Home 正規分布1 正規分布2 カイ2乗分布 t分布 F分布
1. F分布(0.05) | 2. F分布(0.025) | 3. F分布(0.01) | 4. F分布(0.005)
α=0.05 のとき,表頭の自由度 m と表側の自由度 n に対して,F分布の上側 α 点 Fα(m,n) を示す。 \[ \alpha \longmapsto F_\alpha(m,n),\qquad \text{Pr}\{X>F_\alpha(m,n)\}=\alpha \] F1-α(m,n) と Fα(n,m) について, \[ F_{1-\alpha}(m,n)=\frac{1}{F_\alpha(n,m)},\qquad F_{0.95}(m,n)=\frac{1}{F_{0.05}(n,m)} \] が成り立つから,この表を用いて上側 0.95 点を求めることができる。
n∖m | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
1 | 161.4 | 199.5 | 215.7 | 224.6 | 230.2 | 234.0 | 236.8 | 238.9 | 240.5 | 241.9 |
2 | 18.51 | 19.00 | 19.16 | 19.25 | 19.30 | 19.33 | 19.35 | 19.37 | 19.38 | 19.40 |
3 | 10.13 | 9.552 | 9.277 | 9.117 | 9.013 | 8.941 | 8.887 | 8.845 | 8.812 | 8.786 |
4 | 7.709 | 6.944 | 6.591 | 6.388 | 6.256 | 6.163 | 6.094 | 6.041 | 5.999 | 5.964 |
5 | 6.608 | 5.786 | 5.409 | 5.192 | 5.050 | 4.950 | 4.876 | 4.818 | 4.772 | 4.735 |
6 | 5.987 | 5.143 | 4.757 | 4.534 | 4.387 | 4.284 | 4.207 | 4.147 | 4.099 | 4.060 |
7 | 5.591 | 4.737 | 4.347 | 4.120 | 3.972 | 3.866 | 3.787 | 3.726 | 3.677 | 3.637 |
8 | 5.318 | 4.459 | 4.066 | 3.838 | 3.687 | 3.581 | 3.500 | 3.438 | 3.388 | 3.347 |
9 | 5.117 | 4.256 | 3.863 | 3.633 | 3.482 | 3.374 | 3.293 | 3.230 | 3.179 | 3.137 |
10 | 4.965 | 4.103 | 3.708 | 3.478 | 3.326 | 3.217 | 3.135 | 3.072 | 3.020 | 2.978 |
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |
11 | 4.844 | 3.982 | 3.587 | 3.357 | 3.204 | 3.095 | 3.012 | 2.948 | 2.896 | 2.854 |
12 | 4.747 | 3.885 | 3.490 | 3.259 | 3.106 | 2.996 | 2.913 | 2.849 | 2.796 | 2.753 |
13 | 4.667 | 3.806 | 3.411 | 3.179 | 3.025 | 2.915 | 2.832 | 2.767 | 2.714 | 2.671 |
14 | 4.600 | 3.739 | 3.344 | 3.112 | 2.958 | 2.848 | 2.764 | 2.699 | 2.646 | 2.602 |
15 | 4.543 | 3.682 | 3.287 | 3.056 | 2.901 | 2.790 | 2.707 | 2.641 | 2.588 | 2.544 |
16 | 4.494 | 3.634 | 3.239 | 3.007 | 2.852 | 2.741 | 2.657 | 2.591 | 2.538 | 2.494 |
17 | 4.451 | 3.592 | 3.197 | 2.965 | 2.810 | 2.699 | 2.614 | 2.548 | 2.494 | 2.450 |
18 | 4.414 | 3.555 | 3.160 | 2.928 | 2.773 | 2.661 | 2.577 | 2.510 | 2.456 | 2.412 |
19 | 4.381 | 3.522 | 3.127 | 2.895 | 2.740 | 2.628 | 2.544 | 2.477 | 2.423 | 2.378 |
20 | 4.351 | 3.493 | 3.098 | 2.866 | 2.711 | 2.599 | 2.514 | 2.447 | 2.393 | 2.348 |
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |
21 | 4.325 | 3.467 | 3.072 | 2.840 | 2.685 | 2.573 | 2.488 | 2.420 | 2.366 | 2.321 |
22 | 4.301 | 3.443 | 3.049 | 2.817 | 2.661 | 2.549 | 2.464 | 2.397 | 2.342 | 2.297 |
23 | 4.279 | 3.422 | 3.028 | 2.796 | 2.640 | 2.528 | 2.442 | 2.375 | 2.320 | 2.275 |
24 | 4.260 | 3.403 | 3.009 | 2.776 | 2.621 | 2.508 | 2.423 | 2.355 | 2.300 | 2.255 |
25 | 4.242 | 3.385 | 2.991 | 2.759 | 2.603 | 2.490 | 2.405 | 2.337 | 2.282 | 2.236 |
26 | 4.225 | 3.369 | 2.975 | 2.743 | 2.587 | 2.474 | 2.388 | 2.321 | 2.265 | 2.220 |
27 | 4.210 | 3.354 | 2.960 | 2.728 | 2.572 | 2.459 | 2.373 | 2.305 | 2.250 | 2.204 |
28 | 4.196 | 3.340 | 2.947 | 2.714 | 2.558 | 2.445 | 2.359 | 2.291 | 2.236 | 2.190 |
29 | 4.183 | 3.328 | 2.934 | 2.701 | 2.545 | 2.432 | 2.346 | 2.278 | 2.223 | 2.177 |
30 | 4.171 | 3.316 | 2.922 | 2.690 | 2.534 | 2.421 | 2.334 | 2.266 | 2.211 | 2.165 |
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |
31 | 4.160 | 3.305 | 2.911 | 2.679 | 2.523 | 2.409 | 2.323 | 2.255 | 2.199 | 2.153 |
32 | 4.149 | 3.295 | 2.901 | 2.668 | 2.512 | 2.399 | 2.313 | 2.244 | 2.189 | 2.142 |
33 | 4.139 | 3.285 | 2.892 | 2.659 | 2.503 | 2.389 | 2.303 | 2.235 | 2.179 | 2.133 |
34 | 4.130 | 3.276 | 2.883 | 2.650 | 2.494 | 2.380 | 2.294 | 2.225 | 2.170 | 2.123 |
35 | 4.121 | 3.267 | 2.874 | 2.641 | 2.485 | 2.372 | 2.285 | 2.217 | 2.161 | 2.114 |
36 | 4.113 | 3.259 | 2.866 | 2.634 | 2.477 | 2.364 | 2.277 | 2.209 | 2.153 | 2.106 |
37 | 4.105 | 3.252 | 2.859 | 2.626 | 2.470 | 2.356 | 2.270 | 2.201 | 2.145 | 2.098 |
38 | 4.098 | 3.245 | 2.852 | 2.619 | 2.463 | 2.349 | 2.262 | 2.194 | 2.138 | 2.091 |
39 | 4.091 | 3.238 | 2.845 | 2.612 | 2.456 | 2.342 | 2.255 | 2.187 | 2.131 | 2.084 |
40 | 4.085 | 3.232 | 2.839 | 2.606 | 2.449 | 2.336 | 2.249 | 2.180 | 2.124 | 2.077 |
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |
41 | 4.079 | 3.226 | 2.833 | 2.600 | 2.443 | 2.330 | 2.243 | 2.174 | 2.118 | 2.071 |
42 | 4.073 | 3.220 | 2.827 | 2.594 | 2.438 | 2.324 | 2.237 | 2.168 | 2.112 | 2.065 |
43 | 4.067 | 3.214 | 2.822 | 2.589 | 2.432 | 2.318 | 2.232 | 2.163 | 2.106 | 2.059 |
44 | 4.062 | 3.209 | 2.816 | 2.584 | 2.427 | 2.313 | 2.226 | 2.157 | 2.101 | 2.054 |
45 | 4.057 | 3.204 | 2.812 | 2.579 | 2.422 | 2.308 | 2.221 | 2.152 | 2.096 | 2.049 |
46 | 4.052 | 3.200 | 2.807 | 2.574 | 2.417 | 2.304 | 2.216 | 2.147 | 2.091 | 2.044 |
47 | 4.047 | 3.195 | 2.802 | 2.570 | 2.413 | 2.299 | 2.212 | 2.143 | 2.086 | 2.039 |
48 | 4.043 | 3.191 | 2.798 | 2.565 | 2.409 | 2.295 | 2.207 | 2.138 | 2.082 | 2.035 |
49 | 4.038 | 3.187 | 2.794 | 2.561 | 2.404 | 2.290 | 2.203 | 2.134 | 2.077 | 2.030 |
50 | 4.034 | 3.183 | 2.790 | 2.557 | 2.400 | 2.286 | 2.199 | 2.130 | 2.073 | 2.026 |
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |
60 | 4.001 | 3.150 | 2.758 | 2.525 | 2.368 | 2.254 | 2.167 | 2.097 | 2.040 | 1.993 |
70 | 3.978 | 3.128 | 2.736 | 2.503 | 2.346 | 2.231 | 2.143 | 2.074 | 2.017 | 1.969 |
80 | 3.960 | 3.111 | 2.719 | 2.486 | 2.329 | 2.214 | 2.126 | 2.056 | 1.999 | 1.951 |
90 | 3.947 | 3.098 | 2.706 | 2.473 | 2.316 | 2.201 | 2.113 | 2.043 | 1.986 | 1.938 |
100 | 3.936 | 3.087 | 2.696 | 2.463 | 2.305 | 2.191 | 2.103 | 2.032 | 1.975 | 1.927 |
110 | 3.927 | 3.079 | 2.687 | 2.454 | 2.297 | 2.182 | 2.094 | 2.024 | 1.966 | 1.918 |
120 | 3.920 | 3.072 | 2.680 | 2.447 | 2.290 | 2.175 | 2.087 | 2.016 | 1.959 | 1.910 |
130 | 3.914 | 3.066 | 2.674 | 2.441 | 2.284 | 2.169 | 2.081 | 2.010 | 1.953 | 1.904 |
140 | 3.909 | 3.061 | 2.669 | 2.436 | 2.279 | 2.164 | 2.076 | 2.005 | 1.947 | 1.899 |
150 | 3.904 | 3.056 | 2.665 | 2.432 | 2.274 | 2.160 | 2.071 | 2.001 | 1.943 | 1.894 |
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |
160 | 3.900 | 3.053 | 2.661 | 2.428 | 2.271 | 2.156 | 2.067 | 1.997 | 1.939 | 1.890 |
170 | 3.897 | 3.049 | 2.658 | 2.425 | 2.267 | 2.152 | 2.064 | 1.993 | 1.935 | 1.887 |
180 | 3.894 | 3.046 | 2.655 | 2.422 | 2.264 | 2.149 | 2.061 | 1.990 | 1.932 | 1.884 |
190 | 3.891 | 3.043 | 2.652 | 2.419 | 2.262 | 2.147 | 2.058 | 1.987 | 1.929 | 1.881 |
200 | 3.888 | 3.041 | 2.650 | 2.417 | 2.259 | 2.144 | 2.056 | 1.985 | 1.927 | 1.878 |
210 | 3.886 | 3.039 | 2.648 | 2.415 | 2.257 | 2.142 | 2.053 | 1.983 | 1.925 | 1.876 |
220 | 3.884 | 3.037 | 2.646 | 2.413 | 2.255 | 2.140 | 2.051 | 1.981 | 1.923 | 1.874 |
230 | 3.882 | 3.035 | 2.644 | 2.411 | 2.253 | 2.138 | 2.050 | 1.979 | 1.921 | 1.872 |
240 | 3.880 | 3.033 | 2.642 | 2.409 | 2.252 | 2.136 | 2.048 | 1.977 | 1.919 | 1.870 |
250 | 3.879 | 3.032 | 2.641 | 2.408 | 2.250 | 2.135 | 2.046 | 1.976 | 1.917 | 1.869 |
n∖m | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |
1 | 243.0 | 243.9 | 244.7 | 245.4 | 245.9 | 246.5 | 246.9 | 247.3 | 247.7 | 248.0 |
2 | 19.40 | 19.41 | 19.42 | 19.42 | 19.43 | 19.43 | 19.44 | 19.44 | 19.44 | 19.45 |
3 | 8.763 | 8.745 | 8.729 | 8.715 | 8.703 | 8.692 | 8.683 | 8.675 | 8.667 | 8.660 |
4 | 5.936 | 5.912 | 5.891 | 5.873 | 5.858 | 5.844 | 5.832 | 5.821 | 5.811 | 5.803 |
5 | 4.704 | 4.678 | 4.655 | 4.636 | 4.619 | 4.604 | 4.590 | 4.579 | 4.568 | 4.558 |
6 | 4.027 | 4.000 | 3.976 | 3.956 | 3.938 | 3.922 | 3.908 | 3.896 | 3.884 | 3.874 |
7 | 3.603 | 3.575 | 3.550 | 3.529 | 3.511 | 3.494 | 3.480 | 3.467 | 3.455 | 3.445 |
8 | 3.313 | 3.284 | 3.259 | 3.237 | 3.218 | 3.202 | 3.187 | 3.173 | 3.161 | 3.150 |
9 | 3.102 | 3.073 | 3.048 | 3.025 | 3.006 | 2.989 | 2.974 | 2.960 | 2.948 | 2.936 |
10 | 2.943 | 2.913 | 2.887 | 2.865 | 2.845 | 2.828 | 2.812 | 2.798 | 2.785 | 2.774 |
11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | |
11 | 2.818 | 2.788 | 2.761 | 2.739 | 2.719 | 2.701 | 2.685 | 2.671 | 2.658 | 2.646 |
12 | 2.717 | 2.687 | 2.660 | 2.637 | 2.617 | 2.599 | 2.583 | 2.568 | 2.555 | 2.544 |
13 | 2.635 | 2.604 | 2.577 | 2.554 | 2.533 | 2.515 | 2.499 | 2.484 | 2.471 | 2.459 |
14 | 2.565 | 2.534 | 2.507 | 2.484 | 2.463 | 2.445 | 2.428 | 2.413 | 2.400 | 2.388 |
15 | 2.507 | 2.475 | 2.448 | 2.424 | 2.403 | 2.385 | 2.368 | 2.353 | 2.340 | 2.328 |
16 | 2.456 | 2.425 | 2.397 | 2.373 | 2.352 | 2.333 | 2.317 | 2.302 | 2.288 | 2.276 |
17 | 2.413 | 2.381 | 2.353 | 2.329 | 2.308 | 2.289 | 2.272 | 2.257 | 2.243 | 2.230 |
18 | 2.374 | 2.342 | 2.314 | 2.290 | 2.269 | 2.250 | 2.233 | 2.217 | 2.203 | 2.191 |
19 | 2.340 | 2.308 | 2.280 | 2.256 | 2.234 | 2.215 | 2.198 | 2.182 | 2.168 | 2.155 |
20 | 2.310 | 2.278 | 2.250 | 2.225 | 2.203 | 2.184 | 2.167 | 2.151 | 2.137 | 2.124 |
11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | |
21 | 2.283 | 2.250 | 2.222 | 2.197 | 2.176 | 2.156 | 2.139 | 2.123 | 2.109 | 2.096 |
22 | 2.259 | 2.226 | 2.198 | 2.173 | 2.151 | 2.131 | 2.114 | 2.098 | 2.084 | 2.071 |
23 | 2.236 | 2.204 | 2.175 | 2.150 | 2.128 | 2.109 | 2.091 | 2.075 | 2.061 | 2.048 |
24 | 2.216 | 2.183 | 2.155 | 2.130 | 2.108 | 2.088 | 2.070 | 2.054 | 2.040 | 2.027 |
25 | 2.198 | 2.165 | 2.136 | 2.111 | 2.089 | 2.069 | 2.051 | 2.035 | 2.021 | 2.007 |
26 | 2.181 | 2.148 | 2.119 | 2.094 | 2.072 | 2.052 | 2.034 | 2.018 | 2.003 | 1.990 |
27 | 2.166 | 2.132 | 2.103 | 2.078 | 2.056 | 2.036 | 2.018 | 2.002 | 1.987 | 1.974 |
28 | 2.151 | 2.118 | 2.089 | 2.064 | 2.041 | 2.021 | 2.003 | 1.987 | 1.972 | 1.959 |
29 | 2.138 | 2.104 | 2.075 | 2.050 | 2.027 | 2.007 | 1.989 | 1.973 | 1.958 | 1.945 |
30 | 2.126 | 2.092 | 2.063 | 2.037 | 2.015 | 1.995 | 1.976 | 1.960 | 1.945 | 1.932 |
11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | |
31 | 2.114 | 2.080 | 2.051 | 2.026 | 2.003 | 1.983 | 1.965 | 1.948 | 1.933 | 1.920 |
32 | 2.103 | 2.070 | 2.040 | 2.015 | 1.992 | 1.972 | 1.953 | 1.937 | 1.922 | 1.908 |
33 | 2.093 | 2.060 | 2.030 | 2.004 | 1.982 | 1.961 | 1.943 | 1.926 | 1.911 | 1.898 |
