Measure practical differences beyond p-values using robust rank methods. Analyze tied and unequal data confidently. Get clear statistics, confidence cues, plots, exports, and explanations.
Use commas, spaces, semicolons, or line breaks between values. For paired analysis, keep values in the same order across Sample A and Sample B.
| Scenario | Sample A / Group A | Sample B / Group B | Extra groups | Suggested method |
|---|---|---|---|---|
| Independent rank comparison | 12, 14, 15, 17, 18, 19 | 8, 9, 11, 13, 14, 15 | None | Mann-Whitney U |
| Before versus after for the same cases | 52, 50, 48, 46, 54, 57 | 49, 47, 46, 44, 50, 53 | None | Wilcoxon signed-rank |
| Three independent groups | 10, 11, 13, 14, 15 | 16, 18, 17, 19, 20 | Group C: 12, 13, 12, 14, 16 | Kruskal-Wallis |
These example values are only for demonstration. Replace them with your own observations before exporting results.
Use this for two independent groups. The calculator ranks all observations together, applies average ranks for ties, then derives effect sizes from the rank structure.
U₁ = R₁ − n₁(n₁ + 1) / 2 Rank-biserial correlation = [2U₁ / (n₁n₂)] − 1 Cliff's delta = (wins − losses) / (n₁n₂) Common-language effect = (wins + 0.5 × ties) / (n₁n₂) Standardized r = z / √NUse this for paired or repeated measurements. Zero differences are removed before ranking absolute differences.
Matched rank-biserial = (W⁺ − W⁻) / [n(n + 1) / 2] Standardized r = z / √n Median paired difference = median(A − B)Use this for two or more independent groups when rank-based comparison is preferred over parametric assumptions.
H = {12 / [N(N + 1)]} × Σ(Rⱼ² / nⱼ) − 3(N + 1) Tie correction: C = 1 − Σ(t³ − t) / (N³ − N) Corrected H = H / C Epsilon squared = (H − k + 1) / (N − k) Eta squared (H) = (H − k + 1) / (N − 1)Approximate z and p values are provided as practical cues, not exact small-sample inference.
It shows the practical magnitude and direction of differences without depending heavily on normality assumptions. Instead of only asking whether groups differ, it describes how strongly ranks or paired changes separate the samples.
Use Mann-Whitney when you have two independent groups, such as treatment versus control, and you want rank-based effect measures like rank-biserial correlation, Cliff’s delta, and common-language probability.
Use Wilcoxon when the same units are measured twice or when observations are naturally paired. The calculator compares paired differences and converts the signed-rank pattern into effect size measures.
Epsilon squared summarizes how much of the rank variation is associated with group membership. It provides a practical magnitude estimate for multi-group rank comparisons and is often easier to interpret than H alone.
Tied observations receive average ranks. Tie groups also affect the variance correction used for approximate z values and the corrected H statistic, which helps keep the rank-based estimates more realistic.
No. The calculator reports approximate p values from normal-style standardization when available. They are useful screening cues, but exact inference may require dedicated procedures for very small samples.
Yes. You can paste comma-separated, space-separated, semicolon-separated, or line-separated values. Non-numeric tokens are ignored and listed in a warning so you can clean the data quickly.
Report the metric aligned with your test design: rank-biserial or Cliff’s delta for independent groups, matched rank-biserial for paired data, and epsilon squared for Kruskal-Wallis designs. Add medians and sample sizes for context.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.