THRESHOLDS FROM PSYCHOMETRIC FUNCTIONS - SUPERIORITY OF BOOTSTRAP TO INCREMENTAL AND PROBIT VARIANCE ESTIMATORS

The bootstrap method provides a powerful, general procedure for estimating the variance of a parameter of a function. The parametric version of the method was used to estimate the standard deviation of a threshold from a psychometric function and the standard deviation of its slope. Bootstrap standard deviations were compared with those obtained by a classical incremental method and by the asymptotic method of probit analysis. Twelve representative experimental conditions were tested in Monte Carlo studies, each of 1,000 data sets. All methods performed equally well with large data sets, but with small data sets the bootstrap was superior in both percentage bias and relative efficiency.