Mann-Whitney U Test Calculator
Enter two independent samples to evaluate differences in central tendency without assuming normality.
Rank sum (Sample A): 32.0000
Rank sum (Sample B): 23.0000
UA: 17.0000
UB: 8.0000
Smaller U: 8.0000
Normal approximation (z): -0.9400
| Value | Group | Rank |
|---|---|---|
| 80 | B | 1.00 |
| 85 | A | 2.00 |
| 88 | B | 3.00 |
| 90 | A | 4.00 |
| 91 | B | 5.00 |
| 94 | B | 6.00 |
| 95 | A | 7.00 |
| 98 | B | 8.00 |
| 100 | A | 9.00 |
| 102 | A | 10.00 |
How to Use This Calculator
- Enter independent sample data for groups A and B.
- Review rank sums, U statistics, and the smaller U (used for significance tables).
- For large samples, use the provided normal approximation z-value to obtain a p-value.
- Interpret results relative to your chosen significance level to determine differences in distributions.
Formula
Assign ranks to combined samples; average ranks for ties.
UA = Σ ranks of group A − nA(nA + 1) / 2
UB = Σ ranks of group B − nB(nB + 1) / 2
Smaller U is compared against critical values or converted to z for large samples.
Mean of U = nAnB / 2, variance = nAnB(nA + nB + 1) / 12
Full Description
The Mann–Whitney U test, also known as the Wilcoxon rank-sum test, compares two independent samples without assuming normality. It tests whether the distributions differ, especially in their central tendency.
For small samples, consult exact critical value tables. For larger samples (n ≥ 10 per group), the normal approximation is typically adequate.
Frequently Asked Questions
What if there are many ties?
This calculator averages ranks for ties. For extensive ties, variance adjustments may be needed for precise p-values.
Can I use this for paired data?
No. Use the Wilcoxon signed-rank test for paired or matched samples.
Do I need equal sample sizes?
No. The test accommodates unequal sizes. Provide at least one observation per group.
How do I obtain p-values?
Use the smaller U with exact tables or convert z to a p-value using the standard normal distribution.