F分布表(上側確率 0.05)
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 12 | 15 | 20 | 24 | 30 | 40 | 60 | 120 | ∞ | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1 | 161.4 | 199.5 | 215.7 | 224.6 | 230.2 | 234.0 | 236.8 | 238.9 | 240.5 | 241.9 | 243.9 | 245.9 | 248.0 | 249.1 | 250.1 | 251.1 | 252.2 | 253.3 | 254.3 |
2 | 18.51 | 19.00 | 19.16 | 19.25 | 19.30 | 19.33 | 19.35 | 19.37 | 19.38 | 19.40 | 19.41 | 19.43 | 19.45 | 19.45 | 19.46 | 19.47 | 19.48 | 19.49 | 19.50 |
3 | 10.13 | 9.552 | 9.277 | 9.117 | 9.013 | 8.941 | 8.887 | 8.845 | 8.812 | 8.786 | 8.745 | 8.703 | 8.660 | 8.639 | 8.617 | 8.594 | 8.572 | 8.549 | 8.527 |
4 | 7.709 | 6.944 | 6.591 | 6.388 | 6.256 | 6.163 | 6.094 | 6.041 | 5.999 | 5.964 | 5.912 | 5.858 | 5.803 | 5.774 | 5.746 | 5.717 | 5.688 | 5.658 | 5.628 |
5 | 6.608 | 5.786 | 5.409 | 5.192 | 5.050 | 4.950 | 4.876 | 4.818 | 4.772 | 4.735 | 4.678 | 4.619 | 4.558 | 4.527 | 4.496 | 4.464 | 4.431 | 4.398 | 4.365 |
6 | 5.987 | 5.143 | 4.757 | 4.534 | 4.387 | 4.284 | 4.207 | 4.147 | 4.099 | 4.060 | 4.000 | 3.938 | 3.874 | 3.841 | 3.808 | 3.774 | 3.740 | 3.705 | 3.669 |
7 | 5.591 | 4.737 | 4.347 | 4.120 | 3.972 | 3.866 | 3.787 | 3.726 | 3.677 | 3.637 | 3.575 | 3.511 | 3.445 | 3.410 | 3.376 | 3.340 | 3.304 | 3.267 | 3.230 |
8 | 5.318 | 4.459 | 4.066 | 3.838 | 3.687 | 3.581 | 3.500 | 3.438 | 3.388 | 3.347 | 3.284 | 3.218 | 3.150 | 3.115 | 3.079 | 3.043 | 3.005 | 2.967 | 2.928 |
9 | 5.117 | 4.256 | 3.863 | 3.633 | 3.482 | 3.374 | 3.293 | 3.230 | 3.179 | 3.137 | 3.073 | 3.006 | 2.936 | 2.900 | 2.864 | 2.826 | 2.787 | 2.748 | 2.707 |
10 | 4.965 | 4.103 | 3.708 | 3.478 | 3.326 | 3.217 | 3.135 | 3.072 | 3.020 | 2.978 | 2.913 | 2.845 | 2.774 | 2.737 | 2.700 | 2.661 | 2.621 | 2.580 | 2.538 |
11 | 4.844 | 3.982 | 3.587 | 3.357 | 3.204 | 3.095 | 3.012 | 2.948 | 2.896 | 2.854 | 2.788 | 2.719 | 2.646 | 2.609 | 2.570 | 2.531 | 2.490 | 2.448 | 2.405 |
12 | 4.747 | 3.885 | 3.490 | 3.259 | 3.106 | 2.996 | 2.913 | 2.849 | 2.796 | 2.753 | 2.687 | 2.617 | 2.544 | 2.505 | 2.466 | 2.426 | 2.384 | 2.341 | 2.297 |
13 | 4.667 | 3.806 | 3.411 | 3.179 | 3.025 | 2.915 | 2.832 | 2.767 | 2.714 | 2.671 | 2.604 | 2.533 | 2.459 | 2.420 | 2.380 | 2.339 | 2.297 | 2.252 | 2.207 |
