Tabla IV. Distribución χ2
GL/P | 0.999 | 0.995 | 0.99 | 0.975 | 0.95 | 0.90 | 0.75 | 0.50 | 0.25 | 0.10 | 0.05 | 0.025 | 0.01 | 0.005 | 0.001 |
1 | 0.000 | 0.000 | 0.000 | 0.001 | 0.004 | 0.016 | 0.102 | 0.455 | 1.323 | 2.706 | 3.841 | 5.024 | 6.635 | 7.879 | 10.827 |
2 | 0.002 | 0.010 | 0.020 | 0.051 | 0.103 | 0.211 | 0.575 | 1.386 | 2.773 | 4.605 | 5.991 | 7.378 | 9.210 | 10.597 | 13.815 |
3 | 0.024 | 0.072 | 0.115 | 0.216 | 0.352 | 0.584 | 1.213 | 2.366 | 4.108 | 6.251 | 7.815 | 9.348 | 11.345 | 12.838 | 16.266 |
4 | 0.091 | 0.207 | 0.297 | 0.484 | 0.711 | 1.064 | 1.923 | 3.357 | 5.385 | 7.779 | 9.488 | 11.143 | 13.277 | 14.860 | 18.466 |
5 | 0.210 | 0.412 | 0.554 | 0.831 | 1.145 | 1.610 | 2.675 | 4.351 | 6.626 | 9.236 | 11.070 | 12.832 | 15.086 | 16.750 | 20.515 |
6 | 0.381 | 0.676 | 0.872 | 1.237 | 1.635 | 2.204 | 3.455 | 5.348 | 7.841 | 10.645 | 12.592 | 14.449 | 16.812 | 18.548 | 22.457 |
7 | 0.599 | 0.989 | 1.239 | 1.690 | 2.167 | 2.833 | 4.255 | 6.346 | 9.037 | 12.017 | 14.067 | 16.013 | 18.475 | 20.278 | 24.321 |
8 | 0.857 | 1.344 | 1.647 | 2.180 | 2.733 | 3.490 | 5.071 | 7.344 | 10.219 | 13.362 | 15.507 | 17.535 | 20.090 | 21.955 | 26.124 |
9 | 1.152 | 1.735 | 2.088 | 2.700 | 3.325 | 4.168 | 5.899 | 8.343 | 11.389 | 14.684 | 16.919 | 19.023 | 21.666 | 23.589 | 27.877 |
10 | 1.479 | 2.156 | 2.558 | 3.247 | 3.940 | 4.865 | 6.737 | 9.342 | 12.549 | 15.987 | 18.307 | 20.483 | 23.209 | 25.188 | 29.588 |
11 | 1.834 | 2.603 | 3.053 | 3.816 | 4.575 | 5.578 | 7.584 | 10.341 | 13.701 | 17.275 | 19.675 | 21.920 | 24.725 | 26.757 | 31.264 |
12 | 2.214 | 3.074 | 3.571 | 4.404 | 5.226 | 6.304 | 8.438 | 11.340 | 14.845 | 18.549 | 21.026 | 23.337 | 26.217 | 28.300 | 32.909 |
13 | 2.617 | 3.565 | 4.107 | 5.009 | 5.892 | 7.041 | 9.299 | 12.340 | 15.984 | 19.812 | 22.362 | 24.736 | 27.688 | 29.819 | 34.527 |
14 | 3.041 | 4.075 | 4.660 | 5.629 | 6.571 | 7.790 | 10.165 | 13.339 | 17.117 | 21.064 | 23.685 | 26.119 | 29.141 | 31.319 | 36.124 |
15 | 3.483 | 4.601 | 5.229 | 6.262 | 7.261 | 8.547 | 11.037 | 14.339 | 18.245 | 22.307 | 24.996 | 27.488 | 30.578 | 32.801 | 37.698 |
16 | 3.942 | 5.142 | 5.812 | 6.908 | 7.962 | 9.312 | 11.912 | 15.338 | 19.369 | 23.542 | 26.296 | 28.845 | 32.000 | 34.267 | 39.252 |
17 | 4.416 | 5.697 | 6.408 | 7.564 | 8.672 | 10.085 | 12.792 | 16.338 | 20.489 | 24.769 | 27.587 | 30.191 | 33.409 | 35.718 | 40.791 |
18 | 4.905 | 6.265 | 7.015 | 8.231 | 9.390 | 10.865 | 13.675 | 17.338 | 21.605 | 25.989 | 28.869 | 31.526 | 34.805 | 37.156 | 42.312 |
