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Effect sizes for nonparametric tests

Fernanda Fiel Peres · 2025 · 149 citationsRead the paper

Effect size measures are important complements to P values, providing information about the magnitude and practical relevance of research findings. While widely discussed in the context of parametric tests, effect size estimation for nonparametric tests remains less explored. This article reviews standardized effect size measures applicable to four common nonparametric tests: Mann-Whitney, Wilcoxon signed-rank, Kruskal-Wallis, and Friedman. Commonly suggested classifications for these effect sizes are also discussed. This article aims to support researchers in reporting and interpreting effect sizes more effectively in nonparametric contexts.

What the full text shows

Theory or simulation
  • Standardized effect size r for Mann-Whitney U and Wilcoxon signed-rank tests is classified as small (≥ 0.1), medium (≥ 0.3), or large (≥ 0.5). (Based on Cohen's thresholds)
  • Vargha and Delaney’s A (VDA) for independent groups is classified as small (≥ 0.56), medium (≥ 0.64), or large (≥ 0.71). (Probability of superiority)
  • Rank-biserial correlation (rg/δ) for Mann-Whitney U is classified as small (≥ 0.11), medium (≥ 0.28), or large (≥ 0.43). (Based on Vargha and Delaney guidelines)
  • Ordinal eta-squared (η2H) for Kruskal-Wallis is classified as small (≥ 0.01), medium (≥ 0.06), or large (≥ 0.14). (Based on ANOVA eta-squared thresholds)
  • Ordinal epsilon-squared (ε2R) for Kruskal-Wallis is suggested as small (≥ 0.01), medium (≥ 0.08), or large (≥ 0.26). (Based on equivalence to effect size r)
  • Kendall’s W for Friedman test is often classified as small (≥ 0.1), medium (≥ 0.3), or large (≥ 0.5). (Based on Cohen's guidelines for w)
Setup
Literature review and illustrative examples using fasting glucose data (e.g., N=10 or N=50 per group).
How
The paper reviews and synthesizes existing formulas and classification thresholds for effect size measures associated with four nonparametric tests. It provides R functions and an Excel tool for calculating these metrics.
Limitations
Classification thresholds are heuristics and may not align with clinical relevance. · Interpretation of ordinal eta-squared as 'percentage of variance' is conceptually debated. · No empirical research directly compares ordinal epsilon-squared and ordinal eta-squared.

Summarized by Gemma 4 from the open-access full text · 10 Oct 2026. Read it