14 | 4.600 | 3.739 | 3.344 | 3.112 | 2.958 | 2.848 | 2.764 | 2.699 | 2.646 | 2.602 | 2.534 | 2.463 | 2.388 | 2.349 | 2.308 | 2.266 | 2.223 | 2.178 | 2.131 |
15 | 4.543 | 3.682 | 3.287 | 3.056 | 2.901 | 2.790 | 2.707 | 2.641 | 2.588 | 2.544 | 2.475 | 2.403 | 2.328 | 2.288 | 2.247 | 2.204 | 2.160 | 2.114 | 2.066 |
16 | 4.494 | 3.634 | 3.239 | 3.007 | 2.852 | 2.741 | 2.657 | 2.591 | 2.538 | 2.494 | 2.425 | 2.352 | 2.276 | 2.235 | 2.194 | 2.151 | 2.106 | 2.059 | 2.010 |
17 | 4.451 | 3.592 | 3.197 | 2.965 | 2.810 | 2.699 | 2.614 | 2.548 | 2.494 | 2.450 | 2.381 | 2.308 | 2.230 | 2.190 | 2.148 | 2.104 | 2.058 | 2.011 | 1.961 |
18 | 4.414 | 3.555 | 3.160 | 2.928 | 2.773 | 2.661 | 2.577 | 2.510 | 2.456 | 2.412 | 2.342 | 2.269 | 2.191 | 2.150 | 2.107 | 2.063 | 2.017 | 1.968 | 1.917 |
19 | 4.381 | 3.522 | 3.127 | 2.895 | 2.740 | 2.628 | 2.544 | 2.477 | 2.423 | 2.378 | 2.308 | 2.234 | 2.155 | 2.114 | 2.071 | 2.026 | 1.980 | 1.930 | 1.879 |
20 | 4.351 | 3.493 | 3.098 | 2.866 | 2.711 | 2.599 | 2.514 | 2.447 | 2.393 | 2.348 | 2.278 | 2.203 | 2.124 | 2.082 | 2.039 | 1.994 | 1.946 | 1.896 | 1.844 |
21 | 4.325 | 3.467 | 3.072 | 2.840 | 2.685 | 2.573 | 2.488 | 2.420 | 2.366 | 2.321 | 2.250 | 2.176 | 2.096 | 2.054 | 2.010 | 1.965 | 1.916 | 1.866 | 1.812 |
22 | 4.301 | 3.443 | 3.049 | 2.817 | 2.661 | 2.549 | 2.464 | 2.397 | 2.342 | 2.297 | 2.226 | 2.151 | 2.071 | 2.028 | 1.984 | 1.938 | 1.889 | 1.838 | 1.784 |
23 | 4.279 | 3.422 | 3.028 | 2.796 | 2.640 | 2.528 | 2.442 | 2.375 | 2.320 | 2.275 | 2.204 | 2.128 | 2.048 | 2.005 | 1.961 | 1.914 | 1.865 | 1.813 | 1.758 |
24 | 4.260 | 3.403 | 3.009 | 2.776 | 2.621 | 2.508 | 2.423 | 2.355 | 2.300 | 2.255 | 2.183 | 2.108 | 2.027 | 1.984 | 1.939 | 1.892 | 1.842 | 1.790 | 1.734 |
25 | 4.242 | 3.385 | 2.991 | 2.759 | 2.603 | 2.490 | 2.405 | 2.337 | 2.282 | 2.236 | 2.165 | 2.089 | 2.007 | 1.964 | 1.919 | 1.872 | 1.822 | 1.768 | 1.712 |
26 | 4.225 | 3.369 | 2.975 | 2.743 | 2.587 | 2.474 | 2.388 | 2.321 | 2.265 | 2.220 | 2.148 | 2.072 | 1.990 | 1.946 | 1.901 | 1.853 | 1.803 | 1.749 | 1.691 |
27 | 4.210 | 3.354 | 2.960 | 2.728 | 2.572 | 2.459 | 2.373 | 2.305 | 2.250 | 2.204 | 2.132 | 2.056 | 1.974 | 1.930 | 1.884 | 1.836 | 1.785 | 1.731 | 1.672 |
