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Mann-Whitney U Test Calculator

Find the Mann-Whitney U statistic for two small samples.

U statistic 5
U for group A 11
U for group B 5

Formula: U = R - n(n+1)/2 for each group; report the smaller

Step-by-step with your numbers:
1. ▶ Step 1 — Identify Groups:
2. Group A: 7, 9, 12, 15 (n_A = 4)
3. Group B: 6, 8, 10, 11 (n_B = 4)
4.
5. ▶ Step 2 — Rank all values (lowest to highest):
6. Value 6 (Group B) = Rank 1
7. Value 7 (Group A) = Rank 2
8. Value 8 (Group B) = Rank 3
9. Value 9 (Group A) = Rank 4
10. Value 10 (Group B) = Rank 5
11. Value 11 (Group B) = Rank 6
12. Value 12 (Group A) = Rank 7
13. Value 15 (Group A) = Rank 8
14.
15. ▶ Step 3 — Sum the ranks for each group (R):
16. Sum of Ranks for Group A (R_A) = 21
17. Sum of Ranks for Group B (R_B) = 15
18.
19. ▶ Step 4 — Calculate U for each group:
20. Formula: U = R - [n(n+1)] / 2
21. U_A = 21 - [4(4+1)] / 2 = 21 - 10 = 11
22. U_B = 15 - [4(4+1)] / 2 = 15 - 10 = 5
23.
24. ▶ Step 5 — Final U Statistic:
25. The final U statistic is the smaller of U_A and U_B.
26. U = 5
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The Mann-Whitney U test compares two independent samples without assuming normality.

The math behind it

Rank all values together, sum the ranks per group, then U = R - n(n+1)/2. The smaller U is the test statistic.

Worked example

Two 3-4 value groups give a U you compare to the critical value table.

FAQ

When use it over a t-test?

When data is ordinal or not normally distributed.

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