Values of the Chi-squared distribution
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 |
P | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
DF | 0.995 | 0.975 | 0.20 | 0.10 | 0.05 | 0.025 | 0.02 | 0.01 | 0.005 | 0.002 | 0.001 |
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 |
P | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
DF | 0.995 | 0.975 | 0.20 | 0.10 | 0.05 | 0.025 | 0.02 | 0.01 | 0.005 | 0.002 | 0.001 |
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 |
P | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
DF | 0.995 | 0.975 | 0.20 | 0.10 | 0.05 | 0.025 | 0.02 | 0.01 | 0.005 | 0.002 | 0.001 |
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 |
P | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
DF | 0.995 | 0.975 | 0.20 | 0.10 | 0.05 | 0.025 | 0.02 | 0.01 | 0.005 | 0.002 | 0.001 |
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 |
P | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
DF | 0.995 | 0.975 | 0.20 | 0.10 | 0.05 | 0.025 | 0.02 | 0.01 | 0.005 | 0.002 | 0.001 |
101 | 68.146 | 75.083 | 112.726 | 119.589 | 125.458 | 130.700 | 132.287 | 136.971 | 141.351 | 146.780 | 150.667 |
102 | 68.965 | 75.946 | 113.786 | 120.679 | 126.574 | 131.838 | 133.431 | 138.134 | 142.532 | 147.982 | 151.884 |
103 | 69.785 | 76.809 | 114.845 | 121.769 | 127.689 | 132.975 | 134.575 | 139.297 | 143.712 | 149.183 | 153.099 |
104 | 70.606 | 77.672 | 115.903 | 122.858 | 128.804 | 134.111 | 135.718 | 140.459 | 144.891 | 150.383 | 154.314 |
105 | 71.428 | 78.536 | 116.962 | 123.947 | 129.918 | 135.247 | 136.860 | 141.620 | 146.070 | 151.582 | 155.528 |
106 | 72.251 | 79.401 | 118.020 | 125.035 | 131.031 | 136.382 | 138.002 | 142.780 | 147.247 | 152.780 | 156.740 |
107 | 73.075 | 80.267 | 119.078 | 126.123 | 132.144 | 137.517 | 139.143 | 143.940 | 148.424 | 153.977 | 157.952 |
108 | 73.899 | 81.133 | 120.135 | 127.211 | 133.257 | 138.651 | 140.283 | 145.099 | 149.599 | 155.173 | 159.162 |
109 | 74.724 | 82.000 | 121.192 | 128.298 | 134.369 | 139.784 | 141.423 | 146.257 | 150.774 | 156.369 | 160.372 |
110 | 75.550 | 82.867 | 122.250 | 129.385 | 135.480 | 140.917 | 142.562 | 147.414 | 151.948 | 157.563 | 161.581 |
111 | 76.377 | 83.735 | 123.306 | 130.472 | 136.591 | 142.049 | 143.700 | 148.571 | 153.122 | 158.757 | 162.788 |
112 | 77.204 | 84.604 | 124.363 | 131.558 | 137.701 | 143.180 | 144.838 | 149.727 | 154.294 | 159.950 | 163.995 |
113 | 78.033 | 85.473 | 125.419 | 132.643 | 138.811 | 144.311 | 145.975 | 150.882 | 155.466 | 161.141 | 165.201 |
114 | 78.862 | 86.342 | 126.475 | 133.729 | 139.921 | 145.441 | 147.111 | 152.037 | 156.637 | 162.332 | 166.406 |
