For a bivariate sample of size $N$ let $K$ be the number of pairs of observations where the first member of the pair has both $X$ and $Y$ values larger than the second member of the pair. The table entry gives the smallest integer $k$ for which $P [K \leq k]$ is less than or equal to one minus the cumulative distribution as specified. Equivalently the table entry is the corresponding critical value. Kendall's rank correlation coefficient is $(4\cdot K/(N \cdot (N - 1))) - 1$.
Table 1: Critical values for Kendall's rank correlation coefficient.
  Cumulative distribution
  .7 .75 .80 .85 .90 .95 .99 .975 .995 .999
  Significance level
$N$ .3 .25 .20 .15 .10 .05 .01 .025 .005 .001
3 3 3 3 -- -- -- -- -- -- --
4 5 5 5 6 6 6 -- -- -- --
5 7 7 8 8 9 9 10 10 -- --
6 10 10 11 11 12 13 14 14 15 --
7 13 14 14 15 16 17 18 19 20 21
8 17 18 18 19 20 22 23 24 25 26
9 22 22 23 24 25 27 28 30 31 33
10 27 27 28 29 31 33 34 36 37 40
11 32 33 34 35 37 39 41 43 44 47
12 38 39 40 42 43 46 48 51 52 55
13 44 46 47 49 51 53 56 59 61 64
14 51 53 54 56 58 62 64 67 69 73
15 59 60 62 64 67 70 73 77 79 83
16 67 69 70 73 75 79 83 86 89 94
17 75 77 79 82 85 89 93 97 100 105
18 85 87 89 91 95 99 103 108 111 117
19 94 96 99 101 105 110 114 119 123 129
20 104 107 109 112 116 121 126 131 135 142
21 115 117 120 123 127 133 138 144 148 156
22 126 129 132 135 139 146 151 157 161 170
23 138 140 144 147 152 159 164 171 176 184
24 150 153 156 160 165 172 178 185 190 200
25 162 166 169 173 179 186 193 200 205 216