28 | 4.196 | 3.340 | 2.947 | 2.714 | 2.558 | 2.445 | 2.359 | 2.291 | 2.236 | 2.190 | 2.118 | 2.041 | 1.959 | 1.915 | 1.869 | 1.820 | 1.769 | 1.714 | 1.655 |
29 | 4.183 | 3.328 | 2.934 | 2.701 | 2.545 | 2.432 | 2.346 | 2.278 | 2.223 | 2.177 | 2.104 | 2.027 | 1.945 | 1.901 | 1.854 | 1.806 | 1.754 | 1.698 | 1.638 |
30 | 4.171 | 3.316 | 2.922 | 2.690 | 2.534 | 2.421 | 2.334 | 2.266 | 2.211 | 2.165 | 2.092 | 2.015 | 1.932 | 1.887 | 1.841 | 1.792 | 1.740 | 1.683 | 1.623 |
40 | 4.085 | 3.232 | 2.839 | 2.606 | 2.449 | 2.336 | 2.249 | 2.180 | 2.124 | 2.077 | 2.003 | 1.924 | 1.839 | 1.793 | 1.744 | 1.693 | 1.637 | 1.577 | 1.510 |
60 | 4.001 | 3.150 | 2.758 | 2.525 | 2.368 | 2.254 | 2.167 | 2.097 | 2.040 | 1.993 | 1.917 | 1.836 | 1.748 | 1.700 | 1.649 | 1.594 | 1.534 | 1.467 | 1.390 |
120 | 3.920 | 3.072 | 2.680 | 2.447 | 2.290 | 2.175 | 2.087 | 2.016 | 1.959 | 1.910 | 1.834 | 1.750 | 1.659 | 1.608 | 1.554 | 1.495 | 1.429 | 1.352 | 1.255 |
∞ | 3.842 | 2.997 | 2.606 | 2.373 | 2.215 | 2.099 | 2.011 | 1.939 | 1.881 | 1.832 | 1.753 | 1.667 | 1.572 | 1.518 | 1.460 | 1.395 | 1.319 | 1.223 | 1.033 |
F分布表(上側確率 0.01)
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 12 | 15 | 20 | 24 | 30 | 40 | 60 | 120 | ∞ | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1 | 4052. | 4999. | 5403. | 5625. | 5764. | 5859. | 5928. | 5981. | 6022. | 6056. | 6106. | 6157. | 6209. | 6235. | 6261. | 6287. | 6313. | 6339. | 6366. |
2 | 98.50 | 99.00 | 99.17 | 99.25 | 99.30 | 99.33 | 99.36 | 99.37 | 99.39 | 99.40 | 99.42 | 99.43 | 99.45 | 99.46 | 99.47 | 99.47 | 99.48 | 99.49 | 99.50 |
3 | 34.12 | 30.82 | 29.46 | 28.71 | 28.24 | 27.91 | 27.67 | 27.49 | 27.35 | 27.23 | 27.05 | 26.87 | 26.69 | 26.60 | 26.50 | 26.41 | 26.32 | 26.22 | 26.13 |
4 | 21.20 | 18.00 | 16.69 | 15.98 | 15.52 | 15.21 | 14.98 | 14.80 | 14.66 | 14.55 | 14.37 | 14.20 | 14.02 | 13.93 | 13.84 | 13.75 | 13.65 | 13.56 | 13.46 |
5 | 16.26 | 13.27 | 12.06 | 11.39 | 10.97 | 10.67 | 10.46 | 10.29 | 10.16 | 10.05 | 9.888 | 9.722 | 9.553 | 9.466 | 9.379 | 9.291 | 9.202 | 9.112 | 9.022 |
6 | 13.75 | 10.92 | 9.780 | 9.148 | 8.746 | 8.466 | 8.260 | 8.102 | 7.976 | 7.874 | 7.718 | 7.559 | 7.396 | 7.313 | 7.229 | 7.143 | 7.057 | 6.969 | 6.881 |
