Mann-Whitney U Critical Values Table

Find the exact critical value of U for the Mann-Whitney (rank-sum) test, for sample sizes from 4 to 20.

Significance level (α, two-tailed)

Critical U values at α = 0.05 (two-tailed), exact by enumeration

n₁ \ n₂	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20
4	0	1	2	3	4	4	5	6	7	8	9	10	11	11	12	13	14
5	—	2	3	5	6	7	8	9	11	12	13	14	15	17	18	19	20
6	—	—	5	6	8	10	11	13	14	16	17	19	21	22	24	25	27
7	—	—	—	8	10	12	14	16	18	20	22	24	26	28	30	32	34
8	—	—	—	—	13	15	17	19	22	24	26	29	31	34	36	38	41
9	—	—	—	—	—	17	20	23	26	28	31	34	37	39	42	45	48
10	—	—	—	—	—	—	23	26	29	33	36	39	42	45	48	52	55
11	—	—	—	—	—	—	—	30	33	37	40	44	47	51	55	58	62
12	—	—	—	—	—	—	—	—	37	41	45	49	53	57	61	65	69
13	—	—	—	—	—	—	—	—	—	45	50	54	59	63	67	72	76
14	—	—	—	—	—	—	—	—	—	—	55	59	64	69	74	78	83
15	—	—	—	—	—	—	—	—	—	—	—	64	70	75	80	85	90
16	—	—	—	—	—	—	—	—	—	—	—	—	75	81	86	92	98
17	—	—	—	—	—	—	—	—	—	—	—	—	—	87	93	99	105
18	—	—	—	—	—	—	—	—	—	—	—	—	—	—	99	106	112
19	—	—	—	—	—	—	—	—	—	—	—	—	—	—	—	113	119
20	—	—	—	—	—	—	—	—	—	—	—	—	—	—	—	—	127

Reject H₀ (no difference between groups) if your calculated U is less than or equal to the tabled value. Values are the exact critical U from enumerating every possible rank arrangement, not a normal approximation, so they match printed textbook tables exactly for these sample sizes.

How to use this tool

Choose your two-tailed significance level.
Find your smaller sample size, n1, down the left side and your larger sample size, n2, along the top.
Read the critical U value where they meet.
Reject the null hypothesis of no difference between the two groups if your calculated U is less than or equal to the tabled value.

Formula Reference

Mann-Whitney U statistic

the smaller of U1 and U2, from the rank sums of the two groups

Exact null distribution

built by counting every arrangement of ranks between the two groups, not approximated

ArticleNon-Parametric Tests: An Introduction ArticlePermutation Tests: A p-Value Built by Shuffling the Labels Calct-Test Calculator GlossaryGlossary: Non-Parametric Test

Frequently Asked Questions

When should I use the Mann-Whitney test instead of a t-test?+

Use it when comparing two independent groups on an outcome that is ordinal, clearly non-normal, or has outliers that would distort a t-test, since it works on the ranks of the data rather than the raw values.

Why are these values exact rather than approximate?+

For sample sizes this small, the exact distribution of U under the null hypothesis can be found by counting every possible way the ranks could be split between the two groups. Software often switches to a normal approximation for larger samples, where the exact count becomes impractical.

What if my sample sizes are larger than 20?+

A normal approximation to the U statistic becomes quite accurate once both sample sizes are around 20 or more, so most statistics software and calculators switch to it automatically above that range.

Does a smaller U always mean a bigger difference between groups?+

A U value far from its expected value under the null hypothesis, in either direction, suggests a difference. This table gives the lower critical value; by symmetry, a correspondingly large U is equally significant.

n₁ \ n₂

—

105

—

106

112

—

113

119

—

127

How to use this tool

Choose your two-tailed significance level.

Find your smaller sample size, n1, down the left side and your larger sample size, n2, along the top.

Read the critical U value where they meet.

Reject the null hypothesis of no difference between the two groups if your calculated U is less than or equal to the tabled value.