|
| |
home
stats tables
| |
Critical Points of the Chi Square Distribution
|
| D. F. |
Cumulative probability |
|
0.005
|
0.010
|
0.025
|
0.05
|
0.10
|
0.25
|
0.50
|
0.75
|
0.90
|
0.95
|
0.975
|
0.99
|
0.995
|
| |
|
| 1
|
0.39E-4
|
0.00016
|
0.00098
|
0.0039
|
0.0158
|
0.102
|
0.455
|
1.32
|
2.71
|
3.84
|
5.02
|
6.63
|
7.88
|
| 2
|
0.0100
|
0.0201
|
0.0506
|
0.103
|
0.211
|
0.575
|
1.39
|
2.77
|
4.61
|
5.99
|
7.38
|
9.21
|
10.6
|
| 3
|
0.0717
|
0.115
|
0.216
|
0.352
|
0.584
|
1.21
|
2.37
|
4.11
|
6.25
|
7.81
|
9.35
|
11.3
|
12.8
|
| 4
|
0.207
|
0.297
|
0.484
|
0.711
|
1.06
|
1.92
|
3.36
|
5.39
|
7.78
|
9.49
|
11.1
|
13.3
|
14.9
|
| 5
|
0.412
|
0.554
|
0.831
|
1.15
|
1.61
|
2.67
|
4.35
|
6.63
|
9.24
|
11.1
|
12.8
|
15.1
|
16.7
|
| 6
|
0.676
|
0.872
|
1.24
|
1.64
|
2.20
|
3.45
|
5.35
|
7.84
|
10.6
|
12.6
|
14.4
|
16.8
|
18.5
|
| 7
|
0.989
|
1.24
|
1.69
|
2.17
|
2.83
|
4.25
|
6.35
|
9.04
|
12.0
|
14.1
|
16.0
|
18.5
|
20.3
|
| 8
|
1.34
|
1.65
|
2.18
|
2.73
|
3.49
|
5.07
|
7.34
|
10.2
|
13.4
|
15.5
|
17.5
|
20.1
|
22.0
|
| 9
|
1.73
|
2.09
|
2.70
|
3.33
|
4.17
|
5.9
|
8.34
|
11.4
|
14.7
|
16.9
|
19.0
|
21.7
|
23.6
|
| 10
|
2.16
|
2.56
|
3.25
|
3.94
|
4.87
|
6.74
|
9.34
|
12.5
|
16.0
|
18.3
|
20.5
|
23.2
|
25.2
|
| 11
|
2.60
|
3.05
|
3.82
|
4.57
|
5.58
|
7.58
|
10.3
|
13.7
|
17.3
|
19.7
|
21.9
|
24.7
|
26.8
|
| 12
|
3.07
|
3.57
|
4.40
|
5.23
|
6.30
|
8.44
|
11.3
|
14.8
|
18.5
|
21.0
|
23.3
|
26.2
|
28.3
|
| 13
|
3.57
|
4.11
|
5.01
|
5.89
|
7.04
|
9.3
|
12.3
|
16.0
|
19.8
|
22.4
|
24.7
|
27.7
|
29.8
|
| 14
|
4.07
|
4.66
|
5.63
|
6.57
|
7.79
|
10.2
|
13.3
|
17.1
|
21.1
|
23.7
|
26.1
|
29.1
|
31.3
|
| 15
|
4.60
|
5.23
|
6.26
|
7.26
|
8.55
|
11.0
|
14.3
|
18.2
|
22.3
|
25.0
|
27.5
|
30.6
|
32.8
|
| 16
|
5.14
|
5.81
|
6.91
|
7.96
|
9.31
|
11.9
|
15.3
|
19.4
|
23.5
|
26.3
|
28.8
|
32.0
|
34.3
|
| 17
|
5.70
|
6.41
|
7.56
|
8.67
|
10.1
|
12.8
|
16.3
|
20.5
|
24.8
|
27.6
|
30.2
|
33.4
|
35.7
|
| 18
|
6.26
|
7.01
|
8.23
|
9.39
|
10.9
|
13.7
|
17.3
|
21.6
|
26.0
|
28.9
|
31.5
|
34.8
|
37.2
|
| 19
|
6.84
|
7.63
|
8.91
|
10.1
|
11.7
|
14.6
|
18.3
|
22.7
|
27.2
|
30.1
|
32.9
|
36.2
|
38.6
|
| 20
|
7.43
|
8.26
|
9.59
|
10.9
|
12.4
|
15.5
|
19.3
|
23.8
|
28.4
|
31.4
|
34.2
|
37.6
|
40.0
|
| 21
|
8.03
|
8.90
|
10.3
|
11.6
|
13.2
|
16.3
|
20.3
|
24.9
|
29.6
|
32.7
|
35.5
|
38.9
|
41.4
|
| 22
|
8.64
|
9.54
|
11.0
|
12.3
|
14.0
|
17.2
|
21.3
|
26.0
|
30.8
|
33.9
|
36.8
|
40.3
|
42.8
|
| 23
|
9.26
|
10.2
|
11.7
|
13.1
|
14.8
|
18.1
|
22.3
|
27.1
|
32.0
|
