A Unified Approach to Constructing Nonparametric Rank Tests.
Abstract
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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 06, 1986
- Accession Number
- ADA169815
Entities
People
- Douglas E. Critchlow
Organizations
- Stanford University