July 16, 2014
Z03_HOGG2358_09_GE_APP02
page 501
Table IV The Chi-Square Distribution
0.10
0.10
χ2(8)
χ2(8)
0.05
0.05
α
0
2
4
6
8
10
12 x14
16
P(X ≤ x) =
18
x
0
20
0
1
(r/2)2r/2
2
4
6
8
10
χ2α(8)
16
18
20
wr/2−1 e−w/2 dw
P(X ≤ x)
0.010
0.025
0.050
0.100
0.900
0.950
0.975
0.990
r
2 (r)
χ0.99
2
χ0.975
(r)
2 (r)
χ0.95
2 (r)
χ0.90
2 (r)
χ0.10
2 (r)
χ0.05
2
χ0.025
(r)
2 (r)
χ0.01
1
2
3
4
5
0.000
0.020
0.115
0.297
0.554
0.001
0.051
0.216
0.484
0.831
0.004
0.103
0.352
0.711
1.145
0.016
0.211
0.584
1.064
1.610
2.706
4.605
6.251
7.779
9.236
3.841
5.991
7.815
9.488
11.07
5.024
7.378
9.348
11.14
12.83
6.635
9.210
11.34
13.28
15.09
6
7
8
9
10
0.872
1.239
1.646
2.088
2.558
1.237
1.690
2.180
2.700
3.247
1.635
2.167
2.733
3.325
3.940
2.204
2.833
3.490
4.168
4.865
10.64
12.02
13.36
14.68
15.99
12.59
14.07
15.51
16.92
18.31
14.45
16.01
17.54
19.02
20.48
16.81
18.48
20.09
21.67
23.21
11
12
13
14
15
3.053
3.571
4.107
4.660
5.229
3.816
4.404
5.009
5.629
6.262
4.575
5.226
5.892
6.571
7.261
5.578
6.304
7.042
7.790
8.547
17.28
18.55
19.81
21.06
22.31
19.68
21.03
22.36
23.68
25.00
21.92
23.34
24.74
26.12
27.49
24.72
26.22
27.69
29.14
30.58
16
17
18
19
20
5.812
6.408
7.015
7.633
8.260
6.908
7.564
8.231
8.907
9.591
7.962
8.672
9.390
10.12
10.85
9.312
10.08
10.86
11.65
12.44
23.54
24.77
25.99
27.20
28.41
26.30
27.59
28.87
30.14
31.41
28.84
30.19
31.53
32.85
34.17
32.00
33.41
34.80
36.19
37.57
21
22
23
24
25
8.897
9.542
10.20
10.86
11.52
10.28
10.98
11.69
12.40
13.12
11.59
12.34
13.09
13.85
14.61
13.24
14.04
14.85
15.66
16.47
29.62
30.81
32.01
33.20
34.38
32.67
33.92
35.17
36.42
37.65
35.48
36.78
38.08
39.36
40.65
38.93
40.29
41.64
42.98
44.31
26
27
28
29
30
12.20
12.88
13.56
14.26
14.95
13.84
14.57
15.31
16.05
16.79
15.38
16.15
16.93
17.71
18.49
17.29
18.11
18.94
19.77
20.60
35.56
36.74
37.92
39.09
40.26
38.88
40.11
41.34
42.56
43.77
41.92
43.19
44.46
45.72
46.98
45.64
46.96
48.28
49.59
50.89
40
50
60
70
80
22.16
29.71
37.48
45.44
53.34
24.43
32.36
40.48
48.76
57.15
26.51
34.76
43.19
51.74
60.39
29.05
37.69
46.46
55.33
64.28
51.80
63.17
74.40
85.53
96.58
55.76
67.50
79.08
90.53
101.9
59.34
71.42
83.30
95.02
106.6
63.69
76.15
88.38
100.4
112.3
This table is abridged and adapted from Table III in Biometrika Tables for Statisticians, edited by E.S.Pearson and H.O.Hartley.