35.2
|
38.1
|
41.6
|
44.2
|
| 24
|
9.89
|
10.9
|
12.4
|
13.8
|
15.7
|
19.0
|
23.3
|
28.2
|
33.2
|
36.4
|
39.4
|
43.0
|
45.6
|
| 25
|
10.5
|
11.5
|
13.1
|
14.6
|
16.5
|
19.9
|
24.3
|
29.3
|
34.4
|
37.7
|
40.6
|
44.3
|
46.9
|
| 26
|
11.2
|
12.2
|
13.8
|
15.4
|
17.3
|
20.8
|
25.3
|
30.4
|
35.6
|
38.9
|
41.9
|
45.6
|
48.3
|
| 27
|
11.8
|
12.9
|
14.6
|
16.2
|
18.1
|
21.7
|
26.3
|
31.5
|
36.7
|
40.1
|
43.2
|
47.0
|
49.6
|
| 28
|
12.5
|
13.6
|
15.3
|
16.9
|
18.9
|
22.7
|
27.3
|
32.6
|
37.9
|
41.3
|
44.5
|
48.3
|
51.0
|
| 29
|
13.1
|
14.3
|
16.0
|
17.7
|
19.8
|
23.6
|
28.3
|
33.7
|
39.1
|
42.6
|
45.7
|
49.6
|
52.3
|
| 30
|
13.8
|
15.0
|
16.8
|
18.5
|
20.6
|
24.5
|
29.3
|
34.8
|
40.3
|
43.8
|
47.0
|
50.9
|
53.7
|
| 31
|
14.5
|
15.7
|
17.5
|
19.3
|
21.4
|
25.4
|
30.3
|
35.9
|
41.4
|
45.0
|
48.2
|
52.2
|
55.0
|
| 32
|
15.1
|
16.4
|
18.3
|
20.1
|
22.3
|
26.3
|
31.3
|
37.0
|
42.6
|
46.2
|
49.5
|
53.5
|
56.3
|
| 33
|
15.8
|
17.1
|
19.0
|
20.9
|
23.1
|
27.2
|
32.3
|
38.1
|
43.7
|
47.4
|
50.7
|
54.8
|
57.6
|
| 34
|
16.5
|
17.8
|
19.8
|
21.7
|
24.0
|
28.1
|
33.3
|
39.1
|
44.9
|
48.6
|
52.0
|
56.1
|
59.0
|
| 35
|
17.2
|
18.5
|
20.6
|
22.5
|
24.8
|
29.1
|
34.3
|
40.2
|
46.1
|
49.8
|
53.2
|
57.3
|
60.3
|
| 36
|
17.9
|
19.2
|
21.3
|
23.3
|
25.6
|
30.0
|
35.3
|
41.3
|
47.2
|
51.0
|
54.4
|
58.6
|
61.6
|
| 37
|
18.6
|
20.0
|
22.1
|
24.1
|
26.5
|
30.9
|
36.3
|
42.4
|
48.4
|
52.2
|
55.7
|
59.9
|
62.9
|
| 38
|
19.3
|
20.7
|
22.9
|
24.9
|
27.3
|
31.8
|
37.3
|
43.5
|
49.5
|
53.4
|
56.9
|
61.2
|
64.2
|
| 39
|
20.0
|
21.4
|
23.7
|
25.7
|
28.2
|
32.7
|
38.3
|
44.5
|
50.7
|
54.6
|
58.1
|
62.4
|
65.5
|
| 40
|
20.7
|
22.2
|
24.4
|
26.5
|
29.1
|
33.7
|
39.3
|
45.6
|
51.8
|
55.8
|
59.3
|
63.7
|
66.8
|
| 41
|
21.4
|
22.9
|
25.2
|
27.3
|
29.9
|
34.6
|
40.3
|
46.7
|
52.9
|
56.9
|
60.6
|
65.0
|
68.1
|
| 42
|
22.1
|
23.7
|
26.0
|
28.1
|
30.8
|
35.5
|
41.3
|
47.8
|
54.1
|
58.1
|
61.8
|
66.2
|
69.3
|
| 43
|
22.9
|
24.4
|
26.8
|
29.0
|
31.6
|
36.4
|
42.3
|
48.8
|
55.2
|
59.3
|
63.0
|
67.5
|
70.6
|
| 44
|
23.6
|
25.1
|
27.6
|
29.8
|
32.5
|
37.4
|
43.3
|
49.9
|
56.4
|
60.5
|
64.2
|
68.7
|
71.9
|
| 45
|
24.3
|
25.9
|
28.4
|
30.6
|
33.4
|
38.3
|
44.3
|
51.0
|
57.5
|
61.7
|
65.4
|
70.0
|
73.2
|
|
| |
0.005
|
0.010
|
0.025
|
0.05
|
0.10
|
0.25
|
0.50
|
0.75
|
0.90
|
0.95
|
0.975
|
0.99
|
0.995
|
| D. F. |
Cumulative Probability |
This public table is in the public domain. It was
produced using APL programs written by the author,
William Knight / Univ. of New
Brunswick / Canada |
|