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 "The Wilcoxon test" can refer to several statistical tests

Wilcoxon's name is used to describe several statistical tests.

The Wilcoxon matched-pairs signed-rank test is a nonparametric method to compare before-after, or matched subjects. It is sometimes called simply the Wilcoxon matched-pairs test.

The Wilcoxon signed rank test is a nonparametric test that compares the median of a set of numbers against a hypothetical median.

The Wilcoxon rank sum test is a nonparametric test to compare two unmatched groups. It is equivalent to the Mann-Whitney test.

The Gehan-Wilcoxon test is a method to compare survival curves.

The first two tests listed above are related. The matched-pairs signed-rank test works by first computing the difference between each set of matched pairs, and then using the Wilcoxon signed rank test to ask if the median of these differences differs from zero. Often the term "Wilcoxon signed rank" test is used to refer to either test. This is not really confusing as it is usually obvious whether the test is comparing one set of numbers against a hypothetical median, or comparing a set of differences between matched values against a hypothetical median difference of zero.