34 | 2.084 | 2.050 | 2.021 | 1.995 | 1.972 | 1.952 | 1.933 | 1.917 | 1.902 | 1.888 |
35 | 2.075 | 2.041 | 2.012 | 1.986 | 1.963 | 1.942 | 1.924 | 1.907 | 1.892 | 1.878 |
36 | 2.067 | 2.033 | 2.003 | 1.977 | 1.954 | 1.934 | 1.915 | 1.899 | 1.883 | 1.870 |
37 | 2.059 | 2.025 | 1.995 | 1.969 | 1.946 | 1.926 | 1.907 | 1.890 | 1.875 | 1.861 |
38 | 2.051 | 2.017 | 1.988 | 1.962 | 1.939 | 1.918 | 1.899 | 1.883 | 1.867 | 1.853 |
39 | 2.044 | 2.010 | 1.981 | 1.954 | 1.931 | 1.911 | 1.892 | 1.875 | 1.860 | 1.846 |
40 | 2.038 | 2.003 | 1.974 | 1.948 | 1.924 | 1.904 | 1.885 | 1.868 | 1.853 | 1.839 |
11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | |
41 | 2.031 | 1.997 | 1.967 | 1.941 | 1.918 | 1.897 | 1.879 | 1.862 | 1.846 | 1.832 |
42 | 2.025 | 1.991 | 1.961 | 1.935 | 1.912 | 1.891 | 1.872 | 1.855 | 1.840 | 1.826 |
43 | 2.020 | 1.985 | 1.955 | 1.929 | 1.906 | 1.885 | 1.866 | 1.849 | 1.834 | 1.820 |
44 | 2.014 | 1.980 | 1.950 | 1.924 | 1.900 | 1.879 | 1.861 | 1.844 | 1.828 | 1.814 |
45 | 2.009 | 1.974 | 1.945 | 1.918 | 1.895 | 1.874 | 1.855 | 1.838 | 1.823 | 1.808 |
46 | 2.004 | 1.969 | 1.940 | 1.913 | 1.890 | 1.869 | 1.850 | 1.833 | 1.817 | 1.803 |
47 | 1.999 | 1.965 | 1.935 | 1.908 | 1.885 | 1.864 | 1.845 | 1.828 | 1.812 | 1.798 |
48 | 1.995 | 1.960 | 1.930 | 1.904 | 1.880 | 1.859 | 1.840 | 1.823 | 1.807 | 1.793 |
49 | 1.990 | 1.956 | 1.926 | 1.899 | 1.876 | 1.855 | 1.836 | 1.819 | 1.803 | 1.789 |
50 | 1.986 | 1.952 | 1.921 | 1.895 | 1.871 | 1.850 | 1.831 | 1.814 | 1.798 | 1.784 |
11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | |
60 | 1.952 | 1.917 | 1.887 | 1.860 | 1.836 | 1.815 | 1.796 | 1.778 | 1.763 | 1.748 |
70 | 1.928 | 1.893 | 1.863 | 1.836 | 1.812 | 1.790 | 1.771 | 1.753 | 1.737 | 1.722 |
80 | 1.910 | 1.875 | 1.845 | 1.817 | 1.793 | 1.772 | 1.752 | 1.734 | 1.718 | 1.703 |
90 | 1.897 | 1.861 | 1.830 | 1.803 | 1.779 | 1.757 | 1.737 | 1.720 | 1.703 | 1.688 |
100 | 1.886 | 1.850 | 1.819 | 1.792 | 1.768 | 1.746 | 1.726 | 1.708 | 1.691 | 1.676 |
110 | 1.877 | 1.841 | 1.810 | 1.783 | 1.758 | 1.736 | 1.716 | 1.698 | 1.682 | 1.667 |
120 | 1.869 | 1.834 | 1.803 | 1.775 | 1.750 | 1.728 | 1.709 | 1.690 | 1.674 | 1.659 |
130 | 1.863 | 1.827 | 1.796 | 1.769 | 1.744 | 1.722 | 1.702 | 1.684 | 1.667 | 1.652 |
140 | 1.858 | 1.822 | 1.791 | 1.763 | 1.738 | 1.716 | 1.696 | 1.678 | 1.661 | 1.646 |
150 | 1.853 | 1.817 | 1.786 | 1.758 | 1.734 | 1.711 | 1.691 | 1.673 | 1.656 | 1.641 |
11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | |
160 | 1.849 | 1.813 | 1.782 | 1.754 | 1.729 | 1.707 | 1.687 | 1.669 | 1.652 | 1.637 |
170 | 1.845 | 1.810 | 1.778 | 1.750 | 1.726 | 1.703 | 1.683 | 1.665 | 1.648 | 1.633 |
180 | 1.842 | 1.806 | 1.775 | 1.747 | 1.722 | 1.700 | 1.680 | 1.661 | 1.645 | 1.629 |
190 | 1.839 | 1.803 | 1.772 | 1.744 | 1.719 | 1.697 | 1.677 | 1.658 | 1.642 | 1.626 |
200 | 1.837 | 1.801 | 1.769 | 1.742 | 1.717 | 1.694 | 1.674 | 1.656 | 1.639 | 1.623 |
210 | 1.834 | 1.799 | 1.767 | 1.739 | 1.714 | 1.692 | 1.672 | 1.653 | 1.636 | 1.621 |
220 | 1.832 | 1.796 | 1.765 | 1.737 | 1.712 | 1.690 | 1.669 | 1.651 | 1.634 | 1.618 |
230 | 1.830 | 1.794 | 1.763 | 1.735 | 1.710 | 1.688 | 1.667 | 1.649 | 1.632 | 1.616 |
240 | 1.829 | 1.793 | 1.761 | 1.733 | 1.708 | 1.686 | 1.665 | 1.647 | 1.630 | 1.614 |
250 | 1.827 | 1.791 | 1.759 | 1.732 | 1.707 | 1.684 | 1.664 | 1.645 | 1.628 | 1.613 |
n∖m | 30 | 40 | 50 | 60 | 70 | 80 | 90 | 100 | 110 | 120 |
1 | 250.1 | 251.1 | 251.8 | 252.2 | 252.5 | 252.7 | 252.9 | 253.0 | 253.2 | 253.3 |
2 | 19.46 | 19.47 | 19.48 | 19.48 | 19.48 | 19.48 | 19.48 | 19.49 | 19.49 | 19.49 |
3 | 8.617 | 8.594 | 8.581 | 8.572 | 8.566 | 8.561 | 8.557 | 8.554 | 8.551 | 8.549 |
4 | 5.746 | 5.717 | 5.699 | 5.688 | 5.679 | 5.673 | 5.668 | 5.664 | 5.661 | 5.658 |
5 | 4.496 | 4.464 | 4.444 | 4.431 | 4.422 | 4.415 | 4.409 | 4.405 | 4.401 | 4.398 |
6 | 3.808 | 3.774 | 3.754 | 3.740 | 3.730 | 3.722 | 3.716 | 3.712 | 3.708 | 3.705 |
7 | 3.376 | 3.340 | 3.319 | 3.304 | 3.294 | 3.286 | 3.280 | 3.275 | 3.271 | 3.267 |
8 | 3.079 | 3.043 | 3.020 | 3.005 | 2.994 | 2.986 | 2.980 | 2.975 | 2.970 | 2.967 |
9 | 2.864 | 2.826 | 2.803 | 2.787 | 2.776 | 2.768 | 2.761 | 2.756 | 2.751 | 2.748 |
10 | 2.700 | 2.661 | 2.637 | 2.621 | 2.610 | 2.601 | 2.594 | 2.588 | 2.584 | 2.580 |
30 | 40 | 50 | 60 | 70 | 80 | 90 | 100 | 110 | 120 | |
11 | 2.570 | 2.531 | 2.507 | 2.490 | 2.478 | 2.469 | 2.462 | 2.457 | 2.452 | 2.448 |
12 | 2.466 | 2.426 | 2.401 | 2.384 | 2.372 | 2.363 | 2.356 | 2.350 | 2.345 | 2.341 |
13 | 2.380 | 2.339 | 2.314 | 2.297 | 2.284 | 2.275 | 2.267 | 2.261 | 2.257 | 2.252 |
14 | 2.308 | 2.266 | 2.241 | 2.223 | 2.210 | 2.201 | 2.193 | 2.187 | 2.182 | 2.178 |
15 | 2.247 | 2.204 | 2.178 | 2.160 | 2.147 | 2.137 | 2.130 | 2.123 | 2.118 | 2.114 |
16 | 2.194 | 2.151 | 2.124 | 2.106 | 2.093 | 2.083 | 2.075 | 2.068 | 2.063 | 2.059 |
17 | 2.148 | 2.104 | 2.077 | 2.058 | 2.045 | 2.035 | 2.027 | 2.020 | 2.015 | 2.011 |
18 | 2.107 | 2.063 | 2.035 | 2.017 | 2.003 | 1.993 | 1.985 | 1.978 | 1.973 | 1.968 |
19 | 2.071 | 2.026 | 1.999 | 1.980 | 1.966 | 1.955 | 1.947 | 1.940 | 1.935 | 1.930 |
20 | 2.039 | 1.994 | 1.966 | 1.946 | 1.932 | 1.922 | 1.913 | 1.907 | 1.901 | 1.896 |
30 | 40 | 50 | 60 | 70 | 80 | 90 | 100 | 110 | 120 | |
21 | 2.010 | 1.965 | 1.936 | 1.916 | 1.902 | 1.891 | 1.883 | 1.876 | 1.870 | 1.866 |
22 | 1.984 | 1.938 | 1.909 | 1.889 | 1.875 | 1.864 | 1.856 | 1.849 | 1.843 | 1.838 |
23 | 1.961 | 1.914 | 1.885 | 1.865 | 1.850 | 1.839 | 1.830 | 1.823 | 1.818 | 1.813 |
24 | 1.939 | 1.892 | 1.863 | 1.842 | 1.828 | 1.816 | 1.808 | 1.800 | 1.795 | 1.790 |
25 | 1.919 | 1.872 | 1.842 | 1.822 | 1.807 | 1.796 | 1.787 | 1.779 | 1.773 | 1.768 |
26 | 1.901 | 1.853 | 1.823 | 1.803 | 1.788 | 1.776 | 1.767 | 1.760 | 1.754 | 1.749 |
27 | 1.884 | 1.836 | 1.806 | 1.785 | 1.770 | 1.758 | 1.749 | 1.742 | 1.736 | 1.731 |
28 | 1.869 | 1.820 | 1.790 | 1.769 | 1.754 | 1.742 | 1.733 | 1.725 | 1.719 | 1.714 |
29 | 1.854 | 1.806 | 1.775 | 1.754 | 1.738 | 1.726 | 1.717 | 1.710 | 1.703 | 1.698 |
30 | 1.841 | 1.792 | 1.761 | 1.740 | 1.724 | 1.712 | 1.703 | 1.695 | 1.689 | 1.683 |
30 | 40 | 50 | 60 | 70 | 80 | 90 | 100 | 110 | 120 | |
31 | 1.828 | 1.779 | 1.748 | 1.726 | 1.711 | 1.699 | 1.689 | 1.681 | 1.675 | 1.670 |
32 | 1.817 | 1.767 | 1.736 | 1.714 | 1.698 | 1.686 | 1.676 | 1.669 | 1.662 | 1.657 |
33 | 1.806 | 1.756 | 1.724 | 1.702 | 1.686 | 1.674 | 1.665 | 1.657 | 1.650 | 1.645 |
34 | 1.795 | 1.745 | 1.713 | 1.691 | 1.675 | 1.663 | 1.653 | 1.645 | 1.639 | 1.633 |
35 | 1.786 | 1.735 | 1.703 | 1.681 | 1.665 | 1.652 | 1.643 | 1.635 | 1.628 | 1.623 |
36 | 1.776 | 1.726 | 1.694 | 1.671 | 1.655 | 1.643 | 1.633 | 1.625 | 1.618 | 1.612 |
37 | 1.768 | 1.717 | 1.685 | 1.662 | 1.646 | 1.633 | 1.623 | 1.615 | 1.608 | 1.603 |
38 | 1.760 | 1.708 | 1.676 | 1.653 | 1.637 | 1.624 | 1.614 | 1.606 | 1.599 | 1.594 |
39 | 1.752 | 1.700 | 1.668 | 1.645 | 1.628 | 1.616 | 1.606 | 1.597 | 1.591 | 1.585 |
40 | 1.744 | 1.693 | 1.660 | 1.637 | 1.621 | 1.608 | 1.597 | 1.589 | 1.582 | 1.577 |
30 | 40 | 50 | 60 | 70 | 80 | 90 | 100 | 110 | 120 | |
41 | 1.737 | 1.686 | 1.653 | 1.630 | 1.613 | 1.600 | 1.590 | 1.581 | 1.575 | 1.569 |
42 | 1.731 | 1.679 | 1.646 | 1.623 | 1.606 | 1.593 | 1.582 | 1.574 | 1.567 | 1.561 |
43 | 1.724 | 1.672 | 1.639 | 1.616 | 1.599 | 1.586 | 1.575 | 1.567 | 1.560 | 1.554 |
44 | 1.718 | 1.666 | 1.633 | 1.609 | 1.592 | 1.579 | 1.569 | 1.560 | 1.553 | 1.547 |
45 | 1.713 | 1.660 | 1.626 | 1.603 | 1.586 | 1.573 | 1.562 | 1.554 | 1.547 | 1.541 |
46 | 1.707 | 1.654 | 1.621 | 1.597 | 1.580 | 1.567 | 1.556 | 1.547 | 1.540 | 1.534 |
47 | 1.702 | 1.649 | 1.615 | 1.591 | 1.574 | 1.561 | 1.550 | 1.541 | 1.534 | 1.528 |
48 | 1.697 | 1.644 | 1.610 | 1.586 | 1.568 | 1.555 | 1.544 | 1.536 | 1.528 | 1.522 |
49 | 1.692 | 1.639 | 1.604 | 1.581 | 1.563 | 1.550 | 1.539 | 1.530 | 1.523 | 1.517 |
50 | 1.687 | 1.634 | 1.599 | 1.576 | 1.558 | 1.544 | 1.534 | 1.525 | 1.518 | 1.511 |
30 | 40 | 50 | 60 | 70 | 80 | 90 | 100 | 110 | 120 | |
60 | 1.649 | 1.594 | 1.559 | 1.534 | 1.516 | 1.502 | 1.491 | 1.481 | 1.474 | 1.467 |
70 | 1.622 | 1.566 | 1.530 | 1.505 | 1.486 | 1.471 | 1.459 | 1.450 | 1.442 | 1.435 |
80 | 1.602 | 1.545 | 1.508 | 1.482 | 1.463 | 1.448 | 1.436 | 1.426 | 1.418 | 1.411 |
90 | 1.586 | 1.528 | 1.491 | 1.465 | 1.445 | 1.429 | 1.417 | 1.407 | 1.399 | 1.391 |
100 | 1.573 | 1.515 | 1.477 | 1.450 | 1.430 | 1.415 | 1.402 | 1.392 | 1.383 | 1.376 |
110 | 1.563 | 1.504 | 1.466 | 1.439 | 1.418 | 1.402 | 1.390 | 1.379 | 1.370 | 1.363 |
120 | 1.554 | 1.495 | 1.457 | 1.429 | 1.408 | 1.392 | 1.379 | 1.369 | 1.360 | 1.352 |
130 | 1.547 | 1.488 | 1.449 | 1.421 | 1.400 | 1.383 | 1.370 | 1.359 | 1.350 | 1.343 |
140 | 1.541 | 1.481 | 1.442 | 1.414 | 1.393 | 1.376 | 1.363 | 1.352 | 1.342 | 1.335 |
150 | 1.535 | 1.475 | 1.436 | 1.407 | 1.386 | 1.369 | 1.356 | 1.345 | 1.335 | 1.327 |
30 | 40 | 50 | 60 | 70 | 80 | 90 | 100 | 110 | 120 | |
160 | 1.531 | 1.470 | 1.430 | 1.402 | 1.381 | 1.364 | 1.350 | 1.339 | 1.329 | 1.321 |
170 | 1.526 | 1.466 | 1.426 | 1.397 | 1.376 | 1.359 | 1.345 | 1.334 | 1.324 | 1.316 |
180 | 1.523 | 1.462 | 1.422 | 1.393 | 1.371 | 1.354 | 1.340 | 1.329 | 1.319 | 1.311 |
190 | 1.519 | 1.458 | 1.418 | 1.389 | 1.367 | 1.350 | 1.336 | 1.324 | 1.315 | 1.306 |
200 | 1.516 | 1.455 | 1.415 | 1.386 | 1.364 | 1.346 | 1.332 | 1.321 | 1.311 | 1.302 |
210 | 1.514 | 1.452 | 1.412 | 1.382 | 1.360 | 1.343 | 1.329 | 1.317 | 1.307 | 1.299 |
220 | 1.511 | 1.450 | 1.409 | 1.380 | 1.357 | 1.340 | 1.326 | 1.314 | 1.304 | 1.295 |
230 | 1.509 | 1.447 | 1.406 | 1.377 | 1.355 | 1.337 | 1.323 | 1.311 | 1.301 | 1.292 |
240 | 1.507 | 1.445 | 1.404 | 1.375 | 1.352 | 1.335 | 1.320 | 1.308 | 1.298 | 1.290 |
250 | 1.505 | 1.443 | 1.402 | 1.372 | 1.350 | 1.332 | 1.318 | 1.306 | 1.296 | 1.287 |
