Abstract

We explore a testing problem which involves four hypotheses, i.e., based on observations of two random variables X and Y, we wish to discriminate between four possibilities: identical survival functions, stochastic dominance of X over Y, stochastic dominance of Y over X, or crossing survival functions. Four-decision testing procedures for repeated measurements data are proposed. The tests are based on a permutation approach and do not rely on distributional assumptions. One-sided versions of the Cramer--von Mises, Anderson--Darling, and Kolmogorov--Smirnov statistics are considered. The consistency of the tests is shown. A simulation study indicates good power properties and control of false-detection errors. The proposed tests are applied to data from a psychophysical experiment.
The presentation is based on joint work with Magnus Ekström.