A test for psychometric function shift.

A nonparametric, small-sample-size test for the homogeneity of two psychometric functions against the left- and right-shift alternatives has been developed. The test is designed to determine whether it is safe to amalgamate psychometric functions obtained in different experimental sessions. The sum of the lower and upper p-values of the exact (conditional) Fisher test for several 2 × 2 contingency tables (one for each point of the psychometric function) is employed as the test statistic. The probability distribution of the statistic under the null (homogeneity) hypothesis is evaluated to obtain corresponding p-values. Power functions of the test have been computed by randomly generating samples from Weibull psychometric functions. The test is free of any assumptions about the shape of the psychometric function; it requires only that all observations are statistically independent.