分布表のタイプを選択
1. F分布(0.05) | 2. F分布(0.025) | 3. F分布(0.01) | 4. F分布(0.005)
α=0.025 のとき,表頭の自由度 m と表側の自由度 n に対して,F分布の上側 α 点 Fα(m,n) を示す。 \[ \alpha \longmapsto F_\alpha(m,n),\qquad \text{Pr}\{X>F_\alpha(m,n)\}=\alpha \] F1-α(m,n) と Fα(n,m) について, \[ F_{1-\alpha}(m,n)=\frac{1}{F_\alpha(n,m)},\qquad F_{0.975}(m,n)=\frac{1}{F_{0.025}(n,m)} \] が成り立つから,この表を用いて上側 0.975 点を求めることができる。
n∖m | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
1 | 647.8 | 799.5 | 864.2 | 899.6 | 921.8 | 937.1 | 948.2 | 956.7 | 963.3 | 968.6 |
2 | 38.51 | 39.00 | 39.17 | 39.25 | 39.30 | 39.33 | 39.36 | 39.37 | 39.39 | 39.40 |
3 | 17.44 | 16.04 | 15.44 | 15.10 | 14.88 | 14.73 | 14.62 | 14.54 | 14.47 | 14.42 |
4 | 12.22 | 10.65 | 9.979 | 9.605 | 9.364 | 9.197 | 9.074 | 8.980 | 8.905 | 8.844 |
5 | 10.01 | 8.434 | 7.764 | 7.388 | 7.146 | 6.978 | 6.853 | 6.757 | 6.681 | 6.619 |
6 | 8.813 | 7.260 | 6.599 | 6.227 | 5.988 | 5.820 | 5.695 | 5.600 | 5.523 | 5.461 |
7 | 8.073 | 6.542 | 5.890 | 5.523 | 5.285 | 5.119 | 4.995 | 4.899 | 4.823 | 4.761 |
8 | 7.571 | 6.059 | 5.416 | 5.053 | 4.817 | 4.652 | 4.529 | 4.433 | 4.357 | 4.295 |
9 | 7.209 | 5.715 | 5.078 | 4.718 | 4.484 | 4.320 | 4.197 | 4.102 | 4.026 | 3.964 |
10 | 6.937 | 5.456 | 4.826 | 4.468 | 4.236 | 4.072 | 3.950 | 3.855 | 3.779 | 3.717 |
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |
11 | 6.724 | 5.256 | 4.630 | 4.275 | 4.044 | 3.881 | 3.759 | 3.664 | 3.588 | 3.526 |
12 | 6.554 | 5.096 | 4.474 | 4.121 | 3.891 | 3.728 | 3.607 | 3.512 | 3.436 | 3.374 |
13 | 6.414 | 4.965 | 4.347 | 3.996 | 3.767 | 3.604 | 3.483 | 3.388 | 3.312 | 3.250 |
14 | 6.298 | 4.857 | 4.242 | 3.892 | 3.663 | 3.501 | 3.380 | 3.285 | 3.209 | 3.147 |
15 | 6.200 | 4.765 | 4.153 | 3.804 | 3.576 | 3.415 | 3.293 | 3.199 | 3.123 | 3.060 |
16 | 6.115 | 4.687 | 4.077 | 3.729 | 3.502 | 3.341 | 3.219 | 3.125 | 3.049 | 2.986 |
17 | 6.042 | 4.619 | 4.011 | 3.665 | 3.438 | 3.277 | 3.156 | 3.061 | 2.985 | 2.922 |
18 | 5.978 | 4.560 | 3.954 | 3.608 | 3.382 | 3.221 | 3.100 | 3.005 | 2.929 | 2.866 |
19 | 5.922 | 4.508 | 3.903 | 3.559 | 3.333 | 3.172 | 3.051 | 2.956 | 2.880 | 2.817 |
20 | 5.871 | 4.461 | 3.859 | 3.515 | 3.289 | 3.128 | 3.007 | 2.913 | 2.837 | 2.774 |
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |
21 | 5.827 | 4.420 | 3.819 | 3.475 | 3.250 | 3.090 | 2.969 | 2.874 | 2.798 | 2.735 |
22 | 5.786 | 4.383 | 3.783 | 3.440 | 3.215 | 3.055 | 2.934 | 2.839 | 2.763 | 2.700 |
23 | 5.750 | 4.349 | 3.750 | 3.408 | 3.183 | 3.023 | 2.902 | 2.808 | 2.731 | 2.668 |
24 | 5.717 | 4.319 | 3.721 | 3.379 | 3.155 | 2.995 | 2.874 | 2.779 | 2.703 | 2.640 |
25 | 5.686 | 4.291 | 3.694 | 3.353 | 3.129 | 2.969 | 2.848 | 2.753 | 2.677 | 2.613 |
26 | 5.659 | 4.265 | 3.670 | 3.329 | 3.105 | 2.945 | 2.824 | 2.729 | 2.653 | 2.590 |
27 | 5.633 | 4.242 | 3.647 | 3.307 | 3.083 | 2.923 | 2.802 | 2.707 | 2.631 | 2.568 |
28 | 5.610 | 4.221 | 3.626 | 3.286 | 3.063 | 2.903 | 2.782 | 2.687 | 2.611 | 2.547 |
29 | 5.588 | 4.201 | 3.607 | 3.267 | 3.044 | 2.884 | 2.763 | 2.669 | 2.592 | 2.529 |
30 | 5.568 | 4.182 | 3.589 | 3.250 | 3.026 | 2.867 | 2.746 | 2.651 | 2.575 | 2.511 |
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |
31 | 5.549 | 4.165 | 3.573 | 3.234 | 3.010 | 2.851 | 2.730 | 2.635 | 2.558 | 2.495 |
32 | 5.531 | 4.149 | 3.557 | 3.218 | 2.995 | 2.836 | 2.715 | 2.620 | 2.543 | 2.480 |
33 | 5.515 | 4.134 | 3.543 | 3.204 | 2.981 | 2.822 | 2.701 | 2.606 | 2.529 | 2.466 |
34 | 5.499 | 4.120 | 3.529 | 3.191 | 2.968 | 2.808 | 2.688 | 2.593 | 2.516 | 2.453 |
35 | 5.485 | 4.106 | 3.517 | 3.179 | 2.956 | 2.796 | 2.676 | 2.581 | 2.504 | 2.440 |
36 | 5.471 | 4.094 | 3.505 | 3.167 | 2.944 | 2.785 | 2.664 | 2.569 | 2.492 | 2.429 |
37 | 5.458 | 4.082 | 3.493 | 3.156 | 2.933 | 2.774 | 2.653 | 2.558 | 2.481 | 2.418 |
38 | 5.446 | 4.071 | 3.483 | 3.145 | 2.923 | 2.763 | 2.643 | 2.548 | 2.471 | 2.407 |
39 | 5.435 | 4.061 | 3.473 | 3.135 | 2.913 | 2.754 | 2.633 | 2.538 | 2.461 | 2.397 |
40 | 5.424 | 4.051 | 3.463 | 3.126 | 2.904 | 2.744 | 2.624 | 2.529 | 2.452 | 2.388 |
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |
41 | 5.414 | 4.042 | 3.454 | 3.117 | 2.895 | 2.736 | 2.615 | 2.520 | 2.443 | 2.379 |
42 | 5.404 | 4.033 | 3.446 | 3.109 | 2.887 | 2.727 | 2.607 | 2.512 | 2.435 | 2.371 |
43 | 5.395 | 4.024 | 3.438 | 3.101 | 2.879 | 2.719 | 2.599 | 2.504 | 2.427 | 2.363 |
44 | 5.386 | 4.016 | 3.430 | 3.093 | 2.871 | 2.712 | 2.591 | 2.496 | 2.419 | 2.355 |
45 | 5.377 | 4.009 | 3.422 | 3.086 | 2.864 | 2.705 | 2.584 | 2.489 | 2.412 | 2.348 |
46 | 5.369 | 4.001 | 3.415 | 3.079 | 2.857 | 2.698 | 2.577 | 2.482 | 2.405 | 2.341 |
47 | 5.361 | 3.994 | 3.409 | 3.073 | 2.851 | 2.691 | 2.571 | 2.476 | 2.399 | 2.335 |
48 | 5.354 | 3.987 | 3.402 | 3.066 | 2.844 | 2.685 | 2.565 | 2.470 | 2.393 | 2.329 |
49 | 5.347 | 3.981 | 3.396 | 3.060 | 2.838 | 2.679 | 2.559 | 2.464 | 2.387 | 2.323 |
50 | 5.340 | 3.975 | 3.390 | 3.054 | 2.833 | 2.674 | 2.553 | 2.458 | 2.381 | 2.317 |
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |
60 | 5.286 | 3.925 | 3.343 | 3.008 | 2.786 | 2.627 | 2.507 | 2.412 | 2.334 | 2.270 |
70 | 5.247 | 3.890 | 3.309 | 2.975 | 2.754 | 2.595 | 2.474 | 2.379 | 2.302 | 2.237 |
80 | 5.218 | 3.864 | 3.284 | 2.950 | 2.730 | 2.571 | 2.450 | 2.355 | 2.277 | 2.213 |
90 | 5.196 | 3.844 | 3.265 | 2.932 | 2.711 | 2.552 | 2.432 | 2.336 | 2.259 | 2.194 |
100 | 5.179 | 3.828 | 3.250 | 2.917 | 2.696 | 2.537 | 2.417 | 2.321 | 2.244 | 2.179 |
110 | 5.164 | 3.815 | 3.237 | 2.904 | 2.684 | 2.525 | 2.405 | 2.309 | 2.232 | 2.167 |
120 | 5.152 | 3.805 | 3.227 | 2.894 | 2.674 | 2.515 | 2.395 | 2.299 | 2.222 | 2.157 |
130 | 5.142 | 3.796 | 3.218 | 2.886 | 2.666 | 2.507 | 2.386 | 2.291 | 2.213 | 2.148 |
140 | 5.134 | 3.788 | 3.211 | 2.879 | 2.658 | 2.500 | 2.379 | 2.284 | 2.206 | 2.141 |
150 | 5.126 | 3.781 | 3.204 | 2.872 | 2.652 | 2.494 | 2.373 | 2.278 | 2.200 | 2.135 |
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |
160 | 5.120 | 3.775 | 3.199 | 2.867 | 2.647 | 2.488 | 2.368 | 2.272 | 2.194 | 2.129 |
170 | 5.114 | 3.770 | 3.194 | 2.862 | 2.642 | 2.483 | 2.363 | 2.267 | 2.189 | 2.125 |
180 | 5.109 | 3.766 | 3.189 | 2.858 | 2.638 | 2.479 | 2.359 | 2.263 | 2.185 | 2.120 |
190 | 5.104 | 3.761 | 3.186 | 2.854 | 2.634 | 2.475 | 2.355 | 2.259 | 2.181 | 2.116 |
200 | 5.100 | 3.758 | 3.182 | 2.850 | 2.630 | 2.472 | 2.351 | 2.256 | 2.178 | 2.113 |
210 | 5.097 | 3.754 | 3.179 | 2.847 | 2.627 | 2.469 | 2.348 | 2.253 | 2.175 | 2.110 |
220 | 5.093 | 3.751 | 3.176 | 2.844 | 2.625 | 2.466 | 2.345 | 2.250 | 2.172 | 2.107 |
230 | 5.090 | 3.749 | 3.173 | 2.842 | 2.622 | 2.464 | 2.343 | 2.247 | 2.169 | 2.104 |
240 | 5.088 | 3.746 | 3.171 | 2.839 | 2.620 | 2.461 | 2.341 | 2.245 | 2.167 | 2.102 |
250 | 5.085 | 3.744 | 3.169 | 2.837 | 2.618 | 2.459 | 2.338 | 2.243 | 2.165 | 2.100 |
n∖m | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |
1 | 973.0 | 976.7 | 979.8 | 982.5 | 984.9 | 986.9 | 988.7 | 990.3 | 991.8 | 993.1 |
2 | 39.41 | 39.41 | 39.42 | 39.43 | 39.43 | 39.44 | 39.44 | 39.44 | 39.45 | 39.45 |
3 | 14.37 | 14.34 | 14.30 | 14.28 | 14.25 | 14.23 | 14.21 | 14.20 | 14.18 | 14.17 |
4 | 8.794 | 8.751 | 8.715 | 8.684 | 8.657 | 8.633 | 8.611 | 8.592 | 8.575 | 8.560 |
5 | 6.568 | 6.525 | 6.488 | 6.456 | 6.428 | 6.403 | 6.381 | 6.362 | 6.344 | 6.329 |
6 | 5.410 | 5.366 | 5.329 | 5.297 | 5.269 | 5.244 | 5.222 | 5.202 | 5.184 | 5.168 |
7 | 4.709 | 4.666 | 4.628 | 4.596 | 4.568 | 4.543 | 4.521 | 4.501 | 4.483 | 4.467 |
8 | 4.243 | 4.200 | 4.162 | 4.130 | 4.101 | 4.076 | 4.054 | 4.034 | 4.016 | 3.999 |
9 | 3.912 | 3.868 | 3.831 | 3.798 | 3.769 | 3.744 | 3.722 | 3.701 | 3.683 | 3.667 |
10 | 3.665 | 3.621 | 3.583 | 3.550 | 3.522 | 3.496 | 3.474 | 3.453 | 3.435 | 3.419 |
11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | |
11 | 3.474 | 3.430 | 3.392 | 3.359 | 3.330 | 3.304 | 3.282 | 3.261 | 3.243 | 3.226 |
12 | 3.321 | 3.277 | 3.239 | 3.206 | 3.177 | 3.152 | 3.129 | 3.108 | 3.090 | 3.073 |
13 | 3.197 | 3.153 | 3.115 | 3.082 | 3.053 | 3.027 | 3.004 | 2.983 | 2.965 | 2.948 |
14 | 3.095 | 3.050 | 3.012 | 2.979 | 2.949 | 2.923 | 2.900 | 2.879 | 2.861 | 2.844 |
15 | 3.008 | 2.963 | 2.925 | 2.891 | 2.862 | 2.836 | 2.813 | 2.792 | 2.773 | 2.756 |
16 | 2.934 | 2.889 | 2.851 | 2.817 | 2.788 | 2.761 | 2.738 | 2.717 | 2.698 | 2.681 |
17 | 2.870 | 2.825 | 2.786 | 2.753 | 2.723 | 2.697 | 2.673 | 2.652 | 2.633 | 2.616 |
18 | 2.814 | 2.769 | 2.730 | 2.696 | 2.667 | 2.640 | 2.617 | 2.596 | 2.576 | 2.559 |
19 | 2.765 | 2.720 | 2.681 | 2.647 | 2.617 | 2.591 | 2.567 | 2.546 | 2.526 | 2.509 |
20 | 2.721 | 2.676 | 2.637 | 2.603 | 2.573 | 2.547 | 2.523 | 2.501 | 2.482 | 2.464 |
11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | |
21 | 2.682 | 2.637 | 2.598 | 2.564 | 2.534 | 2.507 | 2.483 | 2.462 | 2.442 | 2.425 |
22 | 2.647 | 2.602 | 2.563 | 2.528 | 2.498 | 2.472 | 2.448 | 2.426 | 2.407 | 2.389 |
23 | 2.615 | 2.570 | 2.531 | 2.497 | 2.466 | 2.440 | 2.416 | 2.394 | 2.374 | 2.357 |
24 | 2.586 | 2.541 | 2.502 | 2.468 | 2.437 | 2.411 | 2.386 | 2.365 | 2.345 | 2.327 |
25 | 2.560 | 2.515 | 2.476 | 2.441 | 2.411 | 2.384 | 2.360 | 2.338 | 2.318 | 2.300 |
26 | 2.536 | 2.491 | 2.451 | 2.417 | 2.387 | 2.360 | 2.335 | 2.314 | 2.294 | 2.276 |
27 | 2.514 | 2.469 | 2.429 | 2.395 | 2.364 | 2.337 | 2.313 | 2.291 | 2.271 | 2.253 |
28 | 2.494 | 2.448 | 2.409 | 2.374 | 2.344 | 2.317 | 2.292 | 2.270 | 2.251 | 2.232 |
29 | 2.475 | 2.430 | 2.390 | 2.355 | 2.325 | 2.298 | 2.273 | 2.251 | 2.231 | 2.213 |
30 | 2.458 | 2.412 | 2.372 | 2.338 | 2.307 | 2.280 | 2.255 | 2.233 | 2.213 | 2.195 |
11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | |
31 | 2.442 | 2.396 | 2.356 | 2.321 | 2.291 | 2.263 | 2.239 | 2.217 | 2.197 | 2.178 |
32 | 2.426 | 2.381 | 2.341 | 2.306 | 2.275 | 2.248 | 2.223 | 2.201 | 2.181 | 2.163 |
33 | 2.412 | 2.366 | 2.327 | 2.292 | 2.261 | 2.234 | 2.209 | 2.187 | 2.167 | 2.148 |
