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Stat 5601 (Geyer) Examples (Wilcoxon Rank Sum Test and Related Procedures)

Contents

General Instructions

To do each example, just click the "Submit" button. You do not have to type in any R instructions or specify a dataset. That's already done for you.

The Wilcoxon Rank Sum Test

Example 4.1 in Hollander and Wolfe.

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Summary

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The Associated Point Estimate (Median of the Pairwise Differences)

The Hodges-Lehmann estimator associated with the rank sum test is the median of the pairwise differences, which are the nx ny differences

Yj - Xi,     for all i and j

Example 4.3 in Hollander and Wolfe.

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Summary

The Associated Confidence Interval

Very similar to the confidence intervals associated with the sign test and signed rank test, the confidence interval has the form

(D(k), D(m + 1 - k))
where m = nx ny is the number of pairwise differences, the Di are the pairwise differences, and, as always, parentheses on subscripts indicates order statistics. That is, one counts in k from each end in the list of sorted pairwise differences to find the confidence interval.

Example 4.4 in Hollander and Wolfe.

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Summary

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The R Function wilcox.test

All of the above can be done in one shot with the R function wilcox.test (on-line help). This function comes with R. It was not written especially for this course.

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