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 ofa function. The parametric version ofthe 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. There are many occasions in which it is desirable to measure the strength ofa stimulus in terms of its response in an organism. Typically, different levels ofa known treatment are applied to subjects and the effects ofthat treatment are recorded at each level. Thus, in psychophysics, one might constructa psychometric./imction, which describes the relationship between the level ofa stimulus and the probability ofa subject making a particular response at that level (Falmagne, 1982). In a biological or