Chi-square distribution table
P | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
DF | 0.995 | 0.975 | 0.20 | 0.10 | 0.05 | 0.025 | 0.02 | 0.01 | 0.005 | 0.002 | 0.001 |
1 | 0.0000393 | 0.000982 | 1.642 | 2.706 | 3.841 | 5.024 | 5.412 | 6.635 | 7.879 | 9.550 | 10.828 |
2 | 0.0100 | 0.0506 | 3.219 | 4.605 | 5.991 | 7.378 | 7.824 | 9.210 | 10.597 | 12.429 | 13.816 |
3 | 0.0717 | 0.216 | 4.642 | 6.251 | 7.815 | 9.348 | 9.837 | 11.345 | 12.838 | 14.796 | 16.266 |
4 | 0.207 | 0.484 | 5.989 | 7.779 | 9.488 | 11.143 | 11.668 | 13.277 | 14.860 | 16.924 | 18.467 |
5 | 0.412 | 0.831 | 7.289 | 9.236 | 11.070 | 12.833 | 13.388 | 15.086 | 16.750 | 18.907 | 20.515 |
6 | 0.676 | 1.237 | 8.558 | 10.645 | 12.592 | 14.449 | 15.033 | 16.812 | 18.548 | 20.791 | 22.458 |
7 | 0.989 | 1.690 | 9.803 | 12.017 | 14.067 | 16.013 | 16.622 | 18.475 | 20.278 | 22.601 | 24.322 |
8 | 1.344 | 2.180 | 11.030 | 13.362 | 15.507 | 17.535 | 18.168 | 20.090 | 21.955 | 24.352 | 26.124 |
9 | 1.735 | 2.700 | 12.242 | 14.684 | 16.919 | 19.023 | 19.679 | 21.666 | 23.589 | 26.056 | 27.877 |
10 | 2.156 | 3.247 | 13.442 | 15.987 | 18.307 | 20.483 | 21.161 | 23.209 | 25.188 | 27.722 | 29.588 |
11 | 2.603 | 3.816 | 14.631 | 17.275 | 19.675 | 21.920 | 22.618 | 24.725 | 26.757 | 29.354 | 31.264 |
12 | 3.074 | 4.404 | 15.812 | 18.549 | 21.026 | 23.337 | 24.054 | 26.217 | 28.300 | 30.957 | 32.909 |
13 | 3.565 | 5.009 | 16.985 | 19.812 | 22.362 | 24.736 | 25.472 | 27.688 | 29.819 | 32.535 | 34.528 |
14 | 4.075 | 5.629 | 18.151 | 21.064 | 23.685 | 26.119 | 26.873 | 29.141 | 31.319 | 34.091 | 36.123 |
15 | 4.601 | 6.262 | 19.311 | 22.307 | 24.996 | 27.488 | 28.259 | 30.578 | 32.801 | 35.628 | 37.697 |
16 | 5.142 | 6.908 | 20.465 | 23.542 | 26.296 | 28.845 | 29.633 | 32.000 | 34.267 | 37.146 | 39.252 |
17 | 5.697 | 7.564 | 21.615 | 24.769 | 27.587 | 30.191 | 30.995 | 33.409 | 35.718 | 38.648 | 40.790 |
18 | 6.265 | 8.231 | 22.760 | 25.989 | 28.869 | 31.526 | 32.346 | 34.805 | 37.156 | 40.136 | 42.312 |
19 | 6.844 | 8.907 | 23.900 | 27.204 | 30.144 | 32.852 | 33.687 | 36.191 | 38.582 | 41.610 | 43.820 |
20 | 7.434 | 9.591 | 25.038 | 28.412 | 31.410 | 34.170 | 35.020 | 37.566 | 39.997 | 43.072 | 45.315 |
21 | 8.034 | 10.283 | 26.171 | 29.615 | 32.671 | 35.479 | 36.343 | 38.932 | 41.401 | 44.522 | 46.797 |
22 | 8.643 | 10.982 | 27.301 | 30.813 | 33.924 | 36.781 | 37.659 | 40.289 | 42.796 | 45.962 | 48.268 |
23 | 9.260 | 11.689 | 28.429 | 32.007 | 35.172 | 38.076 | 38.968 | 41.638 | 44.181 | 47.391 | 49.728 |
24 | 9.886 | 12.401 | 29.553 | 33.196 | 36.415 | 39.364 | 40.270 | 42.980 | 45.559 | 48.812 | 51.179 |
25 | 10.520 | 13.120 | 30.675 | 34.382 | 37.652 | 40.646 | 41.566 | 44.314 | 46.928 | 50.223 | 52.620 |
