On the Asymptotic Equivalence of Two Ranking Methods for K-Sample Linear Rank Statistics

Two methods of ranking K samples for rank tests comparing K populations are considered. The first method ranks the K samples jointly; the second ranks the K samples pairwise. These procedures were first suggested by Dunn (1964), and Steel (1960), respectively. It is shown that both ranking procedures are asymptotically equivalent for rank-sum tests satisfying certain nonrestrictive conditions. The problem is formulated in terms of multiple comparisons, but is applicable to other nonparametric procedures based on K-sample rank statistics.