Abstract
Steel [14] proposed a distribution-free many-one method for comparing k≧2 test treatments with a control or standard in the one-way layout based on Wilcoxon [16] rank sum statistics. An efficient method is presented for computing the necessary probability points for this technique and an expanded table of points is given. The method also works for generalizations of Steel's procedure where the rank sum statistics are replaced by general linear rank statistics. Asymptotic probability points are found for many-one methods based on all linear rank statistics satisfying the conditions of the Chernoff-Savage [2] Theorem. It is shown that the asymptotically optimal design for these many-one methods takes approximately k 1/2 times as many observations from the control as from each test treatment. The asymptotic relative efficiency of two many-one procedures is identical to that of their two-sample counterparts.
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