26 | 11.160 | 13.844 | 31.795 | 35.563 | 38.885 | 41.923 | 42.856 | 45.642 | 48.290 | 51.627 | 54.052 |
27 | 11.808 | 14.573 | 32.912 | 36.741 | 40.113 | 43.195 | 44.140 | 46.963 | 49.645 | 53.023 | 55.476 |
28 | 12.461 | 15.308 | 34.027 | 37.916 | 41.337 | 44.461 | 45.419 | 48.278 | 50.993 | 54.411 | 56.892 |
29 | 13.121 | 16.047 | 35.139 | 39.087 | 42.557 | 45.722 | 46.693 | 49.588 | 52.336 | 55.792 | 58.301 |
30 | 13.787 | 16.791 | 36.250 | 40.256 | 43.773 | 46.979 | 47.962 | 50.892 | 53.672 | 57.167 | 59.703 |
31 | 14.458 | 17.539 | 37.359 | 41.422 | 44.985 | 48.232 | 49.226 | 52.191 | 55.003 | 58.536 | 61.098 |
32 | 15.134 | 18.291 | 38.466 | 42.585 | 46.194 | 49.480 | 50.487 | 53.486 | 56.328 | 59.899 | 62.487 |
33 | 15.815 | 19.047 | 39.572 | 43.745 | 47.400 | 50.725 | 51.743 | 54.776 | 57.648 | 61.256 | 63.870 |
34 | 16.501 | 19.806 | 40.676 | 44.903 | 48.602 | 51.966 | 52.995 | 56.061 | 58.964 | 62.608 | 65.247 |
35 | 17.192 | 20.569 | 41.778 | 46.059 | 49.802 | 53.203 | 54.244 | 57.342 | 60.275 | 63.955 | 66.619 |
36 | 17.887 | 21.336 | 42.879 | 47.212 | 50.998 | 54.437 | 55.489 | 58.619 | 61.581 | 65.296 | 67.985 |
37 | 18.586 | 22.106 | 43.978 | 48.363 | 52.192 | 55.668 | 56.730 | 59.893 | 62.883 | 66.633 | 69.346 |
38 | 19.289 | 22.878 | 45.076 | 49.513 | 53.384 | 56.896 | 57.969 | 61.162 | 64.181 | 67.966 | 70.703 |
39 | 19.996 | 23.654 | 46.173 | 50.660 | 54.572 | 58.120 | 59.204 | 62.428 | 65.476 | 69.294 | 72.055 |
40 | 20.707 | 24.433 | 47.269 | 51.805 | 55.758 | 59.342 | 60.436 | 63.691 | 66.766 | 70.618 | 73.402 |
41 | 21.421 | 25.215 | 48.363 | 52.949 | 56.942 | 60.561 | 61.665 | 64.950 | 68.053 | 71.938 | 74.745 |
42 | 22.138 | 25.999 | 49.456 | 54.090 | 58.124 | 61.777 | 62.892 | 66.206 | 69.336 | 73.254 | 76.084 |
43 | 22.859 | 26.785 | 50.548 | 55.230 | 59.304 | 62.990 | 64.116 | 67.459 | 70.616 | 74.566 | 77.419 |
44 | 23.584 | 27.575 | 51.639 | 56.369 | 60.481 | 64.201 | 65.337 | 68.710 | 71.893 | 75.874 | 78.750 |
45 | 24.311 | 28.366 | 52.729 | 57.505 | 61.656 | 65.410 | 66.555 | 69.957 | 73.166 | 77.179 | 80.077 |
46 | 25.041 | 29.160 | 53.818 | 58.641 | 62.830 | 66.617 | 67.771 | 71.201 | 74.437 | 78.481 | 81.400 |
47 | 25.775 | 29.956 | 54.906 | 59.774 | 64.001 | 67.821 | 68.985 | 72.443 | 75.704 | 79.780 | 82.720 |
48 | 26.511 | 30.755 | 55.993 | 60.907 | 65.171 | 69.023 | 70.197 | 73.683 | 76.969 | 81.075 | 84.037 |
49 | 27.249 | 31.555 | 57.079 | 62.038 | 66.339 | 70.222 | 71.406 | 74.919 | 78.231 | 82.367 | 85.351 |
50 | 27.991 | 32.357 | 58.164 | 63.167 | 67.505 | 71.420 | 72.613 | 76.154 | 79.490 | 83.657 | 86.661 |
51 | 28.735 | 33.162 | 59.248 | 64.295 | 68.669 | 72.616 | 73.818 | 77.386 | 80.747 | 84.943 | 87.968 |