19 | 5.407 | 6.844 | 7.633 | 8.907 | 10.117 | 11.651 | 14.562 | 18.338 | 22.718 | 27.204 | 30.144 | 32.852 | 36.191 | 38.582 | 43.819 |
GL/P | 0.999 | 0.995 | 0.99 | 0.975 | 0.95 | 0.90 | 0.75 | 0.50 | 0.25 | 0.10 | 0.05 | 0.025 | 0.01 | 0.005 | 0.001 |
20 | 5.921 | 7.434 | 8.260 | 9.591 | 10.851 | 12.443 | 15.452 | 19.337 | 23.828 | 28.412 | 31.410 | 34.170 | 37.566 | 39.997 | 45.314 |
21 | 6.447 | 8.034 | 8.897 | 10.283 | 11.591 | 13.240 | 16.344 | 20.337 | 24.935 | 29.615 | 32.671 | 35.479 | 38.932 | 41.401 | 46.796 |
22 | 6.983 | 8.643 | 9.542 | 10.982 | 12.338 | 14.041 | 17.240 | 21.337 | 26.039 | 30.813 | 33.924 | 36.781 | 40.289 | 42.796 | 48.268 |
23 | 7.529 | 9.260 | 10.196 | 11.689 | 13.091 | 14.848 | 18.137 | 22.337 | 27.141 | 32.007 | 35.172 | 38.076 | 41.638 | 44.181 | 49.728 |
24 | 8.085 | 9.886 | 10.856 | 12.401 | 13.848 | 15.659 | 19.037 | 23.337 | 28.241 | 33.196 | 36.415 | 39.364 | 42.980 | 45.558 | 51.179 |
25 | 8.649 | 10.520 | 11.524 | 13.120 | 14.611 | 16.473 | 19.939 | 24.337 | 29.339 | 34.382 | 37.652 | 40.646 | 44.314 | 46.928 | 52.619 |
26 | 9.222 | 11.160 | 12.198 | 13.844 | 15.379 | 17.292 | 20.843 | 25.336 | 30.435 | 35.563 | 38.885 | 41.923 | 45.642 | 48.290 | 54.051 |
27 | 9.803 | 11.808 | 12.878 | 14.573 | 16.151 | 18.114 | 21.749 | 26.336 | 31.528 | 36.741 | 40.113 | 43.195 | 46.963 | 49.645 | 55.475 |
28 | 10.391 | 12.461 | 13.565 | 15.308 | 16.928 | 18.939 | 22.657 | 27.336 | 32.620 | 37.916 | 41.337 | 44.461 | 48.278 | 50.994 | 56.892 |
29 | 10.986 | 13.121 | 14.256 | 16.047 | 17.708 | 19.768 | 23.567 | 28.336 | 33.711 | 39.087 | 42.557 | 45.722 | 49.588 | 52.335 | 58.301 |
30 | 11.588 | 13.787 | 14.953 | 16.791 | 18.493 | 20.599 | 24.478 | 29.336 | 34.800 | 40.256 | 43.773 | 46.979 | 50.892 | 53.672 | 59.702 |
31 | 12.196 | 14.458 | 15.655 | 17.539 | 19.281 | 21.434 | 25.390 | 30.336 | 35.887 | 41.422 | 44.985 | 48.232 | 52.191 | 55.002 | 61.098 |
32 | 12.810 | 15.134 | 16.362 | 18.291 | 20.072 | 22.271 | 26.304 | 31.336 | 36.973 | 42.585 | 46.194 | 49.480 | 53.486 | 56.328 | 62.487 |
33 | 13.431 | 15.815 | 17.073 | 19.047 | 20.867 | 23.110 | 27.219 | 32.336 | 38.058 | 43.745 | 47.400 | 50.725 | 54.775 | 57.648 | 63.869 |
34 | 14.057 | 16.501 | 17.789 | 19.806 | 21.664 | 23.952 | 28.136 | 33.336 | 39.141 | 44.903 | 48.602 | 51.966 | 56.061 | 58.964 | 65.247 |
35 | 14.688 | 17.192 | 18.509 | 20.569 | 22.465 | 24.797 | 29.054 | 34.336 | 40.223 | 46.059 | 49.802 | 53.203 | 57.342 | 60.275 | 66.619 |
