Uploaded December 2021 | Updated September 2026, 13 hours ago

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The Wilcoxon test, or Wilcoxon signed-rank test, checks whether two dependent samples differ significantly from each other. The Wilcoxon test is a non-parametric test and is therefore subject to significantly lower requirements than its parametric counterpart, the t-test for dependent samples. Thus, as soon as the boundary conditions for the t-test for dependent samples are no longer fulfilled, the Wilcoxon test is used.

Assumptions Wilcoxon test
Since the Wilcoxon test is a nonparametric test, the data need not be normally distributed. However, to calculate a Wilcoxon test, the samples must be dependent. Dependent samples are present, for example, when data are obtained from measurement repetition or when so-called natural pairs are involved.

Measurement repetition:
A characteristic of a person, e.g. weight, was measured at two points in time
Natural pairs:
The values do not come from the same person but from persons who belong together, for example lawyer/client, wife/husband and psychologist/patient.
If the data are not available in pairs, the Mann-Whitney U test is used instead of the Wilcoxon test.

Furthermore, the distribution shape of the differences of the two dependent samples should be approximately symmetrical.

To the Wilcoxon Test Calculator
numiqo.com/statistics-calculator/hypothesis-test/wilcoxon-test-calculator

More information about the Wilcoxon signed-rank test
numiqo.com/tutorial/wilcoxon-test