Nonparametric Tests

When to Use Nonparametric Tests

Nonparametric tests make fewer assumptions about the distribution of your data. Use them when:

• ●The data is clearly non-normal and the sample size is too small for the Central Limit Theorem to help (n < 30 per group)
• ●The outcome is ordinal (e.g., Likert scales, disease severity scores)
• ●You have extreme outliers that cannot be removed or transformed
• ●You need to be cautious and want a conservative test

Mann-Whitney U Test (Wilcoxon Rank-Sum)

The Mann-Whitney U test is the nonparametric alternative to the independent samples t-test. It compares whether the distributions of two independent groups differ, using ranked data instead of raw values.

• ●H₀: The distributions of both groups are the same (no tendency for one group to have higher values)
• ●The test ranks all observations from both groups combined, then checks if the ranks are evenly distributed
• ●Report: Median [IQR] for each group, U statistic, p-value, and rank-biserial correlation (effect size)
• ●Effect size: r = Z / √N. Small = 0.1, Medium = 0.3, Large = 0.5

Wilcoxon Signed-Rank Test

The Wilcoxon signed-rank test is the nonparametric alternative to the paired samples t-test. It tests whether the distribution of paired differences is symmetric around zero.

• ●Use when: same subjects measured at two time points, or matched pairs
• ●The test ranks the absolute differences, then checks whether positive or negative differences dominate
• ●H₀: Median of differences = 0

Kruskal-Wallis H Test

The Kruskal-Wallis H test is the nonparametric alternative to one-way ANOVA. It extends the Mann-Whitney U test to three or more groups.

• ●H₀: All group distributions are the same
• ●Like ANOVA, a significant result only tells you that at least one group differs
• ●Post-hoc: Use Dunn's test with Bonferroni correction to identify specific group differences
• ●Effect size: η² = (H - k + 1) / (N - k) where k = number of groups

Reporting Nonparametric Results