115 | 79.692 | 87.213 | 127.531 | 134.813 | 141.030 | 146.571 | 148.247 | 153.191 | 157.808 | 163.523 | 167.610 |
116 | 80.522 | 88.084 | 128.587 | 135.898 | 142.138 | 147.700 | 149.383 | 154.344 | 158.977 | 164.712 | 168.813 |
117 | 81.353 | 88.955 | 129.642 | 136.982 | 143.246 | 148.829 | 150.517 | 155.496 | 160.146 | 165.900 | 170.016 |
118 | 82.185 | 89.827 | 130.697 | 138.066 | 144.354 | 149.957 | 151.652 | 156.648 | 161.314 | 167.088 | 171.217 |
119 | 83.018 | 90.700 | 131.752 | 139.149 | 145.461 | 151.084 | 152.785 | 157.800 | 162.481 | 168.275 | 172.418 |
120 | 83.852 | 91.573 | 132.806 | 140.233 | 146.567 | 152.211 | 153.918 | 158.950 | 163.648 | 169.461 | 173.617 |
P | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
DF | 0.995 | 0.975 | 0.20 | 0.10 | 0.05 | 0.025 | 0.02 | 0.01 | 0.005 | 0.002 | 0.001 |
121 | 84.686 | 92.446 | 133.861 | 141.315 | 147.674 | 153.338 | 155.051 | 160.100 | 164.814 | 170.647 | 174.816 |
122 | 85.520 | 93.320 | 134.915 | 142.398 | 148.779 | 154.464 | 156.183 | 161.250 | 165.980 | 171.831 | 176.014 |
123 | 86.356 | 94.195 | 135.969 | 143.480 | 149.885 | 155.589 | 157.314 | 162.398 | 167.144 | 173.015 | 177.212 |
124 | 87.192 | 95.070 | 137.022 | 144.562 | 150.989 | 156.714 | 158.445 | 163.546 | 168.308 | 174.198 | 178.408 |
125 | 88.029 | 95.946 | 138.076 | 145.643 | 152.094 | 157.839 | 159.575 | 164.694 | 169.471 | 175.380 | 179.604 |
126 | 88.866 | 96.822 | 139.129 | 146.724 | 153.198 | 158.962 | 160.705 | 165.841 | 170.634 | 176.562 | 180.799 |
127 | 89.704 | 97.698 | 140.182 | 147.805 | 154.302 | 160.086 | 161.834 | 166.987 | 171.796 | 177.743 | 181.993 |
128 | 90.543 | 98.576 | 141.235 | 148.885 | 155.405 | 161.209 | 162.963 | 168.133 | 172.957 | 178.923 | 183.186 |
129 | 91.382 | 99.453 | 142.288 | 149.965 | 156.508 | 162.331 | 164.091 | 169.278 | 174.118 | 180.103 | 184.379 |
130 | 92.222 | 100.331 | 143.340 | 151.045 | 157.610 | 163.453 | 165.219 | 170.423 | 175.278 | 181.282 | 185.571 |
131 | 93.063 | 101.210 | 144.392 | 152.125 | 158.712 | 164.575 | 166.346 | 171.567 | 176.438 | 182.460 | 186.762 |
132 | 93.904 | 102.089 | 145.444 | 153.204 | 159.814 | 165.696 | 167.473 | 172.711 | 177.597 | 183.637 | 187.953 |
133 | 94.746 | 102.968 | 146.496 | 154.283 | 160.915 | 166.816 | 168.600 | 173.854 | 178.755 | 184.814 | 189.142 |
134 | 95.588 | 103.848 | 147.548 | 155.361 | 162.016 | 167.936 | 169.725 | 174.996 | 179.913 | 185.990 | 190.331 |
135 | 96.431 | 104.729 | 148.599 | 156.440 | 163.116 | 169.056 | 170.851 | 176.138 | 181.070 | 187.165 | 191.520 |
136 | 97.275 | 105.609 | 149.651 | 157.518 | 164.216 | 170.175 | 171.976 | 177.280 | 182.226 | 188.340 | 192.707 |
