The Wilcoxon test is a nonparametric alternative to t-test for dependent samples. It is designed to test a hypothesis about the location (median) of a population distribution. It often involves the use of matched pairs, for example, "before" and "after" data, in which case it tests for a median difference of zero.

This procedure assumes that the variables under consideration were measured on a scale that allows the rank ordering of observations based on each variable (i.e., ordinal scale) and that allows rank ordering of the differences between variables (this type of scale is sometimes referred to as an ordered metric scale, see Coombs, 1950).

For more details, see Siegel & Castellan, 1988. See also, Nonparametric Statistics.