What is the Wilcoxon Test

The Wilcoxon test, which refers to either the Rank Sum test or the Signed Rank test, is a nonparametric test that compares two paired groups. The test essentially calculates the difference between each set of pairs and analyzes these differences. The Wilcoxon Rank Sum test can be used to test the null hypothesis that two populations have the same continuous distribution. The base assumptions necessary to employ this method of testing is that the data are from the same population and are paired, the data can be measured on at least an interval scale, and the data were chosen randomly and independently.

The Wilcoxon Signed Rank test assumes that there is information in the magnitudes and signs of the differences between paired observations. As the nonparametric equivalent of the paired student's t-test, the Signed Rank can be used as an alternative to the t-test when the population data does not follow a normal distribution.


The Rank Sum and Signed Rank tests were both proposed by American statistician Frank Wilcoxon in a groundbreaking research paper published in 1945. The tests laid the foundation for hypothesis testing of nonparametric statistics, which are used for population data that can be ranked but do not have numerical values, such as customer satisfaction or music reviews. Nonparametric distributions do not have parameters and cannot be defined by an equation like parametric distributions can.