137 | 98.119 | 106.491 | 150.702 | 158.595 | 165.316 | 171.294 | 173.100 | 178.421 | 183.382 | 189.514 | 193.894 |
138 | 98.964 | 107.372 | 151.753 | 159.673 | 166.415 | 172.412 | 174.224 | 179.561 | 184.538 | 190.688 | 195.080 |
139 | 99.809 | 108.254 | 152.803 | 160.750 | 167.514 | 173.530 | 175.348 | 180.701 | 185.693 | 191.861 | 196.266 |
140 | 100.655 | 109.137 | 153.854 | 161.827 | 168.613 | 174.648 | 176.471 | 181.840 | 186.847 | 193.033 | 197.451 |
P | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
DF | 0.995 | 0.975 | 0.20 | 0.10 | 0.05 | 0.025 | 0.02 | 0.01 | 0.005 | 0.002 | 0.001 |
141 | 101.501 | 110.020 | 154.904 | 162.904 | 169.711 | 175.765 | 177.594 | 182.979 | 188.001 | 194.205 | 198.635 |
142 | 102.348 | 110.903 | 155.954 | 163.980 | 170.809 | 176.882 | 178.716 | 184.118 | 189.154 | 195.376 | 199.819 |
143 | 103.196 | 111.787 | 157.004 | 165.056 | 171.907 | 177.998 | 179.838 | 185.256 | 190.306 | 196.546 | 201.002 |
144 | 104.044 | 112.671 | 158.054 | 166.132 | 173.004 | 179.114 | 180.959 | 186.393 | 191.458 | 197.716 | 202.184 |
145 | 104.892 | 113.556 | 159.104 | 167.207 | 174.101 | 180.229 | 182.080 | 187.530 | 192.610 | 198.885 | 203.366 |
146 | 105.741 | 114.441 | 160.153 | 168.283 | 175.198 | 181.344 | 183.200 | 188.666 | 193.761 | 200.054 | 204.547 |
147 | 106.591 | 115.326 | 161.202 | 169.358 | 176.294 | 182.459 | 184.321 | 189.802 | 194.912 | 201.222 | 205.727 |
148 | 107.441 | 116.212 | 162.251 | 170.432 | 177.390 | 183.573 | 185.440 | 190.938 | 196.062 | 202.390 | 206.907 |
149 | 108.291 | 117.098 | 163.300 | 171.507 | 178.485 | 184.687 | 186.560 | 192.073 | 197.211 | 203.557 | 208.086 |
150 | 109.142 | 117.985 | 164.349 | 172.581 | 179.581 | 185.800 | 187.678 | 193.208 | 198.360 | 204.723 | 209.265 |
151 | 109.994 | 118.871 | 165.398 | 173.655 | 180.676 | 186.914 | 188.797 | 194.342 | 199.509 | 205.889 | 210.443 |
152 | 110.846 | 119.759 | 166.446 | 174.729 | 181.770 | 188.026 | 189.915 | 195.476 | 200.657 | 207.054 | 211.620 |
153 | 111.698 | 120.646 | 167.495 | 175.803 | 182.865 | 189.139 | 191.033 | 196.609 | 201.804 | 208.219 | 212.797 |
154 | 112.551 | 121.534 | 168.543 | 176.876 | 183.959 | 190.251 | 192.150 | 197.742 | 202.951 | 209.383 | 213.973 |
155 | 113.405 | 122.423 | 169.591 | 177.949 | 185.052 | 191.362 | 193.267 | 198.874 | 204.098 | 210.547 | 215.149 |
156 | 114.259 | 123.312 | 170.639 | 179.022 | 186.146 | 192.474 | 194.384 | 200.006 | 205.244 | 211.710 | 216.324 |
157 | 115.113 | 124.201 | 171.686 | 180.094 | 187.239 | 193.584 | 195.500 | 201.138 | 206.390 | 212.873 | 217.499 |
