Mann Whitney U Test
The Mann-Whitney U Test compares two independent groups on a continuous or ordinal outcome, without assuming normality. Example: comparing pain scores between two patient groups when the score distribution is skewed.
Step 1 — Provide your data
Three ways to provide data:
- Manual entry — paste two columns into Group 1 and Group 2 text areas
- Excel / CSV upload — supports two layouts:
- Separate columns — Group 1 and Group 2 in different columns
- Stacked format — one value column + one group identifier column
- Download Sample File — template Excel file to fill in
- Generate Random Data — fills inputs with random values
Step 2 — Calculate
Click Calculate Mann-Whitney U Test.
Step 3 — Read the results
| Field | What it shows |
|---|---|
| U Statistic | The Mann-Whitney U value (smaller of U₁ and U₂) |
| Z-score | Standardised Z value |
| P-value (NEJM) | Significance |
| Effect Size (r) | Rank-biserial correlation with interpretation label |
| Group Medians | Median for each group |
| Rank sums | R₁ and R₂ |
Interpretation block with significance and direction statements.
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Statistical methods used
Test statistic
| Component | Formula |
|---|---|
| Combined ranking | All observations merged, sorted, ranked (ties averaged) |
| U₁ | R₁ − n₁(n₁ + 1) / 2 |
| U₂ | R₂ − n₂(n₂ + 1) / 2 |
| U (reported) | min(U₁, U₂) |
Normal approximation for p-value
| Component | Formula |
|---|---|
| μ_U | n₁ × n₂ / 2 |
| σ_U | √(n₁ × n₂ × (n₁ + n₂ + 1) / 12) |
| Z-score | (U − μ_U) / σ_U |
| p-value | `2 × (1 − Φ( |
Hypothesis statement
- H₀: The two groups come from the same distribution
- H₁: The two groups come from different distributions (two-tailed)
- Significance level: α = 0.05
Effect size — Rank-biserial correlation (r)
r = |Z| / √(n₁ + n₂)
| |r| value | Label |
|---|---|
| < 0.10 | Negligible effect |
| 0.10 – 0.30 | Small effect |
| 0.30 – 0.50 | Medium effect |
| ≥ 0.50 | Large effect |
Minimum sample size: 3 values per group.