NUMBAT OER - Open Educational Resources

First, use the Critical Significance Level (α) chosen in Step 2 and sample sizes (n1 and n1) calculated in Step 3 to find the Critical Value of U (Ucritical) using a Critical Value Table such as the one below (e.g. if α = 0.05, n1 = 20 and n2 = 20, then Ucritical = 127).

Second, compare Ucritical with the value for the U statistic calculated in Step 3.

Reject your Null Hypothesis if your calculated value is less than or equal to the Critical value; U ≤ Ucritical (significant result).

Accept your Null Hypothesis if your calculated value is greater than the Critical value; U > Ucritical (non-significant result).

For example, if U = 121 and Ucritical = 127 then reject the Null Hypothesis.

Table of Critical Values for Critical Significance Levels (α) of 0.05 for the U statistic (smaller value) where n1 is the size of the first sample and n2 is the size of the second sample.

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

Critical values of the (two-tailed) Mann-Whitney U distribution, based on Zar (1999) and sources therein.
Zar, JH (1999) Biostatistical Analysis 4th edition. Prentice-Hall, New Jersey.