Combinatorics and Statistical Issues Related to the Kruskal-Wallis Statistic

We explore criteria that data must meet in order for the Kruskal-Wallis test to reject the null hypothesis by computing the number of unique ranked datasets in the balanced case where each of the m alternatives has n observations. We show that the Kruskal-Wallis test tends to be conservative in reje...

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Bibliographic Details
Published in:Communications in statistics. Simulation and computation 2015-01, Vol.44 (2), p.533-550
Main Authors: Bargagliotti, Anna E., Greenwell, Raymond N.
Format: Article
Language:English
Subjects:
Balancing
Columns (structural)
Combinatorial analysis
Combinatorics
Computation
Computer simulation
Continuity correction
Criteria
Kruskal-Wallis
Null hypothesis
Rank-sums
Row-ordered data
Statistics
Tournaments
Young tableaux
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Summary:We explore criteria that data must meet in order for the Kruskal-Wallis test to reject the null hypothesis by computing the number of unique ranked datasets in the balanced case where each of the m alternatives has n observations. We show that the Kruskal-Wallis test tends to be conservative in rejecting the null hypothesis, and we offer a correction that improves its performance. We then compute the number of possible datasets producing unique rank-sums. The most commonly occurring data lead to an uncommonly small set of possible rank-sums. We extend prior findings about row- and column-ordered data structures.
ISSN:0361-0918
1532-4141
DOI:10.1080/03610918.2013.786781