If the null hypothesis for the Wilcoxon rank- sum test is not true, the distributions for the two populations are different from one another which should result in the rank- sum of one sample being relatively smaller than the other.

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The Wilcoxon rank-sum test is a non-parametric test used to compare two independent samples. It tests the null hypothesis that two samples come from the same distribution. If the null hypothesis is not true (i.e., the distributions are different), it often results in the rank sums of the samples being significantly different, as the test is sensitive to differences in both location and shape of the distributions.

If the Null Hypothesis for the Wilcoxon Rank- Sum Test