The Wilcoxon rank-sum test includes a variable,W. It is the sum of the observed values from the larger sample.

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The Wilcoxon rank-sum test, also known as the Mann-Whitney U test, compares the distribution of values between two independent groups. The test statistic is the sum of the ranks of the observations from one sample, with ties given the average rank, and the hypothesis test is based on whether this sum is significantly different from what would be expected under the null hypothesis of no difference between the groups. There is no variable W that represents the sum of observed values from the larger sample in this test.

The Wilcoxon Rank-Sum Test Includes a Variable,W