For a bivariate sample of size
![$N$](img1.png)
let
![$K$](img2.png)
be the number of pairs of observations where the first member of the pair has both
![$X$](img3.png)
and
![$Y$](img4.png)
values larger than the second member of the pair. The table entry gives the smallest integer
![$k$](img5.png)
for which
![$P [K \leq k]$](img6.png)
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
![$(4\cdot K/(N \cdot (N - 1))) - 1$](img7.png)
.
Table 1:
Critical values for Kendall's rank correlation coefficient.
|
Cumulative distribution |
|
.7 |
.75 |
.80 |
.85 |
.90 |
.95 |
.99 |
.975 |
.995 |
.999 |
|
Significance level |
![$N$](img1.png) |
.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 |