A Comparative Power Study of The Bivariate Rank Sum Test and T 2

The small sample performance of the bivariate two-sample Wilcoxon type rank sum test W is studied by Monte Carlo evaluation of power under shift alternatives in the bivariate normal distribution. Two types of alternatives are considered: (a) shift in only one coordinate and (b) equal amounts of shifts in both coordinates. The estimated power of the W test is compared with the power of Hotelling's T ² test. Interestingly, it is found that the empirical power of W substantially exceeds the power of T ² for some normal shift alternatives although the latter is the uniformly most powerful invariant test for the problem.