The Wilcoxon signed rank test is a nonparametric test used for paired samples or to determine if the data is centred over a particular value (often zero) in a single dataset. It uses order statistics; in the case of paired data, the differences are calculated; in the case of checking a central value, it is subtracted form each value. In each case this leads to data where the null hypothesis is that the central value is zero. The absolute values of the data are then ordered and ranked. If the data is centred on zero, the sum of the ranks of the positive and negative values should be similar, and the test uses this to determine a p-value.
For unpaired data use the Mann-Whitney test or Wilcoxon rank sum test, which are nonparametric equivalents of the Student's t test between independent groups.
Used in glossary entries: Mann-Whitney test, nonparametric statistics, null hypothesis, order statistics, p-value, Wilcoxon rank sum test