Target an arbitrary probability of response using weighted staircase procedures

Threshold estimation procedures are widely used to measure the stimulus level corresponding to a specified probability of response. The weighted up-and-down procedure, familiar to many due to its use in standard pure-tone audiometry, allows the experimenter to target any probability of response by using different ascending and descending step sizes. Unfortunately, thresholds have a signed mean error that made using weighted staircases inadvisable. The current study evaluated a correction to eliminate the error. Monte Carlo simulations of weighted staircases were used to test the effectiveness of the proposed correction for yes-no and forced-choice tasks with Gaussian and log-Weibull psychometric functions. Results showed that the proposed correction was effective over a wide range of step size magnitudes and ratios with a symmetric psychometric function and less effective when there was asymmetry due to the shape of the function or a high guess or lapse rate. The proposed correction facilitates the use of weighted staircases to target an arbitrary probability of response.