7 | 12.25 | 9.547 | 8.451 | 7.847 | 7.460 | 7.191 | 6.993 | 6.840 | 6.719 | 6.620 | 6.469 | 6.314 | 6.155 | 6.074 | 5.992 | 5.908 | 5.824 | 5.737 | 5.651 |
8 | 11.26 | 8.649 | 7.591 | 7.006 | 6.632 | 6.371 | 6.178 | 6.029 | 5.911 | 5.814 | 5.667 | 5.515 | 5.359 | 5.279 | 5.198 | 5.116 | 5.032 | 4.946 | 4.860 |
9 | 10.56 | 8.022 | 6.992 | 6.422 | 6.057 | 5.802 | 5.613 | 5.467 | 5.351 | 5.257 | 5.111 | 4.962 | 4.808 | 4.729 | 4.649 | 4.567 | 4.483 | 4.398 | 4.312 |
10 | 10.04 | 7.559 | 6.552 | 5.994 | 5.636 | 5.386 | 5.200 | 5.057 | 4.942 | 4.849 | 4.706 | 4.558 | 4.405 | 4.327 | 4.247 | 4.165 | 4.082 | 3.996 | 3.910 |
11 | 9.646 | 7.206 | 6.217 | 5.668 | 5.316 | 5.069 | 4.886 | 4.744 | 4.632 | 4.539 | 4.397 | 4.251 | 4.099 | 4.021 | 3.941 | 3.860 | 3.776 | 3.690 | 3.604 |
12 | 9.330 | 6.927 | 5.953 | 5.412 | 5.064 | 4.821 | 4.640 | 4.499 | 4.388 | 4.296 | 4.155 | 4.010 | 3.858 | 3.780 | 3.701 | 3.619 | 3.535 | 3.449 | 3.362 |
13 | 9.074 | 6.701 | 5.739 | 5.205 | 4.862 | 4.620 | 4.441 | 4.302 | 4.191 | 4.100 | 3.960 | 3.815 | 3.665 | 3.587 | 3.507 | 3.425 | 3.341 | 3.255 | 3.166 |
14 | 8.862 | 6.515 | 5.564 | 5.035 | 4.695 | 4.456 | 4.278 | 4.140 | 4.030 | 3.939 | 3.800 | 3.656 | 3.505 | 3.427 | 3.348 | 3.266 | 3.181 | 3.094 | 3.005 |
15 | 8.683 | 6.359 | 5.417 | 4.893 | 4.556 | 4.318 | 4.142 | 4.004 | 3.895 | 3.805 | 3.666 | 3.522 | 3.372 | 3.294 | 3.214 | 3.132 | 3.047 | 2.959 | 2.870 |
16 | 8.531 | 6.226 | 5.292 | 4.773 | 4.437 | 4.202 | 4.026 | 3.890 | 3.780 | 3.691 | 3.553 | 3.409 | 3.259 | 3.181 | 3.101 | 3.018 | 2.933 | 2.845 | 2.754 |
17 | 8.400 | 6.112 | 5.185 | 4.669 | 4.336 | 4.102 | 3.927 | 3.791 | 3.682 | 3.593 | 3.455 | 3.312 | 3.162 | 3.084 | 3.003 | 2.920 | 2.835 | 2.746 | 2.654 |
18 | 8.285 | 6.013 | 5.092 | 4.579 | 4.248 | 4.015 | 3.841 | 3.705 | 3.597 | 3.508 | 3.371 | 3.227 | 3.077 | 2.999 | 2.919 | 2.835 | 2.749 | 2.660 | 2.567 |
19 | 8.185 | 5.926 | 5.010 | 4.500 | 4.171 | 3.939 | 3.765 | 3.631 | 3.523 | 3.434 | 3.297 | 3.153 | 3.003 | 2.925 | 2.844 | 2.761 | 2.674 | 2.584 | 2.490 |
20 | 8.096 | 5.849 | 4.938 | 4.431 | 4.103 | 3.871 | 3.699 | 3.564 | 3.457 | 3.368 | 3.231 | 3.088 | 2.938 | 2.859 | 2.778 | 2.695 | 2.608 | 2.517 | 2.422 |