158 | 115.968 | 125.090 | 172.734 | 181.167 | 188.332 | 194.695 | 196.616 | 202.269 | 207.535 | 214.035 | 218.673 |
159 | 116.823 | 125.980 | 173.781 | 182.239 | 189.424 | 195.805 | 197.731 | 203.400 | 208.680 | 215.197 | 219.846 |
160 | 117.679 | 126.870 | 174.828 | 183.311 | 190.516 | 196.915 | 198.846 | 204.530 | 209.824 | 216.358 | 221.019 |
P | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
DF | 0.995 | 0.975 | 0.20 | 0.10 | 0.05 | 0.025 | 0.02 | 0.01 | 0.005 | 0.002 | 0.001 |
161 | 118.536 | 127.761 | 175.875 | 184.382 | 191.608 | 198.025 | 199.961 | 205.660 | 210.968 | 217.518 | 222.191 |
162 | 119.392 | 128.651 | 176.922 | 185.454 | 192.700 | 199.134 | 201.076 | 206.790 | 212.111 | 218.678 | 223.363 |
163 | 120.249 | 129.543 | 177.969 | 186.525 | 193.791 | 200.243 | 202.190 | 207.919 | 213.254 | 219.838 | 224.535 |
164 | 121.107 | 130.434 | 179.016 | 187.596 | 194.883 | 201.351 | 203.303 | 209.047 | 214.396 | 220.997 | 225.705 |
165 | 121.965 | 131.326 | 180.062 | 188.667 | 195.973 | 202.459 | 204.417 | 210.176 | 215.539 | 222.156 | 226.876 |
166 | 122.823 | 132.218 | 181.109 | 189.737 | 197.064 | 203.567 | 205.530 | 211.304 | 216.680 | 223.314 | 228.045 |
167 | 123.682 | 133.111 | 182.155 | 190.808 | 198.154 | 204.675 | 206.642 | 212.431 | 217.821 | 224.472 | 229.215 |
168 | 124.541 | 134.003 | 183.201 | 191.878 | 199.244 | 205.782 | 207.755 | 213.558 | 218.962 | 225.629 | 230.383 |
169 | 125.401 | 134.897 | 184.247 | 192.948 | 200.334 | 206.889 | 208.867 | 214.685 | 220.102 | 226.786 | 231.552 |
170 | 126.261 | 135.790 | 185.293 | 194.017 | 201.423 | 207.995 | 209.978 | 215.812 | 221.242 | 227.942 | 232.719 |
171 | 127.122 | 136.684 | 186.338 | 195.087 | 202.513 | 209.102 | 211.090 | 216.938 | 222.382 | 229.098 | 233.887 |
172 | 127.983 | 137.578 | 187.384 | 196.156 | 203.602 | 210.208 | 212.201 | 218.063 | 223.521 | 230.253 | 235.053 |
173 | 128.844 | 138.472 | 188.429 | 197.225 | 204.690 | 211.313 | 213.311 | 219.189 | 224.660 | 231.408 | 236.220 |
174 | 129.706 | 139.367 | 189.475 | 198.294 | 205.779 | 212.419 | 214.422 | 220.314 | 225.798 | 232.563 | 237.385 |
175 | 130.568 | 140.262 | 190.520 | 199.363 | 206.867 | 213.524 | 215.532 | 221.438 | 226.936 | 233.717 | 238.551 |
176 | 131.430 | 141.157 | 191.565 | 200.432 | 207.955 | 214.628 | 216.641 | 222.563 | 228.074 | 234.870 | 239.716 |
177 | 132.293 | 142.053 | 192.610 | 201.500 | 209.042 | 215.733 | 217.751 | 223.687 | 229.211 | 236.023 | 240.880 |
178 | 133.157 | 142.949 | 193.654 | 202.568 | 210.130 | 216.837 | 218.860 | 224.810 | 230.347 | 237.176 | 242.044 |
179 | 134.020 | 143.845 | 194.699 | 203.636 | 211.217 | 217.941 | 219.969 | 225.933 | 231.484 | 238.328 | 243.207 |
