Non-parametric alternatives
Use ranks while preserving the design
Rank-based alternatives compare outcomes without requiring the same distributional assumptions as classical mean tests. Mann-Whitney concerns independent groups; Wilcoxon signed-rank uses paired differences; Kruskal-Wallis extends independent-group comparisons; Friedman handles related blocks. These procedures have assumptions and distinct null hypotheses, and are not automatically tests of medians.
Use for ordered outcomes or when a rank-based estimand is substantively useful. Match independent, paired or blocked designs and establish whether distributional-shape assumptions support the intended interpretation.
Strengths
- Useful for ordered measurements and some skewed distributions
- Less driven by extreme magnitudes than mean-based tests
Limitations
- Ranking discards magnitude information
- Median interpretations require additional distributional assumptions
Know the boundary
Non-parametric does not mean assumption-free or a universal remedy for a failed normality test.