Comment on a Wilcox Test Statistic for Comparing Means When Variances Are Unequal

Abstract

Wilcox (1989) has proposed an alternative to the James (1951) second-order statistic for comparing population means when variances are heterogeneous. The primary advantage of his approach is its computational simplicity in determining the number of degrees of freedom for the test statistic. We show, however, that the proposed solution can be invalid. With small (but reasonable) sample sizes, population means are underestimated, and mean differences among populations can be overestimated as a result of unequal sample sizes. The degree to which the procedure is invalid depends on the magnitude of the differences in sample sizes, the expected value of the observations, and the population variances.