180 | 134.884 | 144.741 | 195.743 | 204.704 | 212.304 | 219.044 | 221.077 | 227.056 | 232.620 | 239.480 | 244.370 |
P | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
DF | 0.995 | 0.975 | 0.20 | 0.10 | 0.05 | 0.025 | 0.02 | 0.01 | 0.005 | 0.002 | 0.001 |
181 | 135.749 | 145.638 | 196.788 | 205.771 | 213.391 | 220.148 | 222.185 | 228.179 | 233.755 | 240.632 | 245.533 |
182 | 136.614 | 146.535 | 197.832 | 206.839 | 214.477 | 221.251 | 223.293 | 229.301 | 234.891 | 241.783 | 246.695 |
183 | 137.479 | 147.432 | 198.876 | 207.906 | 215.563 | 222.353 | 224.401 | 230.423 | 236.026 | 242.933 | 247.857 |
184 | 138.344 | 148.330 | 199.920 | 208.973 | 216.649 | 223.456 | 225.508 | 231.544 | 237.160 | 244.084 | 249.018 |
185 | 139.210 | 149.228 | 200.964 | 210.040 | 217.735 | 224.558 | 226.615 | 232.665 | 238.294 | 245.234 | 250.179 |
186 | 140.077 | 150.126 | 202.008 | 211.106 | 218.820 | 225.660 | 227.722 | 233.786 | 239.428 | 246.383 | 251.339 |
187 | 140.943 | 151.024 | 203.052 | 212.173 | 219.906 | 226.761 | 228.828 | 234.907 | 240.561 | 247.532 | 252.499 |
188 | 141.810 | 151.923 | 204.095 | 213.239 | 220.991 | 227.863 | 229.935 | 236.027 | 241.694 | 248.681 | 253.659 |
189 | 142.678 | 152.822 | 205.139 | 214.305 | 222.076 | 228.964 | 231.040 | 237.147 | 242.827 | 249.829 | 254.818 |
190 | 143.545 | 153.721 | 206.182 | 215.371 | 223.160 | 230.064 | 232.146 | 238.266 | 243.959 | 250.977 | 255.976 |
191 | 144.413 | 154.621 | 207.225 | 216.437 | 224.245 | 231.165 | 233.251 | 239.386 | 245.091 | 252.124 | 257.135 |
192 | 145.282 | 155.521 | 208.268 | 217.502 | 225.329 | 232.265 | 234.356 | 240.505 | 246.223 | 253.271 | 258.292 |
193 | 146.150 | 156.421 | 209.311 | 218.568 | 226.413 | 233.365 | 235.461 | 241.623 | 247.354 | 254.418 | 259.450 |
194 | 147.020 | 157.321 | 210.354 | 219.633 | 227.496 | 234.465 | 236.566 | 242.742 | 248.485 | 255.564 | 260.607 |
195 | 147.889 | 158.221 | 211.397 | 220.698 | 228.580 | 235.564 | 237.670 | 243.860 | 249.616 | 256.710 | 261.763 |
196 | 148.759 | 159.122 | 212.439 | 221.763 | 229.663 | 236.664 | 238.774 | 244.977 | 250.746 | 257.855 | 262.920 |
197 | 149.629 | 160.023 | 213.482 | 222.828 | 230.746 | 237.763 | 239.877 | 246.095 | 251.876 | 259.001 | 264.075 |
198 | 150.499 | 160.925 | 214.524 | 223.892 | 231.829 | 238.861 | 240.981 | 247.212 | 253.006 | 260.145 | 265.231 |
199 | 151.370 | 161.826 | 215.567 | 224.957 | 232.912 | 239.960 | 242.084 | 248.329 | 254.135 | 261.290 | 266.386 |
200 | 152.241 | 162.728 | 216.609 | 226.021 | 233.994 | 241.058 | 243.187 | 249.445 | 255.264 | 262.434 | 267.541 |
P | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
