Ivo Dinov
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Wilcoxon Rank-Sum Table


Suppose the observed Wilcoxon-Mann-Whitney (WMW) test-statistics Uobs is the smaller of the two calculated rank-sum values (U1 and U2). If Uobs < Ucritical, which is reported in the table below for different combinations of sample-sizes (N1 and N2) and false-positive rates (α), then we would reject the null hypothesis Ho of no group differences bwtween the two samples. For sample sizes (N1 & N2) larger than 20 use Normal Approximation and the Standard Normal Table to calculate critical values. You can also use the diverse SOCR Distirbutions and SOCR Analyses applets to compute accurate estimates of critical-values and p-values. See detailed description and examples on the SOCR SMHS EBook site.
N1 N2 α =0.0005 0.0025 0.005 0.05 0.1
4 4 0 0 0 1 5
4 5 0 0 0 2 6
4 6 0 0 0 3 8
4 7 0 0 0 4 9
4 8 0 0 1 5 11
4 9 0 0 1 6 12
4 10 0 1 2 7 14
4 11 0 1 2 8 16
4 12 0 2 3 9 17
4 13 0 2 3 10 19
4 14 0 3 4 11 20
4 15 0 3 5 12 22
4 16 1 4 5 14 24
4 17 1 4 6 15 25
4 18 1 5 6 16 27
4 19 2 5 7 17 28
4 20 2 5 8 18 30
5 4 0 0 0 2 6
5 5 0 0 0 4 8
5 6 0 0 1 5 10
5 7 0 0 1 6 12
5 8 0 1 2 8 14
5 9 0 2 3 9 16
5 10 0 3 4 11 18
5 11 1 3 5 12 20
5 12 1 4 6 13 22
5 13 2 5 7 15 24
5 14 2 6 7 16 27
5 15 3 6 8 18 29
5 16 3 7 9 19 31
5 17 4 8 10 20 33
5 18 4 9 11 22 35
5 19 5 9 12 23 37
5 20 5 10 13 25 39
6 4 0 0 0 3 8
6 5 0 0 1 5 10
6 6 0 1 2 7 13
6 7 0 2 3 8 15
6 8 0 3 4 10 18
6 9 1 4 5 12 20
6 10 2 5 6 14 23
6 11 2 6 7 16 25
6 12 3 7 9 17 28
6 13 4 8 10 19 30
6 14 5 9 11 21 33
6 15 5 10 12 23 35
6 16 6 11 13 25 38
6 17 7 12 15 26 40
6 18 8 13 16 28 43
6 19 8 14 17 30 45
6 20 9 15 18 32 48
7 4 0 0 0 4 9
7 5 0 0 1 6 12
7 6 0 2 3 8 15
7 7 0 3 4 11 18
7 8 1 4 6 13 21
7 9 2 5 7 15 24
7 10 3 7 9 17 27
7 11 4 8 10 19 30
7 12 5 9 12 21 33
7 13 6 11 13 24 36
7 14 7 12 15 26 39
7 15 8 13 16 28 42
7 16 9 15 18 30 45
7 17 10 16 19 33 48
7 18 11 18 21 35 51
7 19 13 19 22 37 54
7 20 14 20 24 39 57
8 4 0 0 1 5 11
8 5 0 1 2 8 14
8 6 0 3 4 10 18
8 7 1 4 6 13 21
8 8 2 6 7 15 24
8 9 4 7 9 18 28
8 10 5 9 11 20 31
8 11 6 11 13 23 35
8 12 7 12 15 26 38
8 13 9 14 17 28 41
8 14 10 16 18 31 45
8 15 11 17 20 33 48
8 16 13 19 22 36 52
8 17 14 21 24 39 55
8 18 15 22 26 41 59
8 19 17 24 28 44 62
8 20 18 26 30 47 65
9 4 0 0 1 6 12
9 5 0 2 3 9 16
9 6 1 4 5 12 20
9 7 2 5 7 15 24
9 8 4 7 9 18 28
9 9 5 9 11 21 32
9 10 7 11 13 24 36
9 11 8 13 16 27 39
9 12 10 15 18 30 43
9 13 11 17 20 33 47
9 14 13 19 22 36 51
9 15 15 21 24 39 55
9 16 16 23 27 42 59
9 17 18 25 29 45 63
9 18 20 27 31 48 67
9 19 21 29 33 51 71
9 20 23 31 36 54 74
10 4 0 1 2 7 14
10 5 0 3 4 11 18
10 6 2 5 6 14 23
10 7 3 7 9 17 27
10 8 5 9 11 20 31
10 9 7 11 13 24 36
10 10 8 13 16 27 40
10 11 10 16 18 31 44
10 12 12 18 21 34 49
10 13 14 20 24 37 53
10 14 16 23 26 41 57
10 15 18 25 29 44 62
10 16 20 27 31 48 66
10 17 22 30 34 51 70
10 18 24 32 37 55 75
10 19 26 35 39 58 79
10 20 28 37 42 62 83
11 4 0 1 2 8 16
11 5 1 3 5 12 20
11 6 2 6 7 16 25
11 7 4 8 10 19 30
11 8 6 11 13 23 35
11 9 8 13 16 27 39
11 10 10 16 18 31 44
11 11 12 18 21 34 49
11 12 15 21 24 38 54
11 13 17 24 27 42 59
11 14 19 26 30 46 63
11 15 21 29 33 50 68
11 16 24 32 36 54 73
11 17 26 35 39 57 78
11 18 28 37 42 61 83
11 19 31 40 45 65 88