36 | 15.324 | 17.887 | 19.233 | 21.336 | 23.269 | 25.643 | 29.973 | 35.336 | 41.304 | 47.212 | 50.998 | 54.437 | 58.619 | 61.581 | 67.985 |
37 | 15.965 | 18.586 | 19.960 | 22.106 | 24.075 | 26.492 | 30.893 | 36.336 | 42.383 | 48.363 | 52.192 | 55.668 | 59.893 | 62.883 | 69.348 |
38 | 16.611 | 19.289 | 20.691 | 22.878 | 24.884 | 27.343 | 31.815 | 37.335 | 43.462 | 49.513 | 53.384 | 56.895 | 61.162 | 64.181 | 70.704 |
39 | 17.261 | 19.996 | 21.426 | 23.654 | 25.695 | 28.196 | 32.737 | 38.335 | 44.539 | 50.660 | 54.572 | 58.120 | 62.428 | 65.475 | 72.055 |
GL/P | 0.999 | 0.995 | 0.99 | 0.975 | 0.95 | 0.90 | 0.75 | 0.50 | 0.25 | 0.10 | 0.05 | 0.025 | 0.01 | 0.005 | 0.001 |
40 | 17.917 | 20.707 | 22.164 | 24.433 | 26.509 | 29.051 | 33.660 | 39.335 | 45.616 | 51.805 | 55.758 | 59.342 | 63.691 | 66.766 | 73.403 |
41 | 18.576 | 21.421 | 22.906 | 25.215 | 27.326 | 29.907 | 34.585 | 40.335 | 46.692 | 52.949 | 56.942 | 60.561 | 64.950 | 68.053 | 74.744 |
42 | 19.238 | 22.138 | 23.650 | 25.999 | 28.144 | 30.765 | 35.510 | 41.335 | 47.766 | 54.090 | 58.124 | 61.777 | 66.206 | 69.336 | 76.084 |
43 | 19.905 | 22.860 | 24.398 | 26.785 | 28.965 | 31.625 | 36.436 | 42.335 | 48.840 | 55.230 | 59.304 | 62.990 | 67.459 | 70.616 | 77.418 |
44 | 20.576 | 23.584 | 25.148 | 27.575 | 29.787 | 32.487 | 37.363 | 43.335 | 49.913 | 56.369 | 60.481 | 64.201 | 68.710 | 71.892 | 78.749 |
45 | 21.251 | 24.311 | 25.901 | 28.366 | 30.612 | 33.350 | 38.291 | 44.335 | 50.985 | 57.505 | 61.656 | 65.410 | 69.957 | 73.166 | 80.078 |
46 | 21.929 | 25.041 | 26.657 | 29.160 | 31.439 | 34.215 | 39.220 | 45.335 | 52.056 | 58.641 | 62.830 | 66.616 | 71.201 | 74.437 | 81.400 |
47 | 22.610 | 25.775 | 27.416 | 29.956 | 32.268 | 35.081 | 40.149 | 46.335 | 53.127 | 59.774 | 64.001 | 67.821 | 72.443 | 75.704 | 82.720 |
48 | 23.294 | 26.511 | 28.177 | 30.754 | 33.098 | 35.949 | 41.079 | 47.335 | 54.196 | 60.907 | 65.171 | 69.023 | 73.683 | 76.969 | 84.037 |
49 | 23.983 | 27.249 | 28.941 | 31.555 | 33.930 | 36.818 | 42.010 | 48.335 | 55.265 | 62.038 | 66.339 | 70.222 | 74.919 | 78.231 | 85.350 |
50 | 24.674 | 27.991 | 29.707 | 32.357 | 34.764 | 37.689 | 42.942 | 49.335 | 56.334 | 63.167 | 67.505 | 71.420 | 76.154 | 79.490 | 86.660 |
51 | 25.368 | 28.735 | 30.475 | 33.162 | 35.600 | 38.560 | 43.874 | 50.335 | 57.401 | 64.295 | 68.669 | 72.616 | 77.386 | 80.746 | 87.967 |
52 | 26.065 | 29.481 | 31.246 | 33.968 | 36.437 | 39.433 | 44.807 | 51.335 | 58.468 | 65.422 | 69.832 | 73.810 | 78.616 | 82.001 | 89.272 |
