Two-, three-, and four-interval forced-choice staircase procedures: estimator bias and efficiency

Threshold estimates for multiple-interval forced-choice staircase procedures were studied using computer simulations. A sigmoidal psychometric function shape governed the hypothetical subject's responses in the simulations. Parameters varied included the number of trials, the step size for stimulus level change, and decision rules that targeted 70.7% and 79.4% correct performance. Each threshold estimate was calculated by averaging the stimulus levels at which a reversal a stimulus level direction occurred. The results of the simulations suggest that, as the number of alternatives is increased from 2 to 4, the variability of repeated threshold estimates decreases or remains constant, and the accuracy of the estimator, in most cases, improves. A subset of the simulations was compared with data obtained in a detection-in-noise task. The behavioral data were consistent with the simulation results. Two major conclusions were reached. First, 3- and 4-interval forced-choice (IFC) procedures are more efficient than a 2IFC procedure with a decision rule that targets 70.7% correct performance even when the additional time required to complete 3- and 4IFC trials is considered. Second, the accuracy of 2IFC procedures can be improved by fitting the trial history of a staircase run using probit analysis.