Mann-Whitney U Test Calculator
Free Mann-Whitney U test calculator. Compare two independent groups with rank-based test. U statisti
Why This Statistical Analysis Matters
Why: Statistical calculator for analysis.
How: Enter inputs and compute results.
Mann-Whitney U Test โ Two Independent Groups
Non-parametric rank-based test. Use when normality is violated or data are ordinal (pain scores, Likert, skewed).
Real-World Scenarios โ Click to Load
Data Input
Enter numeric values separated by spaces, commas, or newlines. Each group must have at least 2 observations.
Rank Distribution by Group
U-Statistic vs Null Distribution (Normal Approximation)
Calculation Breakdown
Step-by-Step Rank Table
| Value | Rank | Group |
|---|---|---|
| 2 | 2.5 | Group 1 |
| 3 | 4.5 | Group 1 |
| 4 | 6.5 | Group 1 |
| 5 | 8.5 | Group 1 |
| 6 | 10.5 | Group 1 |
| 7 | 12.5 | Group 1 |
| 8 | 14.5 | Group 1 |
| 9 | 16.5 | Group 1 |
| 10 | 18.5 | Group 1 |
| 11 | 20 | Group 1 |
| 1 | 1 | Group 2 |
| 2 | 2.5 | Group 2 |
| 3 | 4.5 | Group 2 |
| 4 | 6.5 | Group 2 |
| 5 | 8.5 | Group 2 |
| 6 | 10.5 | Group 2 |
| 7 | 12.5 | Group 2 |
| 8 | 14.5 | Group 2 |
| 9 | 16.5 | Group 2 |
| 10 | 18.5 | Group 2 |
Quick Interpretation
No significant difference between groups. The observed difference could be due to chance. Consider increasing sample size if you expected a real effect.
โ ๏ธFor educational and informational purposes only. Verify with a qualified professional.
Key Takeaways โ Non-Parametric Use Cases
- โข Mann-Whitney U test: Non-parametric alternative to independent samples t-test when normality is violated or data are ordinal.
- โข Procedure: Combine both samples, rank all N = nโ + nโ observations. Ties get average rank.
- โข U statistic: Uโ = nโnโ + nโ(nโ+1)/2 โ Rโ, Uโ = nโnโ + nโ(nโ+1)/2 โ Rโ. U = min(Uโ, Uโ).
- โข Check: Rโ + Rโ = N(N+1)/2 and Uโ + Uโ = nโnโ.
- โข Large samples (nโ, nโ โฅ 20): Normal approximation: ฮผ_U = nโnโ/2, ฯ_U with tie correction, z = (U โ ฮผ_U)/ฯ_U.
- โข Effect size: r = z/โN (rank-biserial correlation). CLES = Uโ/(nโnโ) = probability a random Group 1 value exceeds a random Group 2 value.
- โข When to use: Ordinal data (Likert, pain scores), skewed distributions, small samples where normality cannot be assumed.
Did You Know?
Formulas
Rโ + Rโ = N(N+1)/2
Sum of ranks check
Uโ = nโnโ + nโ(nโ+1)/2 โ Rโ
Uโ = nโnโ + nโ(nโ+1)/2 โ Rโ
ฮผ_U = nโnโ/2, ฯ_U = โ(nโnโ(N+1)/12)
Tie correction: subtract ฮฃ(tแตขยณโtแตข)/(N(Nโ1)) term
r = z/โN, CLES = Uโ/(nโnโ)
Effect sizes
Frequently Asked Questions
When should I use Mann-Whitney instead of t-test?
When data are ordinal, skewed, or normality is violated. Also for small samples where the central limit theorem may not apply.
What does CLES mean?
Common Language Effect Size. Probability that a randomly chosen value from Group 1 exceeds a randomly chosen value from Group 2. CLES = 0.5 means no difference.
How do I handle ties?
Assign average ranks to tied values. The calculator applies the tie correction to ฯ_U automatically.
What sample size is needed for normal approximation?
nโ and nโ both โฅ 20 is typically safe. For smaller samples, the approximation is still often used; exact tables exist for very small n.
Can I use this for paired data?
No. For paired/matched data, use the Wilcoxon Signed-Rank test instead.
Mann-Whitney vs Wilcoxon Rank-Sum?
They are equivalent for independent samples. Different names, same test. Wilcoxon (1945) came first; Mann-Whitney (1947) provided the U formulation.
Official Data Sources
Disclaimer: This calculator provides statistical guidance. For medical or clinical decisions, consult a qualified professional. For very small samples (nโ, nโ < 8), consult exact Mann-Whitney U tables.