Statistics

Mann-Whitney U Test Calculator

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

Group A value 1

Group A value 2

Group A value 3

Group A value 4

Group B value 1

Group B value 2

Group B value 3

Group B value 4

Calculated Output

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 Breakdown

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)

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 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.

Frequently Asked Questions

When use it over a t-test?

When data is ordinal or not normally distributed.

The math behind it

Worked Example

Frequently Asked Questions

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