forced-choice paradigm, at least 120 trials per point are needed for the 2-point sampling method’s estimated parameters to differ from the known parameter values by less than 5%. The simulation results suggest that 3-alternative or 4-alternative forced-choice is preferable to 2-alternative. Furthermore, when a criterion-free paradigm is not required, the yes–no paradigm is a better procedure than m-alternative forced-choice for obtaining the corresponding psychometric function because of smaller standard deviation of the estimates and smaller number of trials/point required.