Which of the following is essential for applying the Mann-Whitney U test ?
The observations should be independent between groups
The Mann-Whitney U test is a non-parametric test that compares two independent groups using the ranks of the pooled observations. It is the rank-based alternative to the independent-samples t test (S.P. Gupta, Statistical Methods).
All observations from both groups are ranked together and the statistic \(U_1 = n_1 n_2 + \dfrac{n_1(n_1+1)}{2} - R_1\) is computed from the rank sum of one sample. The sampling distribution of U is derived on the assumption that every observation is independent, both within each sample and between the two groups. Independence of observations between groups is therefore essential.
If the two samples are paired, the correct non-parametric test is the Wilcoxon signed-rank test, not the Mann-Whitney test. Normality of both populations is precisely what the test does not require, because it is distribution-free. The samples may be of unequal size, since \(n_1\) and \(n_2\) enter the formula separately.
The observations should be independent between groups option is correct.
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