Comparing Two Samples: Extensions of the t, Rank-Sum, and Log-Rank Tests

Abstract

I consider the problem of testing that two populations are identical with respect to the distribution of a continuous variable against the alternative that values tend to be larger in one population. I observe that the t, rank-sum, and log-rank tests are insensitive for a large class of alternatives that may be expected to occur commonly in practice, propose a criterion for identifying this problem in a particular data set, and propose corresponding extensions of the conventional methods. The proposed methods should be useful for both identifying and interpreting group differences.