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# The KruskalWallis H test is a nonparametric analog of test (11.33) in one-wayanalysis of ISBN: 9781119285427 322

## Solution for problem 2 Chapter 11.9

Probability and Statistics with Reliability, Queuing, and Computer Science Applications | 2nd Edition

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Problem 2

The KruskalWallis H test is a nonparametric analog of test (11.33) in one-wayanalysis of variance [NOET 1976]. This test is a generalization of the Wilcoxonrank sum test considered in Section 10.3.2. Suppose that ni independent observa-tions for treatment level i have been taken. We combine k = ci=1 ni observationsand order them by increasing magnitude. Now we assign ranks to the combinedsample values and let Ri be the sum of the ranks assigned to the ni observationsof treatment level i. The test is based on statistic H, defined byH = 12k(k + 1)ci=1R2ini 3(k + 1).If ni > 5 for all i and if the null hypothesis that the k samples come from iden-tical populations holds, then the distribution of the H statistic is approximatelychi-square with (c 1) degrees of freedom. Apply the H test to the data inExample 11.10 and to the data in problem 1 above.

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##### ISBN: 9781119285427

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