Friday Ewere,Sunday Martins Ogbonmwan
Keywords: Exact test, rank test, permutation test, combinatorics, kruskal-wallis test.
Abstract: Generating the entire permutation sample space has been identified as a major problem in constructing the exact test of significance of a rank statistic. Procedures for most of the existing methods for finding the exact distribution for the common test statistics that are in use today are usually based on asymptotics which only give approximate results. The definition of what constitute a large sample in order to apply the large sample approximation is quite vague. In this paper, a method for obtaining the exact distribution of the Kruskal-Wallis (K-W) test is presented. The proposed method is based on combinatorics in the representation of the probability generating function of the test statistic. Essentially, this paper produces the exact critical values of the K-W test and the minimum sample size required for the application of the large sample approximation of the K-W statistic
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