- A function of the Wilcoxon rank sum statistic is proposed for testing the equality of the marginal distributions when sampling from a bivariate population. The test statistic is asymptotically nonparametric. A comparison is made between the test statistic and several parametric and nonparametric tests in terms of their Pitman relative efficiency and small-sample performance. The test statistic has power comparable to the paired t test when sampling from the bivariate normal distribution and greater power in several important cases. 1983 Biometrika Trust.