The rank transform in the two-sample location problem

Abstract

Abstract In the two-sample location problem, if the t-statistic is computed as a function of the ranks of the observations rather than the observations themselves, the resulting statistic, Tr, is a function of the Wilcoxon statistic. It is shown here that Tr, has approximately a t-distribution. The ARE of the T-test is identical to that of the Wilcoxon test. A Monte Carlo study reveals that the T-test is more robust, with regard to the significance level, than the t-test.