53 | 26.765 | 30.230 | 32.019 | 34.776 | 37.276 | 40.308 | 45.741 | 52.335 | 59.534 | 66.548 | 70.993 | 75.002 | 79.843 | 83.253 | 90.573 |
54 | 27.467 | 30.981 | 32.793 | 35.586 | 38.116 | 41.183 | 46.676 | 53.335 | 60.600 | 67.673 | 72.153 | 76.192 | 81.069 | 84.502 | 91.871 |
55 | 28.173 | 31.735 | 33.571 | 36.398 | 38.958 | 42.060 | 47.610 | 54.335 | 61.665 | 68.796 | 73.311 | 77.380 | 82.292 | 85.749 | 93.167 |
56 | 28.881 | 32.491 | 34.350 | 37.212 | 39.801 | 42.937 | 48.546 | 55.335 | 62.729 | 69.919 | 74.468 | 78.567 | 83.514 | 86.994 | 94.462 |
57 | 29.592 | 33.248 | 35.131 | 38.027 | 40.646 | 43.816 | 49.482 | 56.335 | 63.793 | 71.040 | 75.624 | 79.752 | 84.733 | 88.237 | 95.750 |
58 | 30.305 | 34.008 | 35.914 | 38.844 | 41.492 | 44.696 | 50.419 | 57.335 | 64.857 | 72.160 | 76.778 | 80.936 | 85.950 | 89.477 | 97.038 |
59 | 31.021 | 34.770 | 36.698 | 39.662 | 42.339 | 45.577 | 51.356 | 58.335 | 65.919 | 73.279 | 77.930 | 82.117 | 87.166 | 90.715 | 98.324 |
GL/P | 0.999 | 0.995 | 0.99 | 0.975 | 0.95 | 0.90 | 0.75 | 0.50 | 0.25 | 0.10 | 0.05 | 0.025 | 0.01 | 0.005 | 0.001 |
60 | 31.738 | 35.534 | 37.485 | 40.482 | 43.188 | 46.459 | 52.294 | 59.335 | 66.981 | 74.397 | 79.082 | 83.298 | 88.379 | 91.952 | 99.608 |
61 | 32.458 | 36.300 | 38.273 | 41.303 | 44.038 | 47.342 | 53.232 | 60.335 | 68.043 | 75.514 | 80.232 | 84.476 | 89.591 | 93.186 | 100.887 |
62 | 33.181 | 37.068 | 39.063 | 42.126 | 44.889 | 48.226 | 54.171 | 61.335 | 69.104 | 76.630 | 81.381 | 85.654 | 90.802 | 94.419 | 102.165 |
63 | 33.905 | 37.838 | 39.855 | 42.950 | 45.741 | 49.111 | 55.110 | 62.335 | 70.165 | 77.745 | 82.529 | 86.830 | 92.010 | 95.649 | 103.442 |
64 | 34.632 | 38.610 | 40.649 | 43.776 | 46.595 | 49.996 | 56.050 | 63.335 | 71.225 | 78.860 | 83.675 | 88.004 | 93.217 | 96.878 | 104.717 |
65 | 35.362 | 39.383 | 41.444 | 44.603 | 47.450 | 50.883 | 56.990 | 64.335 | 72.285 | 79.973 | 84.821 | 89.177 | 94.422 | 98.105 | 105.988 |
66 | 36.092 | 40.158 | 42.240 | 45.431 | 48.305 | 51.770 | 57.931 | 65.335 | 73.344 | 81.085 | 85.965 | 90.349 | 95.626 | 99.330 | 107.257 |
67 | 36.826 | 40.935 | 43.038 | 46.261 | 49.162 | 52.659 | 58.872 | 66.335 | 74.403 | 82.197 | 87.108 | 91.519 | 96.828 | 100.554 | 108.525 |
68 | 37.561 | 41.714 | 43.838 | 47.092 | 50.020 | 53.548 | 59.814 | 67.335 | 75.461 | 83.308 | 88.250 | 92.688 | 98.028 | 101.776 | 109.793 |
69 | 38.298 | 42.493 | 44.639 | 47.924 | 50.879 | 54.438 | 60.756 | 68.334 | 76.519 | 84.418 | 89.391 | 93.856 | 99.227 | 102.996 | 111.055 |
