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On Sensitive Rank Tests for Comparing the Effects of Two Treatments on a Single Group

Published online by Cambridge University Press:  01 January 2025

Hans K. Ury
Hans K. Ury*
Affiliation:
Stanford University
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Abstract

The rank test Rn of Cronholm and Revusky [1965] in effect doubles the number of comparisons carried out in the Mann-Whitney test between “Treated” and “Control” subjects chosen from a single group of n and triples the asymptotic Pitman efficiency against shift alternatives by using a series of n – 1 subexperiments. However, the full series can be too costly or time-consuming. It is shown that j appropriately chosen subexperiments will permit one to make at least j/(j + 1) of the number of comparisons possible under Rn, with large sample efficiency of j/(j + 2) relative to Rn against shift alternatives and small sample efficiency greater than that, j = 2, 3, …, n − 2. The resulting test criterion is a sum of j independent Mann-Whitney test statistics. Its null distribution is tabulated for n ≤ 10 and small sample efficiency comparisons are carried out for n = 10.

Type
Original Paper
Information
Psychometrika , Volume 37 , Issue 2 , June 1972 , pp. 149 - 166
Copyright
Copyright © 1972 The Psychometric Society

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