52 | 29.481 | 33.968 | 60.332 | 65.422 | 69.832 | 73.810 | 75.021 | 78.616 | 82.001 | 86.227 | 89.272 |
53 | 30.230 | 34.776 | 61.414 | 66.548 | 70.993 | 75.002 | 76.223 | 79.843 | 83.253 | 87.507 | 90.573 |
54 | 30.981 | 35.586 | 62.496 | 67.673 | 72.153 | 76.192 | 77.422 | 81.069 | 84.502 | 88.786 | 91.872 |
55 | 31.735 | 36.398 | 63.577 | 68.796 | 73.311 | 77.380 | 78.619 | 82.292 | 85.749 | 90.061 | 93.168 |
56 | 32.490 | 37.212 | 64.658 | 69.919 | 74.468 | 78.567 | 79.815 | 83.513 | 86.994 | 91.335 | 94.461 |
57 | 33.248 | 38.027 | 65.737 | 71.040 | 75.624 | 79.752 | 81.009 | 84.733 | 88.236 | 92.605 | 95.751 |
58 | 34.008 | 38.844 | 66.816 | 72.160 | 76.778 | 80.936 | 82.201 | 85.950 | 89.477 | 93.874 | 97.039 |
59 | 34.770 | 39.662 | 67.894 | 73.279 | 77.931 | 82.117 | 83.391 | 87.166 | 90.715 | 95.140 | 98.324 |
60 | 35.534 | 40.482 | 68.972 | 74.397 | 79.082 | 83.298 | 84.580 | 88.379 | 91.952 | 96.404 | 99.607 |
61 | 36.301 | 41.303 | 70.049 | 75.514 | 80.232 | 84.476 | 85.767 | 89.591 | 93.186 | 97.665 | 100.888 |
62 | 37.068 | 42.126 | 71.125 | 76.630 | 81.381 | 85.654 | 86.953 | 90.802 | 94.419 | 98.925 | 102.166 |
63 | 37.838 | 42.950 | 72.201 | 77.745 | 82.529 | 86.830 | 88.137 | 92.010 | 95.649 | 100.182 | 103.442 |
64 | 38.610 | 43.776 | 73.276 | 78.860 | 83.675 | 88.004 | 89.320 | 93.217 | 96.878 | 101.437 | 104.716 |
65 | 39.383 | 44.603 | 74.351 | 79.973 | 84.821 | 89.177 | 90.501 | 94.422 | 98.105 | 102.691 | 105.988 |
66 | 40.158 | 45.431 | 75.424 | 81.085 | 85.965 | 90.349 | 91.681 | 95.626 | 99.330 | 103.942 | 107.258 |
67 | 40.935 | 46.261 | 76.498 | 82.197 | 87.108 | 91.519 | 92.860 | 96.828 | 100.554 | 105.192 | 108.526 |
68 | 41.713 | 47.092 | 77.571 | 83.308 | 88.250 | 92.689 | 94.037 | 98.028 | 101.776 | 106.440 | 109.791 |
69 | 42.494 | 47.924 | 78.643 | 84.418 | 89.391 | 93.856 | 95.213 | 99.228 | 102.996 | 107.685 | 111.055 |
70 | 43.275 | 48.758 | 79.715 | 85.527 | 90.531 | 95.023 | 96.388 | 100.425 | 104.215 | 108.929 | 112.317 |
71 | 44.058 | 49.592 | 80.786 | 86.635 | 91.670 | 96.189 | 97.561 | 101.621 | 105.432 | 110.172 | 113.577 |
72 | 44.843 | 50.428 | 81.857 | 87.743 | 92.808 | 97.353 | 98.733 | 102.816 | 106.648 | 111.412 | 114.835 |
73 | 45.629 | 51.265 | 82.927 | 88.850 | 93.945 | 98.516 | 99.904 | 104.010 | 107.862 | 112.651 | 116.092 |
74 | 46.417 | 52.103 | 83.997 | 89.956 | 95.081 | 99.678 | 101.074 | 105.202 | 109.074 | 113.889 | 117.346 |
75 | 47.206 | 52.942 | 85.066 | 91.061 | 96.217 | 100.839 | 102.243 | 106.393 | 110.286 | 115.125 | 118.599 |
76 | 47.997 | 53.782 | 86.135 | 92.166 | 97.351 | 101.999 | 103.410 | 107.583 | 111.495 | 116.359 | 119.850 |
