ON A CLASS OF NONPARAMETRIC-TESTS FOR THE TREATMENT VS CONTROL PROBLEM

The classical problem of testing treatment versus control is revisited by considering a class of test statistics based on a kernel that depends on a constant 'a'. The proposed class includes the celebrated Wilcoxon Mann Whitney statistics as a special case when `a'= 1. It is shown that, with optimal choice of 'a’ depending on the underlying distribution, the optimal member performs better (in terms of Pitman efficiency) than the Wilcoxon Mann Whitney and the Median tests for a wide range of underlying distributions. An extended Hodges Lehmann type point estimator of the shift parameter corresponding to the proposed 'optimal’ test statistic is also derived. © 1990, Taylor & Francis Group, LLC. All rights reserved.