21 | 8.017 | 5.780 | 4.874 | 4.369 | 4.042 | 3.812 | 3.640 | 3.506 | 3.398 | 3.310 | 3.173 | 3.030 | 2.880 | 2.801 | 2.720 | 2.636 | 2.548 | 2.457 | 2.361 |
22 | 7.945 | 5.719 | 4.817 | 4.313 | 3.988 | 3.758 | 3.587 | 3.453 | 3.346 | 3.258 | 3.121 | 2.978 | 2.827 | 2.749 | 2.667 | 2.583 | 2.495 | 2.403 | 2.307 |
23 | 7.881 | 5.664 | 4.765 | 4.264 | 3.939 | 3.710 | 3.539 | 3.406 | 3.299 | 3.211 | 3.074 | 2.931 | 2.781 | 2.702 | 2.620 | 2.535 | 2.447 | 2.354 | 2.257 |
24 | 7.823 | 5.614 | 4.718 | 4.218 | 3.895 | 3.667 | 3.496 | 3.363 | 3.256 | 3.168 | 3.032 | 2.889 | 2.738 | 2.659 | 2.577 | 2.492 | 2.403 | 2.310 | 2.212 |
25 | 7.770 | 5.568 | 4.675 | 4.177 | 3.855 | 3.627 | 3.457 | 3.324 | 3.217 | 3.129 | 2.993 | 2.850 | 2.699 | 2.620 | 2.538 | 2.453 | 2.364 | 2.270 | 2.171 |
26 | 7.721 | 5.526 | 4.637 | 4.140 | 3.818 | 3.591 | 3.421 | 3.288 | 3.182 | 3.094 | 2.958 | 2.815 | 2.664 | 2.585 | 2.503 | 2.417 | 2.327 | 2.233 | 2.133 |
27 | 7.677 | 5.488 | 4.601 | 4.106 | 3.785 | 3.558 | 3.388 | 3.256 | 3.149 | 3.062 | 2.926 | 2.783 | 2.632 | 2.552 | 2.470 | 2.384 | 2.294 | 2.198 | 2.098 |
28 | 7.636 | 5.453 | 4.568 | 4.074 | 3.754 | 3.528 | 3.358 | 3.226 | 3.120 | 3.032 | 2.896 | 2.753 | 2.602 | 2.522 | 2.440 | 2.354 | 2.263 | 2.167 | 2.065 |
29 | 7.598 | 5.420 | 4.538 | 4.045 | 3.725 | 3.499 | 3.330 | 3.198 | 3.092 | 3.005 | 2.868 | 2.726 | 2.574 | 2.495 | 2.412 | 2.325 | 2.234 | 2.138 | 2.035 |
30 | 7.562 | 5.390 | 4.510 | 4.018 | 3.699 | 3.473 | 3.304 | 3.173 | 3.067 | 2.979 | 2.843 | 2.700 | 2.549 | 2.469 | 2.386 | 2.299 | 2.208 | 2.111 | 2.008 |
40 | 7.314 | 5.179 | 4.313 | 3.828 | 3.514 | 3.291 | 3.124 | 2.993 | 2.888 | 2.801 | 2.665 | 2.522 | 2.369 | 2.288 | 2.203 | 2.114 | 2.019 | 1.917 | 1.806 |
60 | 7.077 | 4.977 | 4.126 | 3.649 | 3.339 | 3.119 | 2.953 | 2.823 | 2.718 | 2.632 | 2.496 | 2.352 | 2.198 | 2.115 | 2.028 | 1.936 | 1.836 | 1.726 | 1.602 |
120 | 6.851 | 4.787 | 3.949 | 3.480 | 3.174 | 2.956 | 2.792 | 2.663 | 2.559 | 2.472 | 2.336 | 2.192 | 2.035 | 1.950 | 1.860 | 1.763 | 1.656 | 1.533 | 1.383 |
∞ | 6.637 | 4.607 | 3.784 | 3.321 | 3.019 | 2.804 | 2.641 | 2.513 | 2.409 | 2.323 | 2.187 | 2.040 | 1.880 | 1.793 | 1.698 | 1.594 | 1.475 | 1.327 | 1.048 |