Estimating the variance of a critical stimulus level from sensory performance data

Measures of sensory performance yielding a nonlinear dependence on stimulus level are often used to derive a critical stimulus level that corresponds to some criterion level of performance. Typical examples include the sigmoidal psychometric function used to estimate a "threshold" stimulus level, and the power-law increment-threshold curve used to estimate a "field sensitivity". Estimates of the variance of an estimated critical stimulus level derived from a single set of performance data are, however, infrequently reported, even though other estimates of reliability may not be available. An application of the classical "combination of observations" method is described here by which such variance estimates may be computed. The method was tested by applying it to sets of simulated psychometric-function data and increment-threshold data and comparing its results with those obtained by Monte-Carlo studies, each comprising 1000 runs. Differences between the estimated root mean variance of the estimated critical stimulus level and the "true" value were found to be not more than about 3% of the true value.