DF | 0.995 | 0.975 | 0.20 | 0.10 | 0.05 | 0.025 | 0.02 | 0.01 | 0.005 | 0.002 | 0.001 |
201 | 153.112 | 163.630 | 217.651 | 227.085 | 235.077 | 242.156 | 244.290 | 250.561 | 256.393 | 263.578 | 268.695 |
202 | 153.984 | 164.532 | 218.693 | 228.149 | 236.159 | 243.254 | 245.392 | 251.677 | 257.521 | 264.721 | 269.849 |
203 | 154.856 | 165.435 | 219.735 | 229.213 | 237.240 | 244.351 | 246.494 | 252.793 | 258.649 | 265.864 | 271.002 |
204 | 155.728 | 166.338 | 220.777 | 230.276 | 238.322 | 245.448 | 247.596 | 253.908 | 259.777 | 267.007 | 272.155 |
205 | 156.601 | 167.241 | 221.818 | 231.340 | 239.403 | 246.545 | 248.698 | 255.023 | 260.904 | 268.149 | 273.308 |
206 | 157.474 | 168.144 | 222.860 | 232.403 | 240.485 | 247.642 | 249.799 | 256.138 | 262.031 | 269.291 | 274.460 |
207 | 158.347 | 169.047 | 223.901 | 233.466 | 241.566 | 248.739 | 250.900 | 257.253 | 263.158 | 270.432 | 275.612 |
208 | 159.221 | 169.951 | 224.943 | 234.529 | 242.647 | 249.835 | 252.001 | 258.367 | 264.285 | 271.574 | 276.764 |
209 | 160.095 | 170.855 | 225.984 | 235.592 | 243.727 | 250.931 | 253.102 | 259.481 | 265.411 | 272.715 | 277.915 |
210 | 160.969 | 171.759 | 227.025 | 236.655 | 244.808 | 252.027 | 254.202 | 260.595 | 266.537 | 273.855 | 279.066 |
211 | 161.843 | 172.664 | 228.066 | 237.717 | 245.888 | 253.122 | 255.302 | 261.708 | 267.662 | 274.995 | 280.217 |
212 | 162.718 | 173.568 | 229.107 | 238.780 | 246.968 | 254.218 | 256.402 | 262.821 | 268.788 | 276.135 | 281.367 |
213 | 163.593 | 174.473 | 230.148 | 239.842 | 248.048 | 255.313 | 257.502 | 263.934 | 269.912 | 277.275 | 282.517 |
214 | 164.469 | 175.378 | 231.189 | 240.904 | 249.128 | 256.408 | 258.601 | 265.047 | 271.037 | 278.414 | 283.666 |
215 | 165.344 | 176.283 | 232.230 | 241.966 | 250.207 | 257.503 | 259.701 | 266.159 | 272.162 | 279.553 | 284.815 |
216 | 166.220 | 177.189 | 233.270 | 243.028 | 251.286 | 258.597 | 260.800 | 267.271 | 273.286 | 280.692 | 285.964 |
217 | 167.096 | 178.095 | 234.311 | 244.090 | 252.365 | 259.691 | 261.898 | 268.383 | 274.409 | 281.830 | 287.112 |
218 | 167.973 | 179.001 | 235.351 | 245.151 | 253.444 | 260.785 | 262.997 | 269.495 | 275.533 | 282.968 | 288.261 |
219 | 168.850 | 179.907 | 236.391 | 246.213 | 254.523 | 261.879 | 264.095 | 270.606 | 276.656 | 284.106 | 289.408 |
220 | 169.727 | 180.813 | 237.432 | 247.274 | 255.602 | 262.973 | 265.193 | 271.717 | 277.779 | 285.243 | 290.556 |
P | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
DF | 0.995 | 0.975 | 0.20 | 0.10 | 0.05 | 0.025 | 0.02 | 0.01 | 0.005 | 0.002 | 0.001 |
221 | 170.604 | 181.720 | 238.472 | 248.335 | 256.680 | 264.066 | 266.291 | 272.828 | 278.902 | 286.380 | 291.703 |