11 20 33 43 48 69 92
12 4 0 2 3 9 17
12 5 1 4 6 13 22
12 6 3 7 9 17 28
12 7 5 9 12 21 33
12 8 7 12 15 26 38
12 9 10 15 18 30 43
12 10 12 18 21 34 49
12 11 15 21 24 38 54
12 12 17 24 27 42 59
12 13 20 27 31 47 64
12 14 22 30 34 51 70
12 15 25 33 37 55 75
12 16 27 36 41 60 80
12 17 30 39 44 64 86
12 18 33 43 47 68 91
12 19 35 46 51 72 96
12 20 38 49 54 77 101
13 4 0 2 3 10 19
13 5 2 5 7 15 24
13 6 4 8 10 19 30
13 7 6 11 13 24 36
13 8 9 14 17 28 41
13 9 11 17 20 33 47
13 10 14 20 24 37 53
13 11 17 24 27 42 59
13 12 20 27 31 47 64
13 13 23 30 34 51 70
13 14 25 34 38 56 76
13 15 28 37 42 61 82
13 16 31 41 45 65 87
13 17 34 44 49 70 93
13 18 37 48 53 75 99
13 19 40 51 57 80 105
13 20 43 55 60 84 110
14 4 0 3 4 11 20
14 5 2 6 7 16 27
14 6 5 9 11 21 33
14 7 7 12 15 26 39
14 8 10 16 18 31 45
14 9 13 19 22 36 51
14 10 16 23 26 41 57
14 11 19 26 30 46 63
14 12 22 30 34 51 70
14 13 25 34 38 56 76
14 14 29 38 42 61 82
14 15 32 41 46 66 88
14 16 35 45 50 71 95
14 17 39 49 54 77 101
14 18 42 53 58 82 107
14 19 45 57 63 87 113
14 20 49 61 67 92 119
15 4 0 3 5 12 22
15 5 3 6 8 18 29
15 6 5 10 12 23 35
15 7 8 13 16 28 42
15 8 11 17 20 33 48
15 9 15 21 24 39 55
15 10 18 25 29 44 62
15 11 21 29 33 50 68
15 12 25 33 37 55 75
15 13 28 37 42 61 82
15 14 32 41 46 66 88
15 15 36 46 51 72 95
15 16 39 50 55 77 102
15 17 43 54 60 83 108
15 18 46 58 64 88 115
15 19 50 62 69 94 122
15 20 54 67 73 100 129
16 4 1 4 5 14 24
16 5 3 7 9 19 31
16 6 6 11 13 25 38
16 7 9 15 18 30 45
16 8 13 19 22 36 52
16 9 16 23 27 42 59
16 10 20 27 31 48 66
16 11 24 32 36 54 73
16 12 27 36 41 60 80
16 13 31 41 45 65 87
16 14 35 45 50 71 95
16 15 39 50 55 77 102
16 16 43 54 60 83 109
16 17 47 59 65 89 116
16 18 51 64 70 95 123
16 19 55 68 74 101 130
16 20 59 73 79 107 138
17 4 1 4 6 15 25
17 5 4 8 10 20 33
17 6 7 12 15 26 40
17 7 10 16 19 33 48
17 8 14 21 24 39 55
17 9 18 25 29 45 63
17 10 22 30 34 51 70
17 11 26 35 39 57 78
17 12 30 39 44 64 86
17 13 34 44 49 70 93
17 14 39 49 54 77 101
17 15 43 54 60 83 108
17 16 47 59 65 89 116
17 17 51 64 70 96 124
17 18 56 69 75 102 131
17 19 60 74 81 109 139
17 20 65 79 86 115 147
18 4 1 5 6 16 27
18 5 4 9 11 22 35
18 6 8 13 16 28 43
18 7 11 18 21 35 51
18 8 15 22 26 41 59
18 9 20 27 31 48 67
18 10 24 32 37 55 75
18 11 28 37 42 61 83
18 12 33 43 47 68 91
18 13 37 48 53 75 99
18 14 42 53 58 82 107
18 15 46 58 64 88 115
18 16 51 64 70 95 123
18 17 56 69 75 102 131
18 18 61 74 81 109 139
18 19 65 80 87 116 148
18 20 70 85 92 123 156
19 4 2 5 7 17 28
19 5 5 9 12 23 37
19 6 8 14 17 30 45
19 7 13 19 22 37 54
19 8 17 24 28 44 62
19 9 21 29 33 51 71
19 10 26 35 39 58 79
19 11 31 40 45 65 88
19 12 35 46 51 72 96
19 13 40 51 57 80 105
19 14 45 57 63 87 113
19 15 50 62 69 94 122
19 16 55 68 74 101 130
19 17 60 74 81 109 139
19 18 65 80 87 116 148
19 19 70 85 93 123 156
19 20 76 91 99 130 165
20 4 2 5 8 18 30
20 5 5 10 13 25 39
20 6 9 15 18 32 48
20 7 14 20 24 39 57
20 8 18 26 30 47 65
20 9 23 31 36 54 74
20 10 28 37 42 62 83
20 11 33 43 48 69 92
20 12 38 49 54 77 101
20 13 43 55 60 84 110
20 14 49 61 67 92 119
20 15 54 67 73 100 129
20 16 59 73 79 107 138
20 17 65 79 86 115 147
20 18 70 85 92 123 156
20 19 76 91 99 130 165
20 20 81 97 105 138 174

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