MINIMUM SIGNIFICANCE AND DISTRIBUTION FREE TESTS1

A general way of testing in the presence of nuisance parameters is to choose from a family of tests the one to maximize evidence against null hypothesis; that is, to minimize the significance level. This method yields exact tests when applied to distribution-free testing in various statistical designs; arbitrary choice of score functions is eliminated. However, the exact null distributions are highly non-normal, and there are problems with both computation and asymptotic theory.