222 | 171.482 | 182.627 | 239.512 | 249.396 | 257.758 | 265.159 | 267.389 | 273.939 | 280.024 | 287.517 | 292.850 |
223 | 172.360 | 183.534 | 240.552 | 250.457 | 258.837 | 266.252 | 268.486 | 275.049 | 281.146 | 288.653 | 293.996 |
224 | 173.238 | 184.441 | 241.592 | 251.517 | 259.914 | 267.345 | 269.584 | 276.159 | 282.268 | 289.789 | 295.142 |
225 | 174.116 | 185.348 | 242.631 | 252.578 | 260.992 | 268.438 | 270.681 | 277.269 | 283.390 | 290.925 | 296.288 |
226 | 174.995 | 186.256 | 243.671 | 253.638 | 262.070 | 269.530 | 271.777 | 278.379 | 284.511 | 292.061 | 297.433 |
227 | 175.874 | 187.164 | 244.711 | 254.699 | 263.147 | 270.622 | 272.874 | 279.488 | 285.632 | 293.196 | 298.579 |
228 | 176.753 | 188.072 | 245.750 | 255.759 | 264.224 | 271.714 | 273.970 | 280.597 | 286.753 | 294.331 | 299.723 |
229 | 177.633 | 188.980 | 246.790 | 256.819 | 265.301 | 272.806 | 275.066 | 281.706 | 287.874 | 295.465 | 300.868 |
230 | 178.512 | 189.889 | 247.829 | 257.879 | 266.378 | 273.898 | 276.162 | 282.814 | 288.994 | 296.600 | 302.012 |
231 | 179.392 | 190.797 | 248.868 | 258.939 | 267.455 | 274.989 | 277.258 | 283.923 | 290.114 | 297.734 | 303.156 |
232 | 180.273 | 191.706 | 249.908 | 259.998 | 268.531 | 276.080 | 278.354 | 285.031 | 291.234 | 298.867 | 304.299 |
233 | 181.153 | 192.615 | 250.947 | 261.058 | 269.608 | 277.171 | 279.449 | 286.139 | 292.353 | 300.001 | 305.443 |
234 | 182.034 | 193.524 | 251.986 | 262.117 | 270.684 | 278.262 | 280.544 | 287.247 | 293.472 | 301.134 | 306.586 |
235 | 182.915 | 194.434 | 253.025 | 263.176 | 271.760 | 279.352 | 281.639 | 288.354 | 294.591 | 302.267 | 307.728 |
236 | 183.796 | 195.343 | 254.063 | 264.235 | 272.836 | 280.443 | 282.734 | 289.461 | 295.710 | 303.400 | 308.871 |
237 | 184.678 | 196.253 | 255.102 | 265.294 | 273.911 | 281.533 | 283.828 | 290.568 | 296.828 | 304.532 | 310.013 |
238 | 185.560 | 197.163 | 256.141 | 266.353 | 274.987 | 282.623 | 284.922 | 291.675 | 297.947 | 305.664 | 311.154 |
239 | 186.442 | 198.073 | 257.179 | 267.412 | 276.062 | 283.713 | 286.016 | 292.782 | 299.065 | 306.796 | 312.296 |
240 | 187.324 | 198.984 | 258.218 | 268.471 | 277.138 | 284.802 | 287.110 | 293.888 | 300.182 | 307.927 | 313.437 |
P | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
DF | 0.995 | 0.975 | 0.20 | 0.10 | 0.05 | 0.025 | 0.02 | 0.01 | 0.005 | 0.002 | 0.001 |
241 | 188.207 | 199.894 | 259.256 | 269.529 | 278.213 | 285.892 | 288.204 | 294.994 | 301.300 | 309.058 | 314.578 |
242 | 189.090 | 200.805 | 260.295 | 270.588 | 279.288 | 286.981 | 289.298 | 296.100 | 302.417 | 310.189 | 315.718 |
