On monotonicity of power of two-sample rany tests when testing the alternative g is stochastically larger than f

Abstract

In rhis pciper we consider the problem of testing the equality of two continuous distribution functions F and G against the alternative G is stochastically larger than F on the basis of two independent random samples. For testing , we say a test is monotone in power if its power function is a nondecreasing function of sample size for all levels of significance and all pairs of continuous distribution functions (F,G) such that G(x) |, F(x) for all x. Examples are given to show that the Wilcoxon, normal scores.- and Van der Waerden tests, or more generally tests based on two-sample rank statistics of a particular form lack the monotonicity of power property. In addition, the examples illustrate some types of undesirable power function behavior which may occur when considering the power function as a function of sample size.