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Barbour, A D; Cartwright, D I; Donnelly, J B; Eagleson, G K (1985). A new rank test for the K-sample problem. Communications in Statistics. Theory and Methods, 14(6):1471-1484.

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Abstract

The treatment sum of squares in the one-way analysis of variance can be expressed in two different ways: as a sum of comparisons between each treatment and the remaining treatments combined, or as a sum of comparisons between the treatments two at a time. When comparisons between treatments are made with the Wilcoxon rank sum statistic, these two expressions lead to two different tests; namely, that of Kruskal and Wallis and one which is essentially the same as that proposed by Crouse (1961,1966). The latter statistic is known to be asymptotically distributed as a chi-squared variable when the numbers of replicates are large. Here it is shown to be asymptotically normal when the replicates are few but the number of treatments is large. For all combinations of numbers of replicates and treatments its empirical distribution is well approximated by a beta distribution

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
DDC:510 Mathematics
Language:English
Date:1985
Deposited On:19 Oct 2009 15:33
Last Modified:28 Nov 2013 01:35
Publisher:Taylor & Francis
ISSN:0361-0926
Publisher DOI:10.1080/03610928508828988
Citations:Web of Science®
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