A Unified Approach to Constructing Nonparametric Rank Tests.
STANFORD UNIV CA DEPT OF STATISTICS
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One shortcoming of the present theory of rank tests is that such stests have usually been constructed on a case by case basis, in a quite ad hoc albeit clever manner. This paper attempts to provide the basis for a more unified approach to rank tests. It investigates a general, yet simple construction, which simultaneously generates many rank test statistics, for a multitude of hypothesis testing situations. The proposed construction uses metrics on the permutation group in a novel way the proposed test statistic is the distance between two sets of permutations. This new construction is applied systematically to the two-sample and multi-sample location problems, the two-way layout problem, the one-sample location problem, the two-sample dispersion problem with equal medians, and the problem of testing for trend. It is shown that the construction works in a variety of testing situations gives rise to many familiar rank test statistics produces several other test statistics which are less familiar, yet equally plausible and enables one to extend rank tests to other hypothesis testing situations. Some connections with the existing nonparametric theory are discussed.
- Statistics and Probability