Category:Definitions/Wilcoxon Rank Sum Test

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The Wilcoxon rank sum test is a distribution-free test of the hypothesis that two independent samples come from the same population.

The alternative hypothesis may specify:

a difference in median only

one population distribution is stochastically larger than the other.

The observations in the combined samples are arranged in ascending order and replaced by their ranks.

Then the test statistic is calculated as the sum of the ranks of the observations in one of the samples.

Then either $p$-values can be calculated, or critical values for given sample sizes looked up in published tables.

For large samples, an approximation to a normal distribution is often used.