70 | 39.036 | 43.275 | 45.442 | 48.758 | 51.739 | 55.329 | 61.698 | 69.334 | 77.577 | 85.527 | 90.531 | 95.023 | 100.425 | 104.215 | 112.317 |
71 | 39.776 | 44.058 | 46.246 | 49.592 | 52.600 | 56.221 | 62.641 | 70.334 | 78.634 | 86.635 | 91.670 | 96.189 | 101.621 | 105.432 | 113.577 |
72 | 40.520 | 44.843 | 47.051 | 50.428 | 53.462 | 57.113 | 63.585 | 71.334 | 79.690 | 87.743 | 92.808 | 97.353 | 102.816 | 106.647 | 114.834 |
73 | 41.263 | 45.629 | 47.858 | 51.265 | 54.325 | 58.006 | 64.528 | 72.334 | 80.747 | 88.850 | 93.945 | 98.516 | 104.010 | 107.862 | 116.092 |
74 | 42.009 | 46.417 | 48.666 | 52.103 | 55.189 | 58.900 | 65.472 | 73.334 | 81.803 | 89.956 | 95.081 | 99.678 | 105.202 | 109.074 | 117.347 |
75 | 42.757 | 47.206 | 49.475 | 52.942 | 56.054 | 59.795 | 66.417 | 74.334 | 82.858 | 91.061 | 96.217 | 100.839 | 106.393 | 110.285 | 118.599 |
76 | 43.507 | 47.996 | 50.286 | 53.782 | 56.920 | 60.690 | 67.362 | 75.334 | 83.913 | 92.166 | 97.351 | 101.999 | 107.582 | 111.495 | 119.850 |
77 | 44.257 | 48.788 | 51.097 | 54.623 | 57.786 | 61.586 | 68.307 | 76.334 | 84.968 | 93.270 | 98.484 | 103.158 | 108.771 | 112.704 | 121.101 |
78 | 45.011 | 49.581 | 51.910 | 55.466 | 58.654 | 62.483 | 69.252 | 77.334 | 86.022 | 94.374 | 99.617 | 104.316 | 109.958 | 113.911 | 122.347 |
79 | 45.764 | 50.376 | 52.725 | 56.309 | 59.522 | 63.380 | 70.198 | 78.334 | 87.077 | 95.476 | 100.749 | 105.473 | 111.144 | 115.116 | 123.595 |
GL/P | 0.999 | 0.995 | 0.99 | 0.975 | 0.95 | 0.90 | 0.75 | 0.50 | 0.25 | 0.10 | 0.05 | 0.025 | 0.01 | 0.005 | 0.001 |
80 | 46.520 | 51.172 | 53.540 | 57.153 | 60.391 | 64.278 | 71.145 | 79.334 | 88.130 | 96.578 | 101.879 | 106.629 | 112.329 | 116.321 | 124.839 |
81 | 47.276 | 51.969 | 54.357 | 57.998 | 61.262 | 65.176 | 72.091 | 80.334 | 89.184 | 97.680 | 103.010 | 107.783 | 113.512 | 117.524 | 126.084 |
82 | 48.036 | 52.767 | 55.174 | 58.845 | 62.132 | 66.076 | 73.038 | 81.334 | 90.237 | 98.780 | 104.139 | 108.937 | 114.695 | 118.726 | 127.324 |
83 | 48.795 | 53.567 | 55.993 | 59.692 | 63.004 | 66.976 | 73.985 | 82.334 | 91.289 | 99.880 | 105.267 | 110.090 | 115.876 | 119.927 | 128.565 |
84 | 49.558 | 54.368 | 56.813 | 60.540 | 63.876 | 67.876 | 74.933 | 83.334 | 92.342 | 100.980 | 106.395 | 111.242 | 117.057 | 121.126 | 129.802 |
85 | 50.320 | 55.170 | 57.634 | 61.389 | 64.749 | 68.777 | 75.881 | 84.334 | 93.394 | 102.079 | 107.522 | 112.393 | 118.236 | 122.324 | 131.043 |
