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Table 6 : PERCENTAGE POINTS OF THE
χ
2
DISTRIBUTION
Table 6 gives the value of
χ
2
α,ν
with the respective value of
α
and
ν
(degrees of freedom) where
χ
α,ν
2
0
α
α
=
1
2
k/
2
Γ(
k/
2)
∞
χ
2
α,ν
x
(
k/
2)
−
1
exp(
−
x/
2)
dx
α
0.005 0.010 0.025 0.050 0.10 0.25 0.50 0.70 0.90 0.95 0.975 0.99 0.995
ν
= 1
7.8794 6.6349 5.0239 3.8415 2.7055 1.3233 0.4549 0.1485 0.0158 0.0039 0.0010 0.0002 0.0000
2
10.5966 9.2103 7.3778 5.9915 4.6052 2.7726 1.3863 0.7133 0.2107 0.1026 0.0506 0.0201 0.0100
3
12.8382 11.3449 9.3484 7.8147 6.2514 4.1083 2.3660 1.4237 0.5844 0.3518 0.2158 0.1148 0.0717
4
14.8603 13.2767 11.1433 9.4877 7.7794 5.3853 3.3567 2.1947 1.0636 0.7107 0.4844 0.2971 0.2070
5
16.7496 15.0863 12.8325 11.0705 9.2364 6.6257 4.3515 2.9999 1.6103 1.1455 0.8312 0.5543 0.4117
6
18.5476 16.8119 14.4494 12.5916 10.6446 7.8408 5.3481 3.8276 2.2041 1.6354 1.2373 0.8721 0.6757
7
20.2777 18.4753 16.0128 14.0671 12.0170 9.0371 6.3458 4.6713 2.8331 2.1673 1.6899 1.2390 0.9893
8
21.9550 20.0902 17.5345 15.5073 13.3616 10.2189 7.3441 5.5274 3.4895 2.7326 2.1797 1.6465 1.3444
9
23.5894 21.6660 19.0228 16.9190 14.6837 11.3888 8.3428 6.3933 4.1682 3.3251 2.7004 2.0879 1.7349
10
25.1882 23.2093 20.4832 18.3070 15.9872 12.5489 9.3418 7.2672 4.8652 3.9403 3.2470 2.5582 2.1559
11
26.7568 24.7250 21.9200 19.6751 17.2750 13.7007 10.3410 8.1479 5.5778 4.5748 3.8157 3.0535 2.6032
12
28.2995 26.2170 23.3367 21.0261 18.5493 14.8454 11.3403 9.0343 6.3038 5.2260 4.4038 3.5706 3.0738
13
29.8195 27.6882 24.7356 22.3620 19.8119 15.9839 12.3398 9.9257 7.0415 5.8919 5.0088 4.1069 3.5650
14
31.3193 29.1412 26.1189 23.6848 21.0641 17.1169 13.3393 10.8215 7.7895 6.5706 5.6287 4.6604 4.0747
15
32.8013 30.5779 27.4884 24.9958 22.3071 18.2451 14.3389 11.7212 8.5468 7.2609 6.2621 5.2293 4.6009
16
34.2672 31.9999 28.8454 26.2962 23.5418 19.3689 15.3385 12.6243 9.3122 7.9616 6.9077 5.8122 5.1422
17
35.7185 33.4087 30.1910 27.5871 24.7690 20.4887 16.3382 13.5307 10.0852 8.6718 7.5642 6.4078 5.6972
18
37.1565 34.8053 31.5264 28.8693 25.9894 21.6049 17.3379 14.4399 10.8649 9.3905 8.2307 7.0149 6.2648
19
38.5823 36.1909 32.8523 30.1435 27.2036 22.7178 18.3377 15.3517 11.6509 10.1170 8.9065 7.6327 6.8440
20
39.9968 37.5662 34.1696 31.4104 28.4120 23.8277 19.3374 16.2659 12.4426 10.8508 9.5908 8.2604 7.4338
21
41.4011 38.9322 35.4789 32.6706 29.6151 24.9348 20.3372 17.1823 13.2396 11.5913 10.2829 8.8972 8.0337
22
42.7957 40.2894 36.7807 33.9244 30.8133 26.0393 21.3370 18.1007 14.0415 12.3380 10.9823 9.5425 8.6427
23
44.1813 41.6384 38.0756 35.1725 32.0069 27.1413 22.3369 19.0211 14.8480 13.0905 11.6886 10.1957 9.2604
24
45.5585 42.9798 39.3641 36.4150 33.1962 28.2412 23.3367 19.9432 15.6587 13.8484 12.4012 10.8564 9.8862
25
46.9279 44.3141 40.6465 37.6525 34.3816 29.3389 24.3366 20.8670 16.4734 14.6114 13.1197 11.5240 10.5197
38