34 | 2.399 | 2.353 | 2.313 | 2.278 | 2.248 | 2.220 | 2.195 | 2.173 | 2.153 | 2.135 |
35 | 2.387 | 2.341 | 2.301 | 2.266 | 2.235 | 2.207 | 2.183 | 2.160 | 2.140 | 2.122 |
36 | 2.375 | 2.329 | 2.289 | 2.254 | 2.223 | 2.196 | 2.171 | 2.148 | 2.128 | 2.110 |
37 | 2.364 | 2.318 | 2.278 | 2.243 | 2.212 | 2.184 | 2.160 | 2.137 | 2.117 | 2.098 |
38 | 2.353 | 2.307 | 2.267 | 2.232 | 2.201 | 2.174 | 2.149 | 2.126 | 2.106 | 2.088 |
39 | 2.344 | 2.298 | 2.257 | 2.222 | 2.191 | 2.164 | 2.139 | 2.116 | 2.096 | 2.077 |
40 | 2.334 | 2.288 | 2.248 | 2.213 | 2.182 | 2.154 | 2.129 | 2.107 | 2.086 | 2.068 |
11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | |
41 | 2.325 | 2.279 | 2.239 | 2.204 | 2.173 | 2.145 | 2.120 | 2.098 | 2.077 | 2.059 |
42 | 2.317 | 2.271 | 2.231 | 2.196 | 2.164 | 2.137 | 2.112 | 2.089 | 2.069 | 2.050 |
43 | 2.309 | 2.263 | 2.223 | 2.187 | 2.156 | 2.128 | 2.103 | 2.081 | 2.060 | 2.042 |
44 | 2.302 | 2.255 | 2.215 | 2.180 | 2.149 | 2.121 | 2.096 | 2.073 | 2.052 | 2.034 |
45 | 2.294 | 2.248 | 2.208 | 2.172 | 2.141 | 2.113 | 2.088 | 2.066 | 2.045 | 2.026 |
46 | 2.287 | 2.241 | 2.201 | 2.165 | 2.134 | 2.106 | 2.081 | 2.058 | 2.038 | 2.019 |
47 | 2.281 | 2.234 | 2.194 | 2.159 | 2.127 | 2.100 | 2.074 | 2.052 | 2.031 | 2.012 |
48 | 2.274 | 2.228 | 2.188 | 2.152 | 2.121 | 2.093 | 2.068 | 2.045 | 2.024 | 2.006 |
49 | 2.268 | 2.222 | 2.182 | 2.146 | 2.115 | 2.087 | 2.062 | 2.039 | 2.018 | 1.999 |
50 | 2.263 | 2.216 | 2.176 | 2.140 | 2.109 | 2.081 | 2.056 | 2.033 | 2.012 | 1.993 |
11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | |
60 | 2.216 | 2.169 | 2.129 | 2.093 | 2.061 | 2.033 | 2.008 | 1.985 | 1.964 | 1.944 |
70 | 2.183 | 2.136 | 2.095 | 2.059 | 2.028 | 1.999 | 1.974 | 1.950 | 1.929 | 1.910 |
80 | 2.158 | 2.111 | 2.071 | 2.035 | 2.003 | 1.974 | 1.948 | 1.925 | 1.904 | 1.884 |
90 | 2.140 | 2.092 | 2.051 | 2.015 | 1.983 | 1.955 | 1.929 | 1.905 | 1.884 | 1.864 |
100 | 2.124 | 2.077 | 2.036 | 2.000 | 1.968 | 1.939 | 1.913 | 1.890 | 1.868 | 1.849 |
110 | 2.112 | 2.065 | 2.024 | 1.988 | 1.955 | 1.927 | 1.901 | 1.877 | 1.855 | 1.836 |
120 | 2.102 | 2.055 | 2.014 | 1.977 | 1.945 | 1.916 | 1.890 | 1.866 | 1.845 | 1.825 |
130 | 2.094 | 2.046 | 2.005 | 1.969 | 1.936 | 1.907 | 1.881 | 1.857 | 1.836 | 1.816 |
140 | 2.086 | 2.039 | 1.998 | 1.961 | 1.929 | 1.900 | 1.873 | 1.850 | 1.828 | 1.808 |
150 | 2.080 | 2.032 | 1.991 | 1.955 | 1.922 | 1.893 | 1.867 | 1.843 | 1.821 | 1.801 |
11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | |
160 | 2.074 | 2.027 | 1.986 | 1.949 | 1.917 | 1.887 | 1.861 | 1.837 | 1.816 | 1.796 |
170 | 2.069 | 2.022 | 1.981 | 1.944 | 1.912 | 1.882 | 1.856 | 1.832 | 1.810 | 1.790 |
180 | 2.065 | 2.018 | 1.976 | 1.940 | 1.907 | 1.878 | 1.852 | 1.828 | 1.806 | 1.786 |
190 | 2.061 | 2.014 | 1.972 | 1.936 | 1.903 | 1.874 | 1.848 | 1.824 | 1.802 | 1.782 |
200 | 2.058 | 2.010 | 1.969 | 1.932 | 1.900 | 1.870 | 1.844 | 1.820 | 1.798 | 1.778 |
210 | 2.055 | 2.007 | 1.966 | 1.929 | 1.896 | 1.867 | 1.841 | 1.817 | 1.795 | 1.775 |
220 | 2.052 | 2.004 | 1.963 | 1.926 | 1.893 | 1.864 | 1.838 | 1.814 | 1.792 | 1.772 |
230 | 2.049 | 2.002 | 1.960 | 1.923 | 1.891 | 1.861 | 1.835 | 1.811 | 1.789 | 1.769 |
240 | 2.047 | 1.999 | 1.958 | 1.921 | 1.888 | 1.859 | 1.833 | 1.808 | 1.787 | 1.766 |
250 | 2.045 | 1.997 | 1.955 | 1.919 | 1.886 | 1.857 | 1.830 | 1.806 | 1.784 | 1.764 |
n∖m | 30 | 40 | 50 | 60 | 70 | 80 | 90 | 100 | 110 | 120 |
1 | 1001 | 1006 | 1008 | 1010 | 1011 | 1012 | 1013 | 1013 | 1014 | 1014 |
2 | 39.46 | 39.47 | 39.48 | 39.48 | 39.48 | 39.49 | 39.49 | 39.49 | 39.49 | 39.49 |
3 | 14.08 | 14.04 | 14.01 | 13.99 | 13.98 | 13.97 | 13.96 | 13.96 | 13.95 | 13.95 |
4 | 8.461 | 8.411 | 8.381 | 8.360 | 8.346 | 8.335 | 8.326 | 8.319 | 8.314 | 8.309 |
5 | 6.227 | 6.175 | 6.144 | 6.123 | 6.107 | 6.096 | 6.087 | 6.080 | 6.074 | 6.069 |
6 | 5.065 | 5.012 | 4.980 | 4.959 | 4.943 | 4.932 | 4.923 | 4.915 | 4.909 | 4.904 |
7 | 4.362 | 4.309 | 4.276 | 4.254 | 4.239 | 4.227 | 4.218 | 4.210 | 4.204 | 4.199 |
8 | 3.894 | 3.840 | 3.807 | 3.784 | 3.768 | 3.756 | 3.747 | 3.739 | 3.733 | 3.728 |
9 | 3.560 | 3.505 | 3.472 | 3.449 | 3.433 | 3.421 | 3.411 | 3.403 | 3.397 | 3.392 |
10 | 3.311 | 3.255 | 3.221 | 3.198 | 3.182 | 3.169 | 3.160 | 3.152 | 3.145 | 3.140 |
30 | 40 | 50 | 60 | 70 | 80 | 90 | 100 | 110 | 120 | |
11 | 3.118 | 3.061 | 3.027 | 3.004 | 2.987 | 2.974 | 2.964 | 2.956 | 2.950 | 2.944 |
12 | 2.963 | 2.906 | 2.871 | 2.848 | 2.831 | 2.818 | 2.808 | 2.800 | 2.793 | 2.787 |
13 | 2.837 | 2.780 | 2.744 | 2.720 | 2.703 | 2.690 | 2.680 | 2.671 | 2.665 | 2.659 |
14 | 2.732 | 2.674 | 2.638 | 2.614 | 2.597 | 2.583 | 2.573 | 2.565 | 2.558 | 2.552 |
15 | 2.644 | 2.585 | 2.549 | 2.524 | 2.506 | 2.493 | 2.482 | 2.474 | 2.467 | 2.461 |
16 | 2.568 | 2.509 | 2.472 | 2.447 | 2.429 | 2.415 | 2.405 | 2.396 | 2.389 | 2.383 |
17 | 2.502 | 2.442 | 2.405 | 2.380 | 2.362 | 2.348 | 2.337 | 2.329 | 2.321 | 2.315 |
18 | 2.445 | 2.384 | 2.347 | 2.321 | 2.303 | 2.289 | 2.278 | 2.269 | 2.262 | 2.256 |
19 | 2.394 | 2.333 | 2.295 | 2.270 | 2.251 | 2.237 | 2.226 | 2.217 | 2.209 | 2.203 |
20 | 2.349 | 2.287 | 2.249 | 2.223 | 2.205 | 2.190 | 2.179 | 2.170 | 2.162 | 2.156 |
30 | 40 | 50 | 60 | 70 | 80 | 90 | 100 | 110 | 120 | |
21 | 2.308 | 2.246 | 2.208 | 2.182 | 2.163 | 2.148 | 2.137 | 2.128 | 2.120 | 2.114 |
22 | 2.272 | 2.210 | 2.171 | 2.145 | 2.125 | 2.111 | 2.099 | 2.090 | 2.082 | 2.076 |
23 | 2.239 | 2.176 | 2.137 | 2.111 | 2.091 | 2.077 | 2.065 | 2.056 | 2.048 | 2.041 |
24 | 2.209 | 2.146 | 2.107 | 2.080 | 2.060 | 2.045 | 2.034 | 2.024 | 2.016 | 2.010 |
25 | 2.182 | 2.118 | 2.079 | 2.052 | 2.032 | 2.017 | 2.005 | 1.996 | 1.988 | 1.981 |
26 | 2.157 | 2.093 | 2.053 | 2.026 | 2.006 | 1.991 | 1.979 | 1.969 | 1.961 | 1.954 |
27 | 2.133 | 2.069 | 2.029 | 2.002 | 1.982 | 1.966 | 1.954 | 1.945 | 1.937 | 1.930 |
28 | 2.112 | 2.048 | 2.007 | 1.980 | 1.959 | 1.944 | 1.932 | 1.922 | 1.914 | 1.907 |
29 | 2.092 | 2.028 | 1.987 | 1.959 | 1.939 | 1.923 | 1.911 | 1.901 | 1.893 | 1.886 |
30 | 2.074 | 2.009 | 1.968 | 1.940 | 1.920 | 1.904 | 1.892 | 1.882 | 1.873 | 1.866 |
30 | 40 | 50 | 60 | 70 | 80 | 90 | 100 | 110 | 120 | |
31 | 2.057 | 1.991 | 1.950 | 1.922 | 1.902 | 1.886 | 1.873 | 1.863 | 1.855 | 1.848 |
32 | 2.041 | 1.975 | 1.934 | 1.905 | 1.885 | 1.869 | 1.856 | 1.846 | 1.838 | 1.831 |
33 | 2.026 | 1.960 | 1.918 | 1.890 | 1.869 | 1.853 | 1.840 | 1.830 | 1.822 | 1.815 |
34 | 2.012 | 1.946 | 1.904 | 1.875 | 1.854 | 1.838 | 1.825 | 1.815 | 1.807 | 1.799 |
35 | 1.999 | 1.932 | 1.890 | 1.861 | 1.840 | 1.824 | 1.811 | 1.801 | 1.792 | 1.785 |
36 | 1.986 | 1.919 | 1.877 | 1.848 | 1.827 | 1.811 | 1.798 | 1.787 | 1.779 | 1.772 |
37 | 1.974 | 1.907 | 1.865 | 1.836 | 1.815 | 1.798 | 1.785 | 1.775 | 1.766 | 1.759 |
38 | 1.963 | 1.896 | 1.854 | 1.824 | 1.803 | 1.786 | 1.773 | 1.763 | 1.754 | 1.747 |
39 | 1.953 | 1.885 | 1.843 | 1.813 | 1.792 | 1.775 | 1.762 | 1.751 | 1.743 | 1.735 |
40 | 1.943 | 1.875 | 1.832 | 1.803 | 1.781 | 1.764 | 1.751 | 1.741 | 1.732 | 1.724 |
30 | 40 | 50 | 60 | 70 | 80 | 90 | 100 | 110 | 120 | |
41 | 1.933 | 1.866 | 1.823 | 1.793 | 1.771 | 1.754 | 1.741 | 1.730 | 1.721 | 1.714 |
42 | 1.924 | 1.856 | 1.813 | 1.783 | 1.761 | 1.745 | 1.731 | 1.720 | 1.711 | 1.704 |
43 | 1.916 | 1.848 | 1.804 | 1.774 | 1.752 | 1.735 | 1.722 | 1.711 | 1.702 | 1.694 |
44 | 1.908 | 1.839 | 1.796 | 1.766 | 1.743 | 1.726 | 1.713 | 1.702 | 1.693 | 1.685 |
45 | 1.900 | 1.831 | 1.788 | 1.757 | 1.735 | 1.718 | 1.705 | 1.694 | 1.684 | 1.677 |
46 | 1.893 | 1.824 | 1.780 | 1.750 | 1.727 | 1.710 | 1.696 | 1.685 | 1.676 | 1.668 |
47 | 1.885 | 1.816 | 1.772 | 1.742 | 1.720 | 1.702 | 1.689 | 1.678 | 1.668 | 1.661 |
48 | 1.879 | 1.809 | 1.765 | 1.735 | 1.712 | 1.695 | 1.681 | 1.670 | 1.661 | 1.653 |
49 | 1.872 | 1.803 | 1.759 | 1.728 | 1.705 | 1.688 | 1.674 | 1.663 | 1.653 | 1.646 |
50 | 1.866 | 1.796 | 1.752 | 1.721 | 1.698 | 1.681 | 1.667 | 1.656 | 1.647 | 1.639 |
30 | 40 | 50 | 60 | 70 | 80 | 90 | 100 | 110 | 120 | |
60 | 1.815 | 1.744 | 1.699 | 1.667 | 1.643 | 1.625 | 1.611 | 1.599 | 1.589 | 1.581 |
70 | 1.779 | 1.707 | 1.660 | 1.628 | 1.604 | 1.585 | 1.570 | 1.558 | 1.548 | 1.539 |
80 | 1.752 | 1.679 | 1.632 | 1.599 | 1.574 | 1.555 | 1.540 | 1.527 | 1.517 | 1.508 |
90 | 1.731 | 1.657 | 1.610 | 1.576 | 1.551 | 1.531 | 1.516 | 1.503 | 1.492 | 1.483 |
100 | 1.715 | 1.640 | 1.592 | 1.558 | 1.532 | 1.512 | 1.496 | 1.483 | 1.472 | 1.463 |
110 | 1.701 | 1.626 | 1.577 | 1.543 | 1.517 | 1.497 | 1.480 | 1.467 | 1.456 | 1.447 |
120 | 1.690 | 1.614 | 1.565 | 1.530 | 1.504 | 1.483 | 1.467 | 1.454 | 1.442 | 1.433 |
130 | 1.680 | 1.604 | 1.555 | 1.519 | 1.493 | 1.472 | 1.456 | 1.442 | 1.431 | 1.421 |
140 | 1.672 | 1.596 | 1.546 | 1.510 | 1.483 | 1.463 | 1.446 | 1.432 | 1.420 | 1.411 |
150 | 1.665 | 1.588 | 1.538 | 1.502 | 1.475 | 1.454 | 1.437 | 1.423 | 1.412 | 1.402 |
30 | 40 | 50 | 60 | 70 | 80 | 90 | 100 | 110 | 120 | |
160 | 1.659 | 1.582 | 1.531 | 1.495 | 1.468 | 1.447 | 1.430 | 1.416 | 1.404 | 1.394 |
170 | 1.653 | 1.576 | 1.525 | 1.489 | 1.462 | 1.440 | 1.423 | 1.409 | 1.397 | 1.387 |
180 | 1.649 | 1.571 | 1.520 | 1.484 | 1.456 | 1.435 | 1.417 | 1.403 | 1.391 | 1.381 |
190 | 1.644 | 1.566 | 1.515 | 1.479 | 1.451 | 1.429 | 1.412 | 1.398 | 1.385 | 1.375 |
200 | 1.640 | 1.562 | 1.511 | 1.474 | 1.447 | 1.425 | 1.407 | 1.393 | 1.380 | 1.370 |
210 | 1.637 | 1.558 | 1.507 | 1.470 | 1.442 | 1.421 | 1.403 | 1.388 | 1.376 | 1.365 |
220 | 1.634 | 1.555 | 1.503 | 1.467 | 1.439 | 1.417 | 1.399 | 1.384 | 1.372 | 1.361 |
230 | 1.631 | 1.552 | 1.500 | 1.463 | 1.435 | 1.413 | 1.395 | 1.381 | 1.368 | 1.357 |
240 | 1.628 | 1.549 | 1.497 | 1.460 | 1.432 | 1.410 | 1.392 | 1.377 | 1.365 | 1.354 |
250 | 1.625 | 1.546 | 1.495 | 1.457 | 1.429 | 1.407 | 1.389 | 1.374 | 1.361 | 1.351 |
分布表のタイプを選択