77 | 48.788 | 54.623 | 87.203 | 93.270 | 98.484 | 103.158 | 104.576 | 108.771 | 112.704 | 117.591 | 121.100 |
78 | 49.582 | 55.466 | 88.271 | 94.374 | 99.617 | 104.316 | 105.742 | 109.958 | 113.911 | 118.823 | 122.348 |
79 | 50.376 | 56.309 | 89.338 | 95.476 | 100.749 | 105.473 | 106.906 | 111.144 | 115.117 | 120.052 | 123.594 |
80 | 51.172 | 57.153 | 90.405 | 96.578 | 101.879 | 106.629 | 108.069 | 112.329 | 116.321 | 121.280 | 124.839 |
81 | 51.969 | 57.998 | 91.472 | 97.680 | 103.010 | 107.783 | 109.232 | 113.512 | 117.524 | 122.507 | 126.083 |
82 | 52.767 | 58.845 | 92.538 | 98.780 | 104.139 | 108.937 | 110.393 | 114.695 | 118.726 | 123.733 | 127.324 |
83 | 53.567 | 59.692 | 93.604 | 99.880 | 105.267 | 110.090 | 111.553 | 115.876 | 119.927 | 124.957 | 128.565 |
84 | 54.368 | 60.540 | 94.669 | 100.980 | 106.395 | 111.242 | 112.712 | 117.057 | 121.126 | 126.179 | 129.804 |
85 | 55.170 | 61.389 | 95.734 | 102.079 | 107.522 | 112.393 | 113.871 | 118.236 | 122.325 | 127.401 | 131.041 |
86 | 55.973 | 62.239 | 96.799 | 103.177 | 108.648 | 113.544 | 115.028 | 119.414 | 123.522 | 128.621 | 132.277 |
87 | 56.777 | 63.089 | 97.863 | 104.275 | 109.773 | 114.693 | 116.184 | 120.591 | 124.718 | 129.840 | 133.512 |
88 | 57.582 | 63.941 | 98.927 | 105.372 | 110.898 | 115.841 | 117.340 | 121.767 | 125.913 | 131.057 | 134.745 |
89 | 58.389 | 64.793 | 99.991 | 106.469 | 112.022 | 116.989 | 118.495 | 122.942 | 127.106 | 132.273 | 135.978 |
90 | 59.196 | 65.647 | 101.054 | 107.565 | 113.145 | 118.136 | 119.648 | 124.116 | 128.299 | 133.489 | 137.208 |
91 | 60.005 | 66.501 | 102.117 | 108.661 | 114.268 | 119.282 | 120.801 | 125.289 | 129.491 | 134.702 | 138.438 |
92 | 60.815 | 67.356 | 103.179 | 109.756 | 115.390 | 120.427 | 121.954 | 126.462 | 130.681 | 135.915 | 139.666 |
93 | 61.625 | 68.211 | 104.241 | 110.850 | 116.511 | 121.571 | 123.105 | 127.633 | 131.871 | 137.127 | 140.893 |
94 | 62.437 | 69.068 | 105.303 | 111.944 | 117.632 | 122.715 | 124.255 | 128.803 | 133.059 | 138.337 | 142.119 |
95 | 63.250 | 69.925 | 106.364 | 113.038 | 118.752 | 123.858 | 125.405 | 129.973 | 134.247 | 139.546 | 143.344 |
96 | 64.063 | 70.783 | 107.425 | 114.131 | 119.871 | 125.000 | 126.554 | 131.141 | 135.433 | 140.755 | 144.567 |
97 | 64.878 | 71.642 | 108.486 | 115.223 | 120.990 | 126.141 | 127.702 | 132.309 | 136.619 | 141.962 | 145.789 |
98 | 65.694 | 72.501 | 109.547 | 116.315 | 122.108 | 127.282 | 128.849 | 133.476 | 137.803 | 143.168 | 147.010 |
99 | 66.510 | 73.361 | 110.607 | 117.407 | 123.225 | 128.422 | 129.996 | 134.642 | 138.987 | 144.373 | 148.230 |
100 | 67.328 | 74.222 | 111.667 | 118.498 | 124.342 | 129.561 | 131.142 | 135.807 | 140.169 | 145.577 | 149.449 |
J.Santillan
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