243 | 189.973 | 201.716 | 261.333 | 271.646 | 280.362 | 288.070 | 290.391 | 297.206 | 303.534 | 311.320 | 316.859 |
244 | 190.856 | 202.627 | 262.371 | 272.704 | 281.437 | 289.159 | 291.484 | 298.311 | 304.651 | 312.450 | 317.999 |
245 | 191.739 | 203.539 | 263.409 | 273.762 | 282.511 | 290.248 | 292.577 | 299.417 | 305.767 | 313.580 | 319.138 |
246 | 192.623 | 204.450 | 264.447 | 274.820 | 283.586 | 291.336 | 293.670 | 300.522 | 306.883 | 314.710 | 320.278 |
247 | 193.507 | 205.362 | 265.485 | 275.878 | 284.660 | 292.425 | 294.762 | 301.626 | 307.999 | 315.840 | 321.417 |
248 | 194.391 | 206.274 | 266.523 | 276.935 | 285.734 | 293.513 | 295.855 | 302.731 | 309.115 | 316.969 | 322.556 |
249 | 195.276 | 207.186 | 267.561 | 277.993 | 286.808 | 294.601 | 296.947 | 303.835 | 310.231 | 318.098 | 323.694 |
250 | 196.161 | 208.098 | 268.599 | 279.050 | 287.882 | 295.689 | 298.039 | 304.940 | 311.346 | 319.227 | 324.832 |
300 | 240.663 | 253.912 | 320.397 | 331.789 | 341.395 | 349.874 | 352.425 | 359.906 | 366.844 | 375.369 | 381.425 |
350 | 285.608 | 300.064 | 372.051 | 384.306 | 394.626 | 403.723 | 406.457 | 414.474 | 421.900 | 431.017 | 437.488 |
400 | 330.903 | 346.482 | 423.590 | 436.649 | 447.632 | 457.305 | 460.211 | 468.724 | 476.606 | 486.274 | 493.132 |
450 | 376.483 | 393.118 | 475.035 | 488.849 | 500.456 | 510.670 | 513.736 | 522.717 | 531.026 | 541.212 | 548.432 |
500 | 422.303 | 439.936 | 526.401 | 540.930 | 553.127 | 563.852 | 567.070 | 576.493 | 585.207 | 595.882 | 603.446 |
550 | 468.328 | 486.910 | 577.701 | 592.909 | 605.667 | 616.878 | 620.241 | 630.084 | 639.183 | 650.324 | 658.215 |
600 | 514.529 | 534.019 | 628.943 | 644.800 | 658.094 | 669.769 | 673.270 | 683.516 | 692.982 | 704.568 | 712.771 |
650 | 560.885 | 581.245 | 680.134 | 696.614 | 710.421 | 722.542 | 726.176 | 736.807 | 746.625 | 758.639 | 767.141 |
700 | 607.380 | 628.577 | 731.280 | 748.359 | 762.661 | 775.211 | 778.972 | 789.974 | 800.131 | 812.556 | 821.347 |
750 | 653.997 | 676.003 | 782.386 | 800.043 | 814.822 | 827.785 | 831.670 | 843.029 | 853.514 | 866.336 | 875.404 |
800 | 700.725 | 723.513 | 833.456 | 851.671 | 866.911 | 880.275 | 884.279 | 895.984 | 906.786 | 919.991 | 929.329 |
850 | 747.554 | 771.099 | 884.492 | 903.249 | 918.937 | 932.689 | 936.808 | 948.848 | 959.957 | 973.534 | 983.133 |
900 | 794.475 | 818.756 | 935.499 | 954.782 | 970.904 | 985.032 | 989.263 | 1001.630 | 1013.036 | 1026.974 | 1036.826 |
950 | 841.480 | 866.477 | 986.478 | 1006.272 | 1022.816 | 1037.311 | 1041.651 | 1054.334 | 1066.031 | 1080.320 | 1090.418 |
1000 | 888.564 | 914.257 | 1037.431 | 1057.724 | 1074.679 | 1089.531 | 1093.977 | 1106.969 | 1118.948 | 1133.579 | 1143.917 |