1. F分布(0.05) | 2. F分布(0.025) | 3. F分布(0.01) | 4. F分布(0.005)
α=0.01 のとき,表頭の自由度 m と表側の自由度 n に対して,F分布の上側 α 点 Fα(m,n) を示す。 \[ \alpha \longmapsto F_\alpha(m,n),\qquad \text{Pr}\{X>F_\alpha(m,n)\}=\alpha \] F1-α(m,n) と Fα(n,m) について, \[ F_{1-\alpha}(m,n)=\frac{1}{F_\alpha(n,m)},\qquad F_{0.99}(m,n)=\frac{1}{F_{0.01}(n,m)} \] が成り立つから,この表を用いて上側 0.99 点を求めることができる。
n∖m | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
1 | 4052 | 4999 | 5403 | 5625 | 5764 | 5859 | 5928 | 5981 | 6022 | 6056 |
2 | 98.50 | 99.00 | 99.17 | 99.25 | 99.30 | 99.33 | 99.36 | 99.37 | 99.39 | 99.40 |
3 | 34.12 | 30.82 | 29.46 | 28.71 | 28.24 | 27.91 | 27.67 | 27.49 | 27.35 | 27.23 |
4 | 21.20 | 18.00 | 16.69 | 15.98 | 15.52 | 15.21 | 14.98 | 14.80 | 14.66 | 14.55 |
5 | 16.26 | 13.27 | 12.06 | 11.39 | 10.97 | 10.67 | 10.46 | 10.29 | 10.16 | 10.05 |
6 | 13.75 | 10.92 | 9.780 | 9.148 | 8.746 | 8.466 | 8.260 | 8.102 | 7.976 | 7.874 |
7 | 12.25 | 9.547 | 8.451 | 7.847 | 7.460 | 7.191 | 6.993 | 6.840 | 6.719 | 6.620 |
8 | 11.26 | 8.649 | 7.591 | 7.006 | 6.632 | 6.371 | 6.178 | 6.029 | 5.911 | 5.814 |
9 | 10.56 | 8.022 | 6.992 | 6.422 | 6.057 | 5.802 | 5.613 | 5.467 | 5.351 | 5.257 |
10 | 10.04 | 7.559 | 6.552 | 5.994 | 5.636 | 5.386 | 5.200 | 5.057 | 4.942 | 4.849 |
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |
11 | 9.646 | 7.206 | 6.217 | 5.668 | 5.316 | 5.069 | 4.886 | 4.744 | 4.632 | 4.539 |
12 | 9.330 | 6.927 | 5.953 | 5.412 | 5.064 | 4.821 | 4.640 | 4.499 | 4.388 | 4.296 |
13 | 9.074 | 6.701 | 5.739 | 5.205 | 4.862 | 4.620 | 4.441 | 4.302 | 4.191 | 4.100 |
14 | 8.862 | 6.515 | 5.564 | 5.035 | 4.695 | 4.456 | 4.278 | 4.140 | 4.030 | 3.939 |
15 | 8.683 | 6.359 | 5.417 | 4.893 | 4.556 | 4.318 | 4.142 | 4.004 | 3.895 | 3.805 |
16 | 8.531 | 6.226 | 5.292 | 4.773 | 4.437 | 4.202 | 4.026 | 3.890 | 3.780 | 3.691 |
17 | 8.400 | 6.112 | 5.185 | 4.669 | 4.336 | 4.102 | 3.927 | 3.791 | 3.682 | 3.593 |
18 | 8.285 | 6.013 | 5.092 | 4.579 | 4.248 | 4.015 | 3.841 | 3.705 | 3.597 | 3.508 |
19 | 8.185 | 5.926 | 5.010 | 4.500 | 4.171 | 3.939 | 3.765 | 3.631 | 3.523 | 3.434 |
20 | 8.096 | 5.849 | 4.938 | 4.431 | 4.103 | 3.871 | 3.699 | 3.564 | 3.457 | 3.368 |
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |
21 | 8.017 | 5.780 | 4.874 | 4.369 | 4.042 | 3.812 | 3.640 | 3.506 | 3.398 | 3.310 |
22 | 7.945 | 5.719 | 4.817 | 4.313 | 3.988 | 3.758 | 3.587 | 3.453 | 3.346 | 3.258 |
23 | 7.881 | 5.664 | 4.765 | 4.264 | 3.939 | 3.710 | 3.539 | 3.406 | 3.299 | 3.211 |
24 | 7.823 | 5.614 | 4.718 | 4.218 | 3.895 | 3.667 | 3.496 | 3.363 | 3.256 | 3.168 |
25 | 7.770 | 5.568 | 4.675 | 4.177 | 3.855 | 3.627 | 3.457 | 3.324 | 3.217 | 3.129 |
26 | 7.721 | 5.526 | 4.637 | 4.140 | 3.818 | 3.591 | 3.421 | 3.288 | 3.182 | 3.094 |
27 | 7.677 | 5.488 | 4.601 | 4.106 | 3.785 | 3.558 | 3.388 | 3.256 | 3.149 | 3.062 |
28 | 7.636 | 5.453 | 4.568 | 4.074 | 3.754 | 3.528 | 3.358 | 3.226 | 3.120 | 3.032 |
29 | 7.598 | 5.420 | 4.538 | 4.045 | 3.725 | 3.499 | 3.330 | 3.198 | 3.092 | 3.005 |
30 | 7.562 | 5.390 | 4.510 | 4.018 | 3.699 | 3.473 | 3.304 | 3.173 | 3.067 | 2.979 |
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |
31 | 7.530 | 5.362 | 4.484 | 3.993 | 3.675 | 3.449 | 3.281 | 3.149 | 3.043 | 2.955 |
32 | 7.499 | 5.336 | 4.459 | 3.969 | 3.652 | 3.427 | 3.258 | 3.127 | 3.021 | 2.934 |
33 | 7.471 | 5.312 | 4.437 | 3.948 | 3.630 | 3.406 | 3.238 | 3.106 | 3.000 | 2.913 |
34 | 7.444 | 5.289 | 4.416 | 3.927 | 3.611 | 3.386 | 3.218 | 3.087 | 2.981 | 2.894 |
35 | 7.419 | 5.268 | 4.396 | 3.908 | 3.592 | 3.368 | 3.200 | 3.069 | 2.963 | 2.876 |
36 | 7.396 | 5.248 | 4.377 | 3.890 | 3.574 | 3.351 | 3.183 | 3.052 | 2.946 | 2.859 |
37 | 7.373 | 5.229 | 4.360 | 3.873 | 3.558 | 3.334 | 3.167 | 3.036 | 2.930 | 2.843 |
38 | 7.353 | 5.211 | 4.343 | 3.858 | 3.542 | 3.319 | 3.152 | 3.021 | 2.915 | 2.828 |
39 | 7.333 | 5.194 | 4.327 | 3.843 | 3.528 | 3.305 | 3.137 | 3.006 | 2.901 | 2.814 |
40 | 7.314 | 5.179 | 4.313 | 3.828 | 3.514 | 3.291 | 3.124 | 2.993 | 2.888 | 2.801 |
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |
41 | 7.296 | 5.163 | 4.299 | 3.815 | 3.501 | 3.278 | 3.111 | 2.980 | 2.875 | 2.788 |
42 | 7.280 | 5.149 | 4.285 | 3.802 | 3.488 | 3.266 | 3.099 | 2.968 | 2.863 | 2.776 |
43 | 7.264 | 5.136 | 4.273 | 3.790 | 3.476 | 3.254 | 3.087 | 2.957 | 2.851 | 2.764 |
44 | 7.248 | 5.123 | 4.261 | 3.778 | 3.465 | 3.243 | 3.076 | 2.946 | 2.840 | 2.754 |
45 | 7.234 | 5.110 | 4.249 | 3.767 | 3.454 | 3.232 | 3.066 | 2.935 | 2.830 | 2.743 |
46 | 7.220 | 5.099 | 4.238 | 3.757 | 3.444 | 3.222 | 3.056 | 2.925 | 2.820 | 2.733 |
47 | 7.207 | 5.087 | 4.228 | 3.747 | 3.434 | 3.213 | 3.046 | 2.916 | 2.811 | 2.724 |
48 | 7.194 | 5.077 | 4.218 | 3.737 | 3.425 | 3.204 | 3.037 | 2.907 | 2.802 | 2.715 |
49 | 7.182 | 5.066 | 4.208 | 3.728 | 3.416 | 3.195 | 3.028 | 2.898 | 2.793 | 2.706 |
50 | 7.171 | 5.057 | 4.199 | 3.720 | 3.408 | 3.186 | 3.020 | 2.890 | 2.785 | 2.698 |
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |
60 | 7.077 | 4.977 | 4.126 | 3.649 | 3.339 | 3.119 | 2.953 | 2.823 | 2.718 | 2.632 |
70 | 7.011 | 4.922 | 4.074 | 3.600 | 3.291 | 3.071 | 2.906 | 2.777 | 2.672 | 2.585 |
80 | 6.963 | 4.881 | 4.036 | 3.563 | 3.255 | 3.036 | 2.871 | 2.742 | 2.637 | 2.551 |
90 | 6.925 | 4.849 | 4.007 | 3.535 | 3.228 | 3.009 | 2.845 | 2.715 | 2.611 | 2.524 |
100 | 6.895 | 4.824 | 3.984 | 3.513 | 3.206 | 2.988 | 2.823 | 2.694 | 2.590 | 2.503 |
110 | 6.871 | 4.803 | 3.965 | 3.495 | 3.188 | 2.970 | 2.806 | 2.677 | 2.573 | 2.486 |
120 | 6.851 | 4.787 | 3.949 | 3.480 | 3.174 | 2.956 | 2.792 | 2.663 | 2.559 | 2.472 |
130 | 6.834 | 4.772 | 3.936 | 3.467 | 3.161 | 2.944 | 2.780 | 2.651 | 2.547 | 2.460 |
140 | 6.819 | 4.760 | 3.925 | 3.456 | 3.151 | 2.933 | 2.769 | 2.641 | 2.536 | 2.450 |
150 | 6.807 | 4.749 | 3.915 | 3.447 | 3.142 | 2.924 | 2.761 | 2.632 | 2.528 | 2.441 |
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |
160 | 6.796 | 4.740 | 3.906 | 3.439 | 3.134 | 2.917 | 2.753 | 2.624 | 2.520 | 2.434 |
170 | 6.786 | 4.732 | 3.899 | 3.431 | 3.127 | 2.910 | 2.746 | 2.617 | 2.513 | 2.427 |
180 | 6.778 | 4.725 | 3.892 | 3.425 | 3.120 | 2.904 | 2.740 | 2.611 | 2.507 | 2.421 |
190 | 6.770 | 4.719 | 3.886 | 3.419 | 3.115 | 2.898 | 2.735 | 2.606 | 2.502 | 2.415 |
200 | 6.763 | 4.713 | 3.881 | 3.414 | 3.110 | 2.893 | 2.730 | 2.601 | 2.497 | 2.411 |
210 | 6.757 | 4.708 | 3.876 | 3.410 | 3.105 | 2.889 | 2.725 | 2.597 | 2.493 | 2.406 |
220 | 6.751 | 4.703 | 3.872 | 3.406 | 3.101 | 2.885 | 2.721 | 2.593 | 2.489 | 2.402 |
230 | 6.746 | 4.699 | 3.868 | 3.402 | 3.098 | 2.881 | 2.718 | 2.589 | 2.485 | 2.399 |
240 | 6.742 | 4.695 | 3.864 | 3.398 | 3.094 | 2.878 | 2.714 | 2.586 | 2.482 | 2.395 |
250 | 6.737 | 4.691 | 3.861 | 3.395 | 3.091 | 2.875 | 2.711 | 2.583 | 2.479 | 2.392 |
n∖m | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |
1 | 6083 | 6106 | 6126 | 6143 | 6157 | 6170 | 6181 | 6192 | 6201 | 6209 |
2 | 99.41 | 99.42 | 99.42 | 99.43 | 99.43 | 99.44 | 99.44 | 99.44 | 99.45 | 99.45 |
3 | 27.13 | 27.05 | 26.98 | 26.92 | 26.87 | 26.83 | 26.79 | 26.75 | 26.72 | 26.69 |
4 | 14.45 | 14.37 | 14.31 | 14.25 | 14.20 | 14.15 | 14.11 | 14.08 | 14.05 | 14.02 |
5 | 9.963 | 9.888 | 9.825 | 9.770 | 9.722 | 9.680 | 9.643 | 9.610 | 9.580 | 9.553 |
6 | 7.790 | 7.718 | 7.657 | 7.605 | 7.559 | 7.519 | 7.483 | 7.451 | 7.422 | 7.396 |
7 | 6.538 | 6.469 | 6.410 | 6.359 | 6.314 | 6.275 | 6.240 | 6.209 | 6.181 | 6.155 |
8 | 5.734 | 5.667 | 5.609 | 5.559 | 5.515 | 5.477 | 5.442 | 5.412 | 5.384 | 5.359 |
9 | 5.178 | 5.111 | 5.055 | 5.005 | 4.962 | 4.924 | 4.890 | 4.860 | 4.833 | 4.808 |
10 | 4.772 | 4.706 | 4.650 | 4.601 | 4.558 | 4.520 | 4.487 | 4.457 | 4.430 | 4.405 |
11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | |
11 | 4.462 | 4.397 | 4.342 | 4.293 | 4.251 | 4.213 | 4.180 | 4.150 | 4.123 | 4.099 |
12 | 4.220 | 4.155 | 4.100 | 4.052 | 4.010 | 3.972 | 3.939 | 3.909 | 3.883 | 3.858 |
13 | 4.025 | 3.960 | 3.905 | 3.857 | 3.815 | 3.778 | 3.745 | 3.716 | 3.689 | 3.665 |
14 | 3.864 | 3.800 | 3.745 | 3.698 | 3.656 | 3.619 | 3.586 | 3.556 | 3.529 | 3.505 |
15 | 3.730 | 3.666 | 3.612 | 3.564 | 3.522 | 3.485 | 3.452 | 3.423 | 3.396 | 3.372 |
16 | 3.616 | 3.553 | 3.498 | 3.451 | 3.409 | 3.372 | 3.339 | 3.310 | 3.283 | 3.259 |
17 | 3.519 | 3.455 | 3.401 | 3.353 | 3.312 | 3.275 | 3.242 | 3.212 | 3.186 | 3.162 |
18 | 3.434 | 3.371 | 3.316 | 3.269 | 3.227 | 3.190 | 3.158 | 3.128 | 3.101 | 3.077 |
19 | 3.360 | 3.297 | 3.242 | 3.195 | 3.153 | 3.116 | 3.084 | 3.054 | 3.027 | 3.003 |
20 | 3.294 | 3.231 | 3.177 | 3.130 | 3.088 | 3.051 | 3.018 | 2.989 | 2.962 | 2.938 |
11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | |
21 | 3.236 | 3.173 | 3.119 | 3.072 | 3.030 | 2.993 | 2.960 | 2.931 | 2.904 | 2.880 |
22 | 3.184 | 3.121 | 3.067 | 3.019 | 2.978 | 2.941 | 2.908 | 2.879 | 2.852 | 2.827 |
23 | 3.137 | 3.074 | 3.020 | 2.973 | 2.931 | 2.894 | 2.861 | 2.832 | 2.805 | 2.781 |
24 | 3.094 | 3.032 | 2.977 | 2.930 | 2.889 | 2.852 | 2.819 | 2.789 | 2.762 | 2.738 |
25 | 3.056 | 2.993 | 2.939 | 2.892 | 2.850 | 2.813 | 2.780 | 2.751 | 2.724 | 2.699 |
26 | 3.021 | 2.958 | 2.904 | 2.857 | 2.815 | 2.778 | 2.745 | 2.715 | 2.688 | 2.664 |
27 | 2.988 | 2.926 | 2.871 | 2.824 | 2.783 | 2.746 | 2.713 | 2.683 | 2.656 | 2.632 |
28 | 2.959 | 2.896 | 2.842 | 2.795 | 2.753 | 2.716 | 2.683 | 2.653 | 2.626 | 2.602 |
29 | 2.931 | 2.868 | 2.814 | 2.767 | 2.726 | 2.689 | 2.656 | 2.626 | 2.599 | 2.574 |
30 | 2.906 | 2.843 | 2.789 | 2.742 | 2.700 | 2.663 | 2.630 | 2.600 | 2.573 | 2.549 |
11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | |
31 | 2.882 | 2.820 | 2.765 | 2.718 | 2.677 | 2.640 | 2.606 | 2.577 | 2.550 | 2.525 |
32 | 2.860 | 2.798 | 2.744 | 2.696 | 2.655 | 2.618 | 2.584 | 2.555 | 2.527 | 2.503 |
33 | 2.840 | 2.777 | 2.723 | 2.676 | 2.634 | 2.597 | 2.564 | 2.534 | 2.507 | 2.482 |
