**Definition**

*noun*

A non-parametric test of two samples which support exclusively on the order of observations in which the two samples fall and this is an alternative option of the parametric two sample t-test.

**Supplement**

This test can be used to assess the null hypothesis of two populations that contains the same continuous distributions.

There are assumptions that need to consider in using this test such as; that all observations from both groups are independent, the response must be ordinal, in the alternative hypothesis the probability of an observations from one population must exceeds from the second population which is not equal to 0.5 and under null hypothesis the distributions of both groups must be equal so that the probability of an observation from one population should exceed the observation from second population or vice versa, thus there is a symmetry between populations with respect to the probability of random sampling from a large population.

Under more strict assumptions, if the responses are assumed to be continuous and the alternative is restricted the significance of *W* is hard to interpret, yet it can be assessed using Hodges-Lehman estimate of the difference in central tendency between two populations differs from zero.

**Compare:**

• Paired Samples t-test

**Related terms:**

• Wilcoxon Signed-rank test

• Two Sample t-test

**See also:**

• Mann-Whitney U test

• Hodges-Lehman estimate

Dictionary > Wilcoxon rank-sum test

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