Question: 15.4.4 Some texts define the Wilcoxon signed rank statistic as j , = C jj,Rtiwhere jj, = 1 if X, > 00 and 0 otherwise.

15.4.4 Some texts define the Wilcoxon signed rank statistic as j , = C jj,Rtiwhere jj, = 1 if X, > 00 and 0 otherwise. Determine the mean and variance of S,, and show that tests based on S, and on 8, are equivalent in the following sense: under a null hypothesis, S, = .$, - $;, where .!?, and j * have the same distribution.

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