34 | 2.821 | 2.758 | 2.704 | 2.657 | 2.615 | 2.578 | 2.545 | 2.515 | 2.488 | 2.463 |
35 | 2.803 | 2.740 | 2.686 | 2.639 | 2.597 | 2.560 | 2.527 | 2.497 | 2.470 | 2.445 |
36 | 2.786 | 2.723 | 2.669 | 2.622 | 2.580 | 2.543 | 2.510 | 2.480 | 2.453 | 2.428 |
37 | 2.770 | 2.707 | 2.653 | 2.606 | 2.564 | 2.527 | 2.494 | 2.464 | 2.437 | 2.412 |
38 | 2.755 | 2.692 | 2.638 | 2.591 | 2.549 | 2.512 | 2.479 | 2.449 | 2.421 | 2.397 |
39 | 2.741 | 2.678 | 2.624 | 2.577 | 2.535 | 2.498 | 2.465 | 2.434 | 2.407 | 2.382 |
40 | 2.727 | 2.665 | 2.611 | 2.563 | 2.522 | 2.484 | 2.451 | 2.421 | 2.394 | 2.369 |
11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | |
41 | 2.715 | 2.652 | 2.598 | 2.551 | 2.509 | 2.472 | 2.438 | 2.408 | 2.381 | 2.356 |
42 | 2.703 | 2.640 | 2.586 | 2.539 | 2.497 | 2.460 | 2.426 | 2.396 | 2.369 | 2.344 |
43 | 2.691 | 2.629 | 2.575 | 2.527 | 2.485 | 2.448 | 2.415 | 2.385 | 2.357 | 2.332 |
44 | 2.680 | 2.618 | 2.564 | 2.516 | 2.475 | 2.437 | 2.404 | 2.374 | 2.346 | 2.321 |
45 | 2.670 | 2.608 | 2.553 | 2.506 | 2.464 | 2.427 | 2.393 | 2.363 | 2.336 | 2.311 |
46 | 2.660 | 2.598 | 2.544 | 2.496 | 2.454 | 2.417 | 2.384 | 2.353 | 2.326 | 2.301 |
47 | 2.651 | 2.588 | 2.534 | 2.487 | 2.445 | 2.408 | 2.374 | 2.344 | 2.316 | 2.291 |
48 | 2.642 | 2.579 | 2.525 | 2.478 | 2.436 | 2.399 | 2.365 | 2.335 | 2.307 | 2.282 |
49 | 2.633 | 2.571 | 2.517 | 2.469 | 2.427 | 2.390 | 2.356 | 2.326 | 2.299 | 2.274 |
50 | 2.625 | 2.562 | 2.508 | 2.461 | 2.419 | 2.382 | 2.348 | 2.318 | 2.290 | 2.265 |
11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | |
60 | 2.559 | 2.496 | 2.442 | 2.394 | 2.352 | 2.315 | 2.281 | 2.251 | 2.223 | 2.198 |
70 | 2.512 | 2.450 | 2.395 | 2.348 | 2.306 | 2.268 | 2.234 | 2.204 | 2.176 | 2.150 |
80 | 2.478 | 2.415 | 2.361 | 2.313 | 2.271 | 2.233 | 2.199 | 2.169 | 2.141 | 2.115 |
90 | 2.451 | 2.389 | 2.334 | 2.286 | 2.244 | 2.206 | 2.172 | 2.142 | 2.114 | 2.088 |
100 | 2.430 | 2.368 | 2.313 | 2.265 | 2.223 | 2.185 | 2.151 | 2.120 | 2.092 | 2.067 |
110 | 2.413 | 2.350 | 2.296 | 2.248 | 2.206 | 2.168 | 2.134 | 2.103 | 2.075 | 2.049 |
120 | 2.399 | 2.336 | 2.282 | 2.234 | 2.192 | 2.154 | 2.119 | 2.089 | 2.060 | 2.035 |
130 | 2.387 | 2.324 | 2.270 | 2.222 | 2.179 | 2.141 | 2.107 | 2.076 | 2.048 | 2.022 |
140 | 2.377 | 2.314 | 2.260 | 2.212 | 2.169 | 2.131 | 2.097 | 2.066 | 2.038 | 2.012 |
150 | 2.368 | 2.305 | 2.251 | 2.203 | 2.160 | 2.122 | 2.088 | 2.057 | 2.029 | 2.003 |
11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | |
160 | 2.360 | 2.298 | 2.243 | 2.195 | 2.153 | 2.114 | 2.080 | 2.049 | 2.021 | 1.995 |
170 | 2.354 | 2.291 | 2.236 | 2.188 | 2.146 | 2.108 | 2.073 | 2.042 | 2.014 | 1.988 |
180 | 2.348 | 2.285 | 2.230 | 2.182 | 2.140 | 2.102 | 2.067 | 2.036 | 2.008 | 1.982 |
190 | 2.342 | 2.280 | 2.225 | 2.177 | 2.134 | 2.096 | 2.062 | 2.031 | 2.002 | 1.976 |
200 | 2.338 | 2.275 | 2.220 | 2.172 | 2.129 | 2.091 | 2.057 | 2.026 | 1.997 | 1.971 |
210 | 2.333 | 2.270 | 2.216 | 2.168 | 2.125 | 2.087 | 2.052 | 2.021 | 1.993 | 1.967 |
220 | 2.329 | 2.266 | 2.212 | 2.164 | 2.121 | 2.083 | 2.048 | 2.017 | 1.989 | 1.963 |
230 | 2.326 | 2.263 | 2.208 | 2.160 | 2.117 | 2.079 | 2.045 | 2.014 | 1.985 | 1.959 |
240 | 2.322 | 2.260 | 2.205 | 2.157 | 2.114 | 2.076 | 2.041 | 2.010 | 1.982 | 1.956 |
250 | 2.319 | 2.257 | 2.202 | 2.154 | 2.111 | 2.073 | 2.038 | 2.007 | 1.979 | 1.953 |
n∖m | 30 | 40 | 50 | 60 | 70 | 80 | 90 | 100 | 110 | 120 |
1 | 6261 | 6287 | 6303 | 6313 | 6321 | 6326 | 6331 | 6334 | 6337 | 6339 |
2 | 99.47 | 99.47 | 99.48 | 99.48 | 99.48 | 99.49 | 99.49 | 99.49 | 99.49 | 99.49 |
3 | 26.50 | 26.41 | 26.35 | 26.32 | 26.29 | 26.27 | 26.25 | 26.24 | 26.23 | 26.22 |
4 | 13.84 | 13.75 | 13.69 | 13.65 | 13.63 | 13.61 | 13.59 | 13.58 | 13.57 | 13.56 |
5 | 9.379 | 9.291 | 9.238 | 9.202 | 9.176 | 9.157 | 9.142 | 9.130 | 9.120 | 9.112 |
6 | 7.229 | 7.143 | 7.091 | 7.057 | 7.032 | 7.013 | 6.998 | 6.987 | 6.977 | 6.969 |
7 | 5.992 | 5.908 | 5.858 | 5.824 | 5.799 | 5.781 | 5.766 | 5.755 | 5.745 | 5.737 |
8 | 5.198 | 5.116 | 5.065 | 5.032 | 5.007 | 4.989 | 4.975 | 4.963 | 4.954 | 4.946 |
9 | 4.649 | 4.567 | 4.517 | 4.483 | 4.459 | 4.441 | 4.426 | 4.415 | 4.406 | 4.398 |
10 | 4.247 | 4.165 | 4.115 | 4.082 | 4.058 | 4.039 | 4.025 | 4.014 | 4.004 | 3.996 |
30 | 40 | 50 | 60 | 70 | 80 | 90 | 100 | 110 | 120 | |
11 | 3.941 | 3.860 | 3.810 | 3.776 | 3.752 | 3.734 | 3.719 | 3.708 | 3.698 | 3.690 |
12 | 3.701 | 3.619 | 3.569 | 3.535 | 3.511 | 3.493 | 3.478 | 3.467 | 3.457 | 3.449 |
13 | 3.507 | 3.425 | 3.375 | 3.341 | 3.317 | 3.298 | 3.284 | 3.272 | 3.263 | 3.255 |
14 | 3.348 | 3.266 | 3.215 | 3.181 | 3.157 | 3.138 | 3.124 | 3.112 | 3.102 | 3.094 |
15 | 3.214 | 3.132 | 3.081 | 3.047 | 3.022 | 3.004 | 2.989 | 2.977 | 2.968 | 2.959 |
16 | 3.101 | 3.018 | 2.967 | 2.933 | 2.908 | 2.889 | 2.875 | 2.863 | 2.853 | 2.845 |
17 | 3.003 | 2.920 | 2.869 | 2.835 | 2.810 | 2.791 | 2.776 | 2.764 | 2.754 | 2.746 |
18 | 2.919 | 2.835 | 2.784 | 2.749 | 2.724 | 2.705 | 2.690 | 2.678 | 2.668 | 2.660 |
19 | 2.844 | 2.761 | 2.709 | 2.674 | 2.649 | 2.630 | 2.614 | 2.602 | 2.592 | 2.584 |
20 | 2.778 | 2.695 | 2.643 | 2.608 | 2.582 | 2.563 | 2.548 | 2.535 | 2.525 | 2.517 |
30 | 40 | 50 | 60 | 70 | 80 | 90 | 100 | 110 | 120 | |
21 | 2.720 | 2.636 | 2.584 | 2.548 | 2.523 | 2.503 | 2.488 | 2.475 | 2.465 | 2.457 |
22 | 2.667 | 2.583 | 2.531 | 2.495 | 2.469 | 2.450 | 2.434 | 2.422 | 2.412 | 2.403 |
23 | 2.620 | 2.535 | 2.483 | 2.447 | 2.421 | 2.401 | 2.386 | 2.373 | 2.363 | 2.354 |
24 | 2.577 | 2.492 | 2.440 | 2.403 | 2.377 | 2.357 | 2.342 | 2.329 | 2.319 | 2.310 |
25 | 2.538 | 2.453 | 2.400 | 2.364 | 2.337 | 2.317 | 2.302 | 2.289 | 2.278 | 2.270 |
26 | 2.503 | 2.417 | 2.364 | 2.327 | 2.301 | 2.281 | 2.265 | 2.252 | 2.241 | 2.233 |
27 | 2.470 | 2.384 | 2.330 | 2.294 | 2.267 | 2.247 | 2.231 | 2.218 | 2.207 | 2.198 |
28 | 2.440 | 2.354 | 2.300 | 2.263 | 2.236 | 2.216 | 2.200 | 2.187 | 2.176 | 2.167 |
29 | 2.412 | 2.325 | 2.271 | 2.234 | 2.207 | 2.187 | 2.171 | 2.158 | 2.147 | 2.138 |
30 | 2.386 | 2.299 | 2.245 | 2.208 | 2.181 | 2.160 | 2.144 | 2.131 | 2.120 | 2.111 |
30 | 40 | 50 | 60 | 70 | 80 | 90 | 100 | 110 | 120 | |
31 | 2.362 | 2.275 | 2.220 | 2.183 | 2.156 | 2.135 | 2.119 | 2.106 | 2.095 | 2.086 |
32 | 2.340 | 2.252 | 2.198 | 2.160 | 2.133 | 2.112 | 2.095 | 2.082 | 2.071 | 2.062 |
33 | 2.319 | 2.231 | 2.176 | 2.139 | 2.111 | 2.090 | 2.074 | 2.060 | 2.049 | 2.040 |
34 | 2.299 | 2.211 | 2.156 | 2.118 | 2.091 | 2.070 | 2.053 | 2.040 | 2.028 | 2.019 |
35 | 2.281 | 2.193 | 2.137 | 2.099 | 2.072 | 2.050 | 2.034 | 2.020 | 2.009 | 2.000 |
36 | 2.263 | 2.175 | 2.120 | 2.082 | 2.054 | 2.032 | 2.016 | 2.002 | 1.991 | 1.981 |
37 | 2.247 | 2.159 | 2.103 | 2.065 | 2.037 | 2.015 | 1.998 | 1.985 | 1.973 | 1.964 |
38 | 2.232 | 2.143 | 2.087 | 2.049 | 2.021 | 1.999 | 1.982 | 1.968 | 1.957 | 1.947 |
39 | 2.217 | 2.128 | 2.072 | 2.034 | 2.005 | 1.984 | 1.967 | 1.953 | 1.942 | 1.932 |
40 | 2.203 | 2.114 | 2.058 | 2.019 | 1.991 | 1.969 | 1.952 | 1.938 | 1.927 | 1.917 |
30 | 40 | 50 | 60 | 70 | 80 | 90 | 100 | 110 | 120 | |
41 | 2.190 | 2.101 | 2.045 | 2.006 | 1.977 | 1.956 | 1.938 | 1.924 | 1.913 | 1.903 |
42 | 2.178 | 2.088 | 2.032 | 1.993 | 1.964 | 1.943 | 1.925 | 1.911 | 1.900 | 1.890 |
43 | 2.166 | 2.076 | 2.020 | 1.981 | 1.952 | 1.930 | 1.913 | 1.899 | 1.887 | 1.877 |
44 | 2.155 | 2.065 | 2.008 | 1.969 | 1.940 | 1.918 | 1.901 | 1.887 | 1.875 | 1.865 |
45 | 2.144 | 2.054 | 1.997 | 1.958 | 1.929 | 1.907 | 1.889 | 1.875 | 1.863 | 1.853 |
46 | 2.134 | 2.044 | 1.987 | 1.947 | 1.918 | 1.896 | 1.878 | 1.864 | 1.852 | 1.842 |
47 | 2.124 | 2.034 | 1.977 | 1.937 | 1.908 | 1.886 | 1.868 | 1.854 | 1.842 | 1.832 |
48 | 2.115 | 2.024 | 1.967 | 1.927 | 1.898 | 1.876 | 1.858 | 1.844 | 1.832 | 1.822 |
49 | 2.106 | 2.015 | 1.958 | 1.918 | 1.889 | 1.866 | 1.848 | 1.834 | 1.822 | 1.812 |
50 | 2.098 | 2.007 | 1.949 | 1.909 | 1.880 | 1.857 | 1.839 | 1.825 | 1.813 | 1.803 |
30 | 40 | 50 | 60 | 70 | 80 | 90 | 100 | 110 | 120 | |
60 | 2.028 | 1.936 | 1.877 | 1.836 | 1.806 | 1.783 | 1.764 | 1.749 | 1.737 | 1.726 |
70 | 1.980 | 1.886 | 1.826 | 1.785 | 1.754 | 1.730 | 1.711 | 1.695 | 1.683 | 1.672 |
80 | 1.944 | 1.849 | 1.788 | 1.746 | 1.714 | 1.690 | 1.671 | 1.655 | 1.642 | 1.630 |
90 | 1.916 | 1.820 | 1.759 | 1.716 | 1.684 | 1.659 | 1.639 | 1.623 | 1.610 | 1.598 |
100 | 1.893 | 1.797 | 1.735 | 1.692 | 1.659 | 1.634 | 1.614 | 1.598 | 1.584 | 1.572 |
110 | 1.875 | 1.778 | 1.716 | 1.672 | 1.639 | 1.614 | 1.593 | 1.577 | 1.563 | 1.551 |
120 | 1.860 | 1.763 | 1.700 | 1.656 | 1.623 | 1.597 | 1.576 | 1.559 | 1.545 | 1.533 |
130 | 1.847 | 1.750 | 1.686 | 1.642 | 1.608 | 1.582 | 1.562 | 1.544 | 1.530 | 1.518 |
140 | 1.836 | 1.738 | 1.675 | 1.630 | 1.596 | 1.570 | 1.549 | 1.532 | 1.517 | 1.505 |
150 | 1.827 | 1.729 | 1.665 | 1.620 | 1.586 | 1.559 | 1.538 | 1.520 | 1.506 | 1.493 |
30 | 40 | 50 | 60 | 70 | 80 | 90 | 100 | 110 | 120 | |
160 | 1.819 | 1.720 | 1.656 | 1.610 | 1.576 | 1.550 | 1.528 | 1.511 | 1.496 | 1.483 |
170 | 1.811 | 1.713 | 1.648 | 1.602 | 1.568 | 1.541 | 1.520 | 1.502 | 1.487 | 1.474 |
180 | 1.805 | 1.706 | 1.641 | 1.595 | 1.561 | 1.534 | 1.512 | 1.494 | 1.479 | 1.466 |
190 | 1.799 | 1.700 | 1.635 | 1.589 | 1.554 | 1.527 | 1.505 | 1.487 | 1.472 | 1.459 |
200 | 1.794 | 1.694 | 1.629 | 1.583 | 1.548 | 1.521 | 1.499 | 1.481 | 1.466 | 1.453 |
210 | 1.789 | 1.690 | 1.624 | 1.578 | 1.543 | 1.516 | 1.494 | 1.475 | 1.460 | 1.447 |
220 | 1.785 | 1.685 | 1.620 | 1.573 | 1.538 | 1.511 | 1.489 | 1.470 | 1.455 | 1.442 |
230 | 1.781 | 1.681 | 1.616 | 1.569 | 1.534 | 1.506 | 1.484 | 1.465 | 1.450 | 1.437 |
240 | 1.778 | 1.677 | 1.612 | 1.565 | 1.530 | 1.502 | 1.480 | 1.461 | 1.446 | 1.432 |
250 | 1.774 | 1.674 | 1.608 | 1.561 | 1.526 | 1.498 | 1.476 | 1.457 | 1.441 | 1.428 |
分布表のタイプを選択
1. F分布(0.05) | 2. F分布(0.025) | 3. F分布(0.01) | 4. F分布(0.005)
