Wilcoxon signed-rank test

Summary

The Wilcoxon signed-rank test is a hypothesis test for the centre of a symmetric distribution, most often applied to the differences within matched pairs. It ranks the absolute values of the observations and adds the ranks of the positive ones. Unlike the sign test, it uses how far each observation lies from the hypothesised centre. So it is usually more powerful, but it assumes that the distribution is symmetric. It is the rank-based counterpart of the one-sample $t$-test.