Definition:Wilcoxon Rank Sum Test

Definition

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.

Also see

• Definition:Mann-Whitney Test

• Results about the Wilcoxon rank sum test can be found here.

Source of Name

This entry was named for Frank Wilcoxon.

Historical Note

The Wilcoxon rank sum test was devised by Frank Wilcoxon in $1945$.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Wilcoxon rank sum test
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Wilcoxon rank sum test