α=0.005 のとき,表頭の自由度 m と表側の自由度 n に対して,F分布の上側 α 点 Fα(m,n) を示す。 \[ \alpha \longmapsto F_\alpha(m,n),\qquad \text{Pr}\{X>F_\alpha(m,n)\}=\alpha \] F1-α(m,n) と Fα(n,m) について, \[ F_{1-\alpha}(m,n)=\frac{1}{F_\alpha(n,m)},\qquad F_{0.995}(m,n)=\frac{1}{F_{0.005}(n,m)} \] が成り立つから,この表を用いて上側 0.995 点を求めることができる。
n∖m | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
1 | 16211 | 19999 | 21615 | 22500 | 23056 | 23437 | 23715 | 23925 | 24091 | 24224 |
2 | 198.5 | 199.0 | 199.2 | 199.2 | 199.3 | 199.3 | 199.4 | 199.4 | 199.4 | 199.4 |
3 | 55.55 | 49.80 | 47.47 | 46.19 | 45.39 | 44.84 | 44.43 | 44.13 | 43.88 | 43.69 |
4 | 31.33 | 26.28 | 24.26 | 23.15 | 22.46 | 21.97 | 21.62 | 21.35 | 21.14 | 20.97 |
5 | 22.78 | 18.31 | 16.53 | 15.56 | 14.94 | 14.51 | 14.20 | 13.96 | 13.77 | 13.62 |
6 | 18.63 | 14.54 | 12.92 | 12.03 | 11.46 | 11.07 | 10.79 | 10.57 | 10.39 | 10.25 |
7 | 16.24 | 12.40 | 10.88 | 10.05 | 9.522 | 9.155 | 8.885 | 8.678 | 8.514 | 8.380 |
8 | 14.69 | 11.04 | 9.596 | 8.805 | 8.302 | 7.952 | 7.694 | 7.496 | 7.339 | 7.211 |
9 | 13.61 | 10.11 | 8.717 | 7.956 | 7.471 | 7.134 | 6.885 | 6.693 | 6.541 | 6.417 |
10 | 12.83 | 9.427 | 8.081 | 7.343 | 6.872 | 6.545 | 6.302 | 6.116 | 5.968 | 5.847 |
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |
11 | 12.23 | 8.912 | 7.600 | 6.881 | 6.422 | 6.102 | 5.865 | 5.682 | 5.537 | 5.418 |
12 | 11.75 | 8.510 | 7.226 | 6.521 | 6.071 | 5.757 | 5.525 | 5.345 | 5.202 | 5.085 |
13 | 11.37 | 8.186 | 6.926 | 6.233 | 5.791 | 5.482 | 5.253 | 5.076 | 4.935 | 4.820 |
14 | 11.06 | 7.922 | 6.680 | 5.998 | 5.562 | 5.257 | 5.031 | 4.857 | 4.717 | 4.603 |
15 | 10.80 | 7.701 | 6.476 | 5.803 | 5.372 | 5.071 | 4.847 | 4.674 | 4.536 | 4.424 |
16 | 10.58 | 7.514 | 6.303 | 5.638 | 5.212 | 4.913 | 4.692 | 4.521 | 4.384 | 4.272 |
17 | 10.38 | 7.354 | 6.156 | 5.497 | 5.075 | 4.779 | 4.559 | 4.389 | 4.254 | 4.142 |
18 | 10.22 | 7.215 | 6.028 | 5.375 | 4.956 | 4.663 | 4.445 | 4.276 | 4.141 | 4.030 |
19 | 10.07 | 7.093 | 5.916 | 5.268 | 4.853 | 4.561 | 4.345 | 4.177 | 4.043 | 3.933 |
20 | 9.944 | 6.986 | 5.818 | 5.174 | 4.762 | 4.472 | 4.257 | 4.090 | 3.956 | 3.847 |
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |
21 | 9.830 | 6.891 | 5.730 | 5.091 | 4.681 | 4.393 | 4.179 | 4.013 | 3.880 | 3.771 |
22 | 9.727 | 6.806 | 5.652 | 5.017 | 4.609 | 4.322 | 4.109 | 3.944 | 3.812 | 3.703 |
23 | 9.635 | 6.730 | 5.582 | 4.950 | 4.544 | 4.259 | 4.047 | 3.882 | 3.750 | 3.642 |
24 | 9.551 | 6.661 | 5.519 | 4.890 | 4.486 | 4.202 | 3.991 | 3.826 | 3.695 | 3.587 |
25 | 9.475 | 6.598 | 5.462 | 4.835 | 4.433 | 4.150 | 3.939 | 3.776 | 3.645 | 3.537 |
26 | 9.406 | 6.541 | 5.409 | 4.785 | 4.384 | 4.103 | 3.893 | 3.730 | 3.599 | 3.492 |
27 | 9.342 | 6.489 | 5.361 | 4.740 | 4.340 | 4.059 | 3.850 | 3.687 | 3.557 | 3.450 |
28 | 9.284 | 6.440 | 5.317 | 4.698 | 4.300 | 4.020 | 3.811 | 3.649 | 3.519 | 3.412 |
29 | 9.230 | 6.396 | 5.276 | 4.659 | 4.262 | 3.983 | 3.775 | 3.613 | 3.483 | 3.377 |
30 | 9.180 | 6.355 | 5.239 | 4.623 | 4.228 | 3.949 | 3.742 | 3.580 | 3.450 | 3.344 |
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |
31 | 9.133 | 6.317 | 5.204 | 4.590 | 4.196 | 3.918 | 3.711 | 3.549 | 3.420 | 3.314 |
32 | 9.090 | 6.281 | 5.171 | 4.559 | 4.166 | 3.889 | 3.682 | 3.521 | 3.392 | 3.286 |
33 | 9.050 | 6.248 | 5.141 | 4.531 | 4.138 | 3.861 | 3.655 | 3.495 | 3.366 | 3.260 |
34 | 9.012 | 6.217 | 5.113 | 4.504 | 4.112 | 3.836 | 3.630 | 3.470 | 3.341 | 3.235 |
35 | 8.976 | 6.188 | 5.086 | 4.479 | 4.088 | 3.812 | 3.607 | 3.447 | 3.318 | 3.212 |
36 | 8.943 | 6.161 | 5.062 | 4.455 | 4.065 | 3.790 | 3.585 | 3.425 | 3.296 | 3.191 |
37 | 8.912 | 6.135 | 5.038 | 4.433 | 4.043 | 3.769 | 3.564 | 3.404 | 3.276 | 3.171 |
38 | 8.882 | 6.111 | 5.016 | 4.412 | 4.023 | 3.749 | 3.545 | 3.385 | 3.257 | 3.152 |
39 | 8.854 | 6.088 | 4.995 | 4.392 | 4.004 | 3.731 | 3.526 | 3.367 | 3.239 | 3.134 |
40 | 8.828 | 6.066 | 4.976 | 4.374 | 3.986 | 3.713 | 3.509 | 3.350 | 3.222 | 3.117 |
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |
41 | 8.803 | 6.046 | 4.957 | 4.356 | 3.969 | 3.696 | 3.492 | 3.334 | 3.206 | 3.101 |
42 | 8.779 | 6.027 | 4.940 | 4.339 | 3.953 | 3.680 | 3.477 | 3.318 | 3.191 | 3.086 |
43 | 8.757 | 6.008 | 4.923 | 4.324 | 3.937 | 3.665 | 3.462 | 3.304 | 3.176 | 3.071 |
44 | 8.735 | 5.991 | 4.907 | 4.308 | 3.923 | 3.651 | 3.448 | 3.290 | 3.162 | 3.057 |
45 | 8.715 | 5.974 | 4.892 | 4.294 | 3.909 | 3.638 | 3.435 | 3.276 | 3.149 | 3.044 |
46 | 8.695 | 5.958 | 4.877 | 4.280 | 3.896 | 3.625 | 3.422 | 3.264 | 3.137 | 3.032 |
47 | 8.677 | 5.943 | 4.864 | 4.267 | 3.883 | 3.612 | 3.410 | 3.252 | 3.125 | 3.020 |
48 | 8.659 | 5.929 | 4.850 | 4.255 | 3.871 | 3.601 | 3.398 | 3.240 | 3.113 | 3.009 |
49 | 8.642 | 5.915 | 4.838 | 4.243 | 3.860 | 3.589 | 3.387 | 3.229 | 3.102 | 2.998 |
50 | 8.626 | 5.902 | 4.826 | 4.232 | 3.849 | 3.579 | 3.376 | 3.219 | 3.092 | 2.988 |
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |
60 | 8.495 | 5.795 | 4.729 | 4.140 | 3.760 | 3.492 | 3.291 | 3.134 | 3.008 | 2.904 |
70 | 8.403 | 5.720 | 4.661 | 4.076 | 3.698 | 3.431 | 3.232 | 3.076 | 2.950 | 2.846 |
80 | 8.335 | 5.665 | 4.611 | 4.029 | 3.652 | 3.387 | 3.188 | 3.032 | 2.907 | 2.803 |
90 | 8.282 | 5.623 | 4.573 | 3.992 | 3.617 | 3.352 | 3.154 | 2.999 | 2.873 | 2.770 |
100 | 8.241 | 5.589 | 4.542 | 3.963 | 3.589 | 3.325 | 3.127 | 2.972 | 2.847 | 2.744 |
110 | 8.207 | 5.562 | 4.518 | 3.940 | 3.567 | 3.303 | 3.105 | 2.951 | 2.826 | 2.723 |
120 | 8.179 | 5.539 | 4.497 | 3.921 | 3.548 | 3.285 | 3.087 | 2.933 | 2.808 | 2.705 |
130 | 8.155 | 5.520 | 4.480 | 3.904 | 3.533 | 3.270 | 3.072 | 2.918 | 2.793 | 2.690 |
140 | 8.135 | 5.504 | 4.465 | 3.890 | 3.519 | 3.256 | 3.059 | 2.905 | 2.781 | 2.678 |
150 | 8.118 | 5.490 | 4.453 | 3.878 | 3.508 | 3.245 | 3.048 | 2.894 | 2.770 | 2.667 |
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |
160 | 8.102 | 5.478 | 4.441 | 3.868 | 3.497 | 3.235 | 3.039 | 2.885 | 2.760 | 2.657 |
170 | 8.089 | 5.467 | 4.432 | 3.859 | 3.489 | 3.227 | 3.030 | 2.876 | 2.752 | 2.649 |
180 | 8.077 | 5.457 | 4.423 | 3.851 | 3.481 | 3.219 | 3.022 | 2.869 | 2.744 | 2.642 |
190 | 8.067 | 5.449 | 4.415 | 3.843 | 3.474 | 3.212 | 3.016 | 2.862 | 2.738 | 2.635 |
200 | 8.057 | 5.441 | 4.408 | 3.837 | 3.467 | 3.206 | 3.010 | 2.856 | 2.732 | 2.629 |
210 | 8.049 | 5.434 | 4.402 | 3.831 | 3.462 | 3.200 | 3.004 | 2.851 | 2.727 | 2.624 |
220 | 8.041 | 5.428 | 4.396 | 3.826 | 3.456 | 3.195 | 2.999 | 2.846 | 2.722 | 2.619 |
230 | 8.034 | 5.422 | 4.391 | 3.821 | 3.452 | 3.191 | 2.995 | 2.841 | 2.717 | 2.615 |
240 | 8.027 | 5.417 | 4.387 | 3.816 | 3.447 | 3.187 | 2.991 | 2.837 | 2.713 | 2.610 |
250 | 8.021 | 5.412 | 4.382 | 3.812 | 3.443 | 3.183 | 2.987 | 2.833 | 2.709 | 2.607 |
n∖m | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |
1 | 24334 | 24426 | 24505 | 24572 | 24630 | 24681 | 24727 | 24767 | 24803 | 24836 |
2 | 199.4 | 199.4 | 199.4 | 199.4 | 199.4 | 199.4 | 199.4 | 199.4 | 199.4 | 199.4 |
3 | 43.52 | 43.39 | 43.27 | 43.17 | 43.08 | 43.01 | 42.94 | 42.88 | 42.83 | 42.78 |
4 | 20.82 | 20.70 | 20.60 | 20.51 | 20.44 | 20.37 | 20.31 | 20.26 | 20.21 | 20.17 |
5 | 13.49 | 13.38 | 13.29 | 13.21 | 13.15 | 13.09 | 13.03 | 12.98 | 12.94 | 12.90 |
6 | 10.13 | 10.03 | 9.950 | 9.877 | 9.814 | 9.758 | 9.709 | 9.664 | 9.625 | 9.589 |
7 | 8.270 | 8.176 | 8.097 | 8.028 | 7.968 | 7.915 | 7.868 | 7.826 | 7.788 | 7.754 |
8 | 7.104 | 7.015 | 6.938 | 6.872 | 6.814 | 6.763 | 6.718 | 6.678 | 6.641 | 6.608 |
9 | 6.314 | 6.227 | 6.153 | 6.089 | 6.032 | 5.983 | 5.939 | 5.899 | 5.864 | 5.832 |
10 | 5.746 | 5.661 | 5.589 | 5.526 | 5.471 | 5.422 | 5.379 | 5.340 | 5.305 | 5.274 |
11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | |
11 | 5.320 | 5.236 | 5.165 | 5.103 | 5.049 | 5.001 | 4.959 | 4.921 | 4.886 | 4.855 |
12 | 4.988 | 4.906 | 4.836 | 4.775 | 4.721 | 4.674 | 4.632 | 4.595 | 4.561 | 4.530 |
13 | 4.724 | 4.643 | 4.573 | 4.513 | 4.460 | 4.413 | 4.372 | 4.334 | 4.301 | 4.270 |
14 | 4.508 | 4.428 | 4.359 | 4.299 | 4.247 | 4.200 | 4.159 | 4.122 | 4.089 | 4.059 |
15 | 4.329 | 4.250 | 4.181 | 4.122 | 4.070 | 4.024 | 3.983 | 3.946 | 3.913 | 3.883 |
16 | 4.179 | 4.099 | 4.031 | 3.972 | 3.920 | 3.875 | 3.834 | 3.797 | 3.764 | 3.734 |
17 | 4.050 | 3.971 | 3.903 | 3.844 | 3.793 | 3.747 | 3.707 | 3.670 | 3.637 | 3.607 |
18 | 3.938 | 3.860 | 3.793 | 3.734 | 3.683 | 3.637 | 3.597 | 3.560 | 3.527 | 3.498 |
19 | 3.841 | 3.763 | 3.696 | 3.638 | 3.587 | 3.541 | 3.501 | 3.465 | 3.432 | 3.402 |
20 | 3.756 | 3.678 | 3.611 | 3.553 | 3.502 | 3.457 | 3.416 | 3.380 | 3.347 | 3.318 |
11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | |
21 | 3.680 | 3.602 | 3.536 | 3.478 | 3.427 | 3.382 | 3.342 | 3.305 | 3.273 | 3.243 |
22 | 3.612 | 3.535 | 3.469 | 3.411 | 3.360 | 3.315 | 3.275 | 3.239 | 3.206 | 3.176 |
23 | 3.551 | 3.475 | 3.408 | 3.351 | 3.300 | 3.255 | 3.215 | 3.179 | 3.146 | 3.116 |
24 | 3.497 | 3.420 | 3.354 | 3.296 | 3.246 | 3.201 | 3.161 | 3.125 | 3.092 | 3.062 |
25 | 3.447 | 3.370 | 3.304 | 3.247 | 3.196 | 3.151 | 3.111 | 3.075 | 3.043 | 3.013 |
26 | 3.402 | 3.325 | 3.259 | 3.202 | 3.151 | 3.107 | 3.067 | 3.031 | 2.998 | 2.968 |
27 | 3.360 | 3.284 | 3.218 | 3.161 | 3.110 | 3.066 | 3.026 | 2.990 | 2.957 | 2.928 |
28 | 3.322 | 3.246 | 3.180 | 3.123 | 3.073 | 3.028 | 2.988 | 2.952 | 2.919 | 2.890 |
29 | 3.287 | 3.211 | 3.145 | 3.088 | 3.038 | 2.993 | 2.953 | 2.917 | 2.885 | 2.855 |
30 | 3.255 | 3.179 | 3.113 | 3.056 | 3.006 | 2.961 | 2.921 | 2.885 | 2.853 | 2.823 |
11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | |
31 | 3.225 | 3.149 | 3.083 | 3.026 | 2.976 | 2.931 | 2.891 | 2.855 | 2.823 | 2.793 |
32 | 3.197 | 3.121 | 3.056 | 2.998 | 2.948 | 2.904 | 2.864 | 2.828 | 2.795 | 2.766 |
33 | 3.171 | 3.095 | 3.030 | 2.973 | 2.922 | 2.878 | 2.838 | 2.802 | 2.769 | 2.740 |
34 | 3.146 | 3.071 | 3.005 | 2.948 | 2.898 | 2.854 | 2.814 | 2.778 | 2.745 | 2.716 |
