Wilcoxtest

Wilcoxtest refers to a family of nonparametric statistical tests attributed to Frank Wilcoxon, used to compare two samples without assuming normality. They are commonly applied when data are ordinal or not normally distributed and aim to assess whether populations differ in central tendency.

The Wilcoxon signed-rank test is used for paired or matched samples. It computes the differences between paired observations, ranks the absolute differences, and sums the ranks with their signs. The resulting statistic is used to test whether the population median difference is zero. Exact p-values are available for small samples, and normal approximations are used for larger samples.

The Wilcoxon rank-sum test, also known as the Mann–Whitney U test, is used for independent samples. It combines all observations, ranks them, and compares the sum of ranks between the groups. It tests whether one population tends to yield larger values than the other. Like the signed-rank test, p-values can be computed exactly or via normal approximation, depending on sample size.

Assumptions include independent observations and at least ordinal data. The rank-sum test assumes similar shapes of distributions in the two groups; the signed-rank test assumes symmetry of the distribution of differences. They are less powerful than their parametric counterparts when normality holds but are more robust when assumptions fail.

In statistical software, these tests are implemented as wilcox.test in R, and as wilcoxon or mannwhitneyu in other packages. They are widely used in biomedical and social sciences as alternatives to the t-test when distributions are not normal.