86 | 51.084 | 55.973 | 58.456 | 62.239 | 65.623 | 69.679 | 76.829 | 85.334 | 94.446 | 103.177 | 108.648 | 113.544 | 119.414 | 123.522 | 132.276 |
87 | 51.850 | 56.777 | 59.279 | 63.089 | 66.498 | 70.581 | 77.777 | 86.334 | 95.497 | 104.275 | 109.773 | 114.693 | 120.591 | 124.718 | 133.511 |
88 | 52.617 | 57.582 | 60.103 | 63.941 | 67.373 | 71.484 | 78.726 | 87.334 | 96.548 | 105.372 | 110.898 | 115.841 | 121.767 | 125.912 | 134.746 |
89 | 53.385 | 58.389 | 60.928 | 64.793 | 68.249 | 72.387 | 79.675 | 88.334 | 97.599 | 106.469 | 112.022 | 116.989 | 122.942 | 127.106 | 135.977 |
90 | 54.156 | 59.196 | 61.754 | 65.647 | 69.126 | 73.291 | 80.625 | 89.334 | 98.650 | 107.565 | 113.145 | 118.136 | 124.116 | 128.299 | 137.208 |
91 | 54.925 | 60.005 | 62.581 | 66.501 | 70.003 | 74.196 | 81.574 | 90.334 | 99.700 | 108.661 | 114.268 | 119.282 | 125.289 | 129.490 | 138.437 |
92 | 55.698 | 60.815 | 63.409 | 67.356 | 70.882 | 75.100 | 82.524 | 91.334 | 100.750 | 109.756 | 115.390 | 120.427 | 126.462 | 130.681 | 139.667 |
93 | 56.471 | 61.625 | 64.238 | 68.211 | 71.760 | 76.006 | 83.474 | 92.334 | 101.800 | 110.850 | 116.511 | 121.571 | 127.633 | 131.871 | 140.894 |
94 | 57.246 | 62.437 | 65.068 | 69.068 | 72.640 | 76.912 | 84.425 | 93.334 | 102.850 | 111.944 | 117.632 | 122.715 | 128.803 | 133.059 | 142.118 |
95 | 58.022 | 63.250 | 65.898 | 69.925 | 73.520 | 77.818 | 85.376 | 94.334 | 103.899 | 113.038 | 118.752 | 123.858 | 129.973 | 134.247 | 143.343 |
96 | 58.800 | 64.063 | 66.730 | 70.783 | 74.401 | 78.725 | 86.327 | 95.334 | 104.948 | 114.131 | 119.871 | 125.000 | 131.141 | 135.433 | 144.566 |
97 | 59.577 | 64.878 | 67.562 | 71.642 | 75.282 | 79.633 | 87.278 | 96.334 | 105.997 | 115.223 | 120.990 | 126.141 | 132.309 | 136.619 | 145.789 |
98 | 60.356 | 65.693 | 68.396 | 72.501 | 76.164 | 80.541 | 88.229 | 97.334 | 107.045 | 116.315 | 122.108 | 127.282 | 133.476 | 137.803 | 147.009 |
99 | 61.136 | 66.510 | 69.230 | 73.361 | 77.046 | 81.449 | 89.181 | 98.334 | 108.093 | 117.407 | 123.225 | 128.422 | 134.641 | 138.987 | 148.230 |
GL/P | 0.999 | 0.995 | 0.99 | 0.975 | 0.95 | 0.90 | 0.75 | 0.50 | 0.25 | 0.10 | 0.05 | 0.025 | 0.01 | 0.005 | 0.001 |
100 | 61.918 | 67.328 | 70.065 | 74.222 | 77.929 | 82.358 | 90.133 | 99.334 | 109.141 | 118.498 | 124.342 | 129.561 | 135.807 | 140.170 | 149.449 |
500 | 407.946 | 422.303 | 429.387 | 439.936 | 449.147 | 459.926 | 478.323 | 499.334 | 520.950 | 540.930 | 553.127 | 563.851 | 576.493 | 585.206 | 603.446 |