35 | 3.124 | 3.048 | 2.983 | 2.926 | 2.876 | 2.831 | 2.791 | 2.755 | 2.723 | 2.693 |
36 | 3.102 | 3.027 | 2.961 | 2.905 | 2.854 | 2.810 | 2.770 | 2.734 | 2.701 | 2.672 |
37 | 3.082 | 3.007 | 2.941 | 2.885 | 2.834 | 2.790 | 2.750 | 2.714 | 2.681 | 2.652 |
38 | 3.063 | 2.988 | 2.923 | 2.866 | 2.816 | 2.771 | 2.731 | 2.695 | 2.663 | 2.633 |
39 | 3.045 | 2.970 | 2.905 | 2.848 | 2.798 | 2.753 | 2.713 | 2.677 | 2.645 | 2.615 |
40 | 3.028 | 2.953 | 2.888 | 2.831 | 2.781 | 2.737 | 2.697 | 2.661 | 2.628 | 2.598 |
11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | |
41 | 3.012 | 2.937 | 2.872 | 2.815 | 2.765 | 2.721 | 2.681 | 2.645 | 2.612 | 2.583 |
42 | 2.997 | 2.922 | 2.857 | 2.800 | 2.750 | 2.706 | 2.666 | 2.630 | 2.597 | 2.567 |
43 | 2.983 | 2.908 | 2.843 | 2.786 | 2.736 | 2.691 | 2.651 | 2.615 | 2.583 | 2.553 |
44 | 2.969 | 2.894 | 2.829 | 2.772 | 2.722 | 2.678 | 2.638 | 2.602 | 2.569 | 2.540 |
45 | 2.956 | 2.881 | 2.816 | 2.759 | 2.709 | 2.665 | 2.625 | 2.589 | 2.556 | 2.527 |
46 | 2.944 | 2.869 | 2.804 | 2.747 | 2.697 | 2.653 | 2.613 | 2.577 | 2.544 | 2.514 |
47 | 2.932 | 2.857 | 2.792 | 2.735 | 2.685 | 2.641 | 2.601 | 2.565 | 2.532 | 2.502 |
48 | 2.921 | 2.846 | 2.781 | 2.724 | 2.674 | 2.630 | 2.590 | 2.554 | 2.521 | 2.491 |
49 | 2.910 | 2.835 | 2.770 | 2.713 | 2.663 | 2.619 | 2.579 | 2.543 | 2.510 | 2.480 |
50 | 2.900 | 2.825 | 2.760 | 2.703 | 2.653 | 2.609 | 2.569 | 2.533 | 2.500 | 2.470 |
11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | |
60 | 2.817 | 2.742 | 2.677 | 2.620 | 2.570 | 2.526 | 2.486 | 2.450 | 2.417 | 2.387 |
70 | 2.759 | 2.684 | 2.619 | 2.563 | 2.513 | 2.468 | 2.428 | 2.392 | 2.359 | 2.329 |
80 | 2.716 | 2.641 | 2.577 | 2.520 | 2.470 | 2.425 | 2.385 | 2.349 | 2.316 | 2.286 |
90 | 2.683 | 2.608 | 2.544 | 2.487 | 2.437 | 2.393 | 2.353 | 2.316 | 2.283 | 2.253 |
100 | 2.657 | 2.583 | 2.518 | 2.461 | 2.411 | 2.367 | 2.326 | 2.290 | 2.257 | 2.227 |
110 | 2.636 | 2.561 | 2.497 | 2.440 | 2.390 | 2.345 | 2.305 | 2.269 | 2.236 | 2.206 |
120 | 2.618 | 2.544 | 2.479 | 2.423 | 2.373 | 2.328 | 2.288 | 2.251 | 2.218 | 2.188 |
130 | 2.604 | 2.529 | 2.465 | 2.408 | 2.358 | 2.313 | 2.273 | 2.237 | 2.204 | 2.173 |
140 | 2.591 | 2.517 | 2.452 | 2.396 | 2.345 | 2.301 | 2.260 | 2.224 | 2.191 | 2.161 |
150 | 2.580 | 2.506 | 2.441 | 2.385 | 2.335 | 2.290 | 2.250 | 2.213 | 2.180 | 2.150 |
11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | |
160 | 2.571 | 2.496 | 2.432 | 2.375 | 2.325 | 2.280 | 2.240 | 2.204 | 2.170 | 2.140 |
170 | 2.562 | 2.488 | 2.424 | 2.367 | 2.317 | 2.272 | 2.232 | 2.195 | 2.162 | 2.132 |
180 | 2.555 | 2.481 | 2.416 | 2.360 | 2.309 | 2.265 | 2.224 | 2.188 | 2.155 | 2.124 |
190 | 2.548 | 2.474 | 2.410 | 2.353 | 2.303 | 2.258 | 2.218 | 2.181 | 2.148 | 2.118 |
200 | 2.543 | 2.468 | 2.404 | 2.347 | 2.297 | 2.252 | 2.212 | 2.175 | 2.142 | 2.112 |
210 | 2.537 | 2.463 | 2.398 | 2.342 | 2.292 | 2.247 | 2.206 | 2.170 | 2.137 | 2.106 |
220 | 2.532 | 2.458 | 2.394 | 2.337 | 2.287 | 2.242 | 2.202 | 2.165 | 2.132 | 2.101 |
230 | 2.528 | 2.454 | 2.389 | 2.333 | 2.282 | 2.238 | 2.197 | 2.161 | 2.127 | 2.097 |
240 | 2.524 | 2.450 | 2.385 | 2.329 | 2.278 | 2.233 | 2.193 | 2.157 | 2.123 | 2.093 |
250 | 2.520 | 2.446 | 2.381 | 2.325 | 2.275 | 2.230 | 2.189 | 2.153 | 2.119 | 2.089 |
n∖m | 30 | 40 | 50 | 60 | 70 | 80 | 90 | 100 | 110 | 120 |
1 | 25044 | 25148 | 25211 | 25253 | 25283 | 25306 | 25323 | 25337 | 25349 | 25359 |
2 | 199.5 | 199.5 | 199.5 | 199.5 | 199.5 | 199.5 | 199.5 | 199.5 | 199.5 | 199.5 |
3 | 42.47 | 42.31 | 42.21 | 42.15 | 42.10 | 42.07 | 42.04 | 42.02 | 42.00 | 41.99 |
4 | 19.89 | 19.75 | 19.67 | 19.61 | 19.57 | 19.54 | 19.52 | 19.50 | 19.48 | 19.47 |
5 | 12.66 | 12.53 | 12.45 | 12.40 | 12.37 | 12.34 | 12.32 | 12.30 | 12.29 | 12.27 |
6 | 9.358 | 9.241 | 9.170 | 9.122 | 9.088 | 9.062 | 9.042 | 9.026 | 9.012 | 9.001 |
7 | 7.534 | 7.422 | 7.354 | 7.309 | 7.276 | 7.251 | 7.232 | 7.217 | 7.204 | 7.193 |
8 | 6.396 | 6.288 | 6.222 | 6.177 | 6.145 | 6.121 | 6.103 | 6.088 | 6.075 | 6.065 |
9 | 5.625 | 5.519 | 5.454 | 5.410 | 5.379 | 5.356 | 5.337 | 5.322 | 5.310 | 5.300 |
10 | 5.071 | 4.966 | 4.902 | 4.859 | 4.828 | 4.805 | 4.787 | 4.772 | 4.760 | 4.750 |
30 | 40 | 50 | 60 | 70 | 80 | 90 | 100 | 110 | 120 | |
11 | 4.654 | 4.551 | 4.488 | 4.445 | 4.414 | 4.391 | 4.373 | 4.359 | 4.347 | 4.337 |
12 | 4.331 | 4.228 | 4.165 | 4.123 | 4.092 | 4.069 | 4.051 | 4.037 | 4.025 | 4.015 |
13 | 4.073 | 3.970 | 3.908 | 3.866 | 3.835 | 3.812 | 3.794 | 3.780 | 3.768 | 3.758 |
14 | 3.862 | 3.760 | 3.698 | 3.655 | 3.625 | 3.602 | 3.584 | 3.569 | 3.557 | 3.547 |
15 | 3.687 | 3.585 | 3.523 | 3.480 | 3.450 | 3.427 | 3.409 | 3.394 | 3.382 | 3.372 |
16 | 3.539 | 3.437 | 3.375 | 3.332 | 3.302 | 3.279 | 3.261 | 3.246 | 3.234 | 3.224 |
17 | 3.412 | 3.311 | 3.248 | 3.206 | 3.175 | 3.152 | 3.134 | 3.119 | 3.107 | 3.097 |
18 | 3.303 | 3.201 | 3.139 | 3.096 | 3.065 | 3.042 | 3.024 | 3.009 | 2.997 | 2.987 |
19 | 3.208 | 3.106 | 3.043 | 3.000 | 2.970 | 2.946 | 2.928 | 2.913 | 2.901 | 2.891 |
20 | 3.123 | 3.022 | 2.959 | 2.916 | 2.885 | 2.861 | 2.843 | 2.828 | 2.816 | 2.806 |
30 | 40 | 50 | 60 | 70 | 80 | 90 | 100 | 110 | 120 | |
21 | 3.049 | 2.947 | 2.884 | 2.841 | 2.810 | 2.786 | 2.768 | 2.753 | 2.740 | 2.730 |
22 | 2.982 | 2.880 | 2.817 | 2.774 | 2.742 | 2.719 | 2.700 | 2.685 | 2.673 | 2.663 |
23 | 2.922 | 2.820 | 2.756 | 2.713 | 2.682 | 2.658 | 2.639 | 2.624 | 2.612 | 2.602 |
24 | 2.868 | 2.765 | 2.702 | 2.658 | 2.627 | 2.603 | 2.584 | 2.569 | 2.557 | 2.546 |
25 | 2.819 | 2.716 | 2.652 | 2.609 | 2.577 | 2.553 | 2.534 | 2.519 | 2.507 | 2.496 |
26 | 2.774 | 2.671 | 2.607 | 2.563 | 2.532 | 2.508 | 2.489 | 2.473 | 2.461 | 2.450 |
27 | 2.733 | 2.630 | 2.565 | 2.522 | 2.490 | 2.466 | 2.447 | 2.431 | 2.419 | 2.408 |
28 | 2.695 | 2.592 | 2.527 | 2.483 | 2.451 | 2.427 | 2.408 | 2.392 | 2.380 | 2.369 |
29 | 2.660 | 2.557 | 2.492 | 2.448 | 2.416 | 2.391 | 2.372 | 2.357 | 2.344 | 2.333 |
30 | 2.628 | 2.524 | 2.459 | 2.415 | 2.383 | 2.358 | 2.339 | 2.323 | 2.311 | 2.300 |
30 | 40 | 50 | 60 | 70 | 80 | 90 | 100 | 110 | 120 | |
31 | 2.598 | 2.494 | 2.429 | 2.385 | 2.352 | 2.328 | 2.308 | 2.293 | 2.280 | 2.269 |
32 | 2.570 | 2.466 | 2.401 | 2.356 | 2.324 | 2.299 | 2.280 | 2.264 | 2.251 | 2.240 |
33 | 2.544 | 2.440 | 2.374 | 2.330 | 2.297 | 2.272 | 2.253 | 2.237 | 2.224 | 2.213 |
34 | 2.520 | 2.415 | 2.350 | 2.305 | 2.272 | 2.247 | 2.228 | 2.212 | 2.199 | 2.188 |
35 | 2.497 | 2.392 | 2.327 | 2.282 | 2.249 | 2.224 | 2.204 | 2.188 | 2.175 | 2.164 |
36 | 2.475 | 2.371 | 2.305 | 2.260 | 2.227 | 2.202 | 2.182 | 2.166 | 2.152 | 2.141 |
37 | 2.455 | 2.350 | 2.284 | 2.239 | 2.206 | 2.181 | 2.161 | 2.145 | 2.131 | 2.120 |
38 | 2.436 | 2.331 | 2.265 | 2.220 | 2.186 | 2.161 | 2.141 | 2.125 | 2.112 | 2.100 |
39 | 2.418 | 2.313 | 2.247 | 2.201 | 2.168 | 2.143 | 2.122 | 2.106 | 2.093 | 2.081 |
40 | 2.401 | 2.296 | 2.230 | 2.184 | 2.150 | 2.125 | 2.105 | 2.088 | 2.075 | 2.064 |
30 | 40 | 50 | 60 | 70 | 80 | 90 | 100 | 110 | 120 | |
41 | 2.385 | 2.280 | 2.213 | 2.167 | 2.134 | 2.108 | 2.088 | 2.072 | 2.058 | 2.047 |
42 | 2.370 | 2.264 | 2.198 | 2.152 | 2.118 | 2.092 | 2.072 | 2.056 | 2.042 | 2.030 |
43 | 2.356 | 2.250 | 2.183 | 2.137 | 2.103 | 2.077 | 2.057 | 2.040 | 2.027 | 2.015 |
44 | 2.342 | 2.236 | 2.169 | 2.123 | 2.089 | 2.063 | 2.042 | 2.026 | 2.012 | 2.000 |
45 | 2.329 | 2.222 | 2.155 | 2.109 | 2.075 | 2.049 | 2.029 | 2.012 | 1.998 | 1.987 |
46 | 2.316 | 2.210 | 2.143 | 2.096 | 2.062 | 2.036 | 2.015 | 1.999 | 1.985 | 1.973 |
47 | 2.304 | 2.198 | 2.130 | 2.084 | 2.050 | 2.024 | 2.003 | 1.986 | 1.972 | 1.960 |
48 | 2.293 | 2.186 | 2.119 | 2.072 | 2.038 | 2.012 | 1.991 | 1.974 | 1.960 | 1.948 |
49 | 2.282 | 2.175 | 2.107 | 2.061 | 2.026 | 2.000 | 1.979 | 1.962 | 1.948 | 1.937 |
50 | 2.272 | 2.164 | 2.097 | 2.050 | 2.015 | 1.989 | 1.968 | 1.951 | 1.937 | 1.925 |
30 | 40 | 50 | 60 | 70 | 80 | 90 | 100 | 110 | 120 | |
60 | 2.187 | 2.079 | 2.010 | 1.962 | 1.927 | 1.900 | 1.878 | 1.861 | 1.846 | 1.834 |
70 | 2.128 | 2.019 | 1.949 | 1.900 | 1.864 | 1.837 | 1.815 | 1.797 | 1.782 | 1.769 |
80 | 2.084 | 1.974 | 1.903 | 1.854 | 1.817 | 1.789 | 1.767 | 1.748 | 1.733 | 1.720 |
90 | 2.051 | 1.939 | 1.868 | 1.818 | 1.781 | 1.752 | 1.730 | 1.711 | 1.695 | 1.682 |
100 | 2.024 | 1.912 | 1.840 | 1.790 | 1.752 | 1.723 | 1.700 | 1.681 | 1.665 | 1.652 |
110 | 2.002 | 1.890 | 1.817 | 1.766 | 1.728 | 1.699 | 1.676 | 1.656 | 1.640 | 1.627 |
120 | 1.984 | 1.871 | 1.798 | 1.747 | 1.709 | 1.679 | 1.655 | 1.636 | 1.619 | 1.606 |
130 | 1.969 | 1.855 | 1.782 | 1.730 | 1.692 | 1.662 | 1.638 | 1.618 | 1.602 | 1.588 |
140 | 1.956 | 1.842 | 1.768 | 1.716 | 1.678 | 1.647 | 1.623 | 1.603 | 1.586 | 1.572 |
150 | 1.944 | 1.830 | 1.756 | 1.704 | 1.665 | 1.635 | 1.610 | 1.590 | 1.573 | 1.559 |
30 | 40 | 50 | 60 | 70 | 80 | 90 | 100 | 110 | 120 | |
160 | 1.935 | 1.820 | 1.746 | 1.693 | 1.654 | 1.624 | 1.599 | 1.579 | 1.562 | 1.547 |
170 | 1.926 | 1.811 | 1.737 | 1.684 | 1.645 | 1.614 | 1.589 | 1.569 | 1.551 | 1.537 |
180 | 1.918 | 1.803 | 1.729 | 1.676 | 1.636 | 1.605 | 1.580 | 1.560 | 1.542 | 1.528 |
190 | 1.911 | 1.796 | 1.721 | 1.668 | 1.628 | 1.597 | 1.572 | 1.551 | 1.534 | 1.519 |
200 | 1.905 | 1.790 | 1.715 | 1.661 | 1.621 | 1.590 | 1.565 | 1.544 | 1.527 | 1.512 |
210 | 1.900 | 1.784 | 1.709 | 1.655 | 1.615 | 1.584 | 1.558 | 1.538 | 1.520 | 1.505 |
220 | 1.894 | 1.779 | 1.703 | 1.650 | 1.610 | 1.578 | 1.553 | 1.532 | 1.514 | 1.499 |
230 | 1.890 | 1.774 | 1.698 | 1.645 | 1.604 | 1.573 | 1.547 | 1.526 | 1.508 | 1.493 |
240 | 1.886 | 1.770 | 1.694 | 1.640 | 1.600 | 1.568 | 1.542 | 1.521 | 1.503 | 1.488 |
250 | 1.882 | 1.765 | 1.690 | 1.636 | 1.595 | 1.563 | 1.538 | 1.516 | 1.498 | 1.483 |
分布表のタイプを選択
2016.8.9 作成 / 2020.2.19 更新
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