Rank-Based Analysis Map for Independent, Paired and Repeated Data
A practical guide to choosing and interpreting Mann–Whitney, Wilcoxon, Kruskal–Wallis and Friedman tests without common misconceptions.
What is a nonparametric test?
Nonparametric methods make inference through ranks, signs or permutations without requiring a fully specified distribution family. They are not assumption-free: independence, measurement scale, sampling and—in some interpretations—similar distribution shapes still matter.
Choose by design, not by one normality p value
Test choice should reflect the research question, independent or paired structure, sample size, outliers, distribution shape and target estimand. A significant Shapiro–Wilk test alone is not a sufficient decision rule.
Core tests
Mann–Whitney U: two independent groups. It compares rank distributions. A median-shift interpretation requires comparable distribution shapes.
Wilcoxon signed-rank: paired or before–after measurements. Symmetry of paired differences matters for a median-difference interpretation.
Kruskal–Wallis: three or more independent groups. A significant omnibus result requires multiplicity-adjusted post-hoc comparisons.
Friedman: three or more related measurements or blocked designs. Pairwise follow-up tests should be adjusted.
When can a parametric model still be appropriate?
t tests and ANOVA can be robust to moderate non-normality, particularly with balanced groups and adequate samples. Model residuals, rather than the raw outcome alone, are often the relevant diagnostic. Large samples can make trivial deviations statistically significant, while small samples may hide important departures. Use Q–Q plots, histograms and subject-matter knowledge.
Alternatives
Depending on the estimand, transformations, bootstrap confidence intervals, robust standard errors, ordinal regression, generalized estimating equations or mixed models may answer the scientific question better than a simple rank test.
Report more than a p value
Provide group summaries, an interpretable effect size and uncertainty. Possible measures include rank-biserial correlation, probability-of-superiority measures and confidence intervals for paired differences. Remember that not every rank test is literally a test of medians.
Common mistakes
Switching automatically after any significant normality test.
Ignoring pairing or repeated measurements.
Calling every Mann–Whitney result a median difference.
Skipping multiplicity correction after an omnibus test.
Reporting no effect size or interval estimate.
References
Accessed 20 June 2026.