F-распределение является асимметричным и обычно используется в дисперсионном анализе. Такую плотность распределения имеют величины, являющиеся отношением двух величин, имеющих хи-квадрат распределение, при этом соответствующее F-распределение определяется двумя значениями числа степеней свободы. Первый индекс всегда соответствует числу степеней свободы для числителя, и этот порядок является существенным, поскольку F(10,12) не равно F(12,10). В столбце показано число степеней свободы числителя, а в строке — число степеней свободы для знаменателя. В названии таблицы указано значение вероятности. Например, критическое значение F-распределения для вероятности 0.01 и степеней свободы 10 и 12 находится на пересечении столбца со значением 10 (числитель) и строки со значением 12 (знаменатель): F(0.01, 10, 12) = 4.296
df1— число степеней свободы большей дисперсии
df2—число степеней свободы меньшей дисперсии
Уровень значимости a =0.01
|
df2/df1 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
12 |
15 |
20 |
24 |
30 |
40 |
60 |
120 |
INF |
|
1 |
4052.181 |
4999.500 |
5403.352 |
5624.583 |
5763.650 |
5858.986 |
5928.356 |
5981.070 |
6022.473 |
6055.847 |
6106.321 |
6157.285 |
6208.730 |
6234.631 |
6260.649 |
6286.782 |
6313.030 |
6339.391 |
6365.864 |
|
2 |
98.503 |
99.000 |
99.166 |
99.249 |
99.299 |
99.333 |
99.356 |
99.374 |
99.388 |
99.399 |
99.416 |
99.433 |
99.449 |
99.458 |
99.466 |
99.474 |
99.482 |
99.491 |
99.499 |
|
3 |
34.116 |
30.817 |
29.457 |
28.710 |
28.237 |
27.911 |
27.672 |
27.489 |
27.345 |
27.229 |
27.052 |
26.872 |
26.690 |
26.598 |
26.505 |
26.411 |
26.316 |
26.221 |
26.125 |
|
4 |
21.198 |
18.000 |
16.694 |
15.977 |
15.522 |
15.207 |
14.976 |
14.799 |
14.659 |
14.546 |
14.374 |
14.198 |
14.020 |
13.929 |
13.838 |
13.745 |
13.652 |
13.558 |
13.463 |
|
5 |
16.258 |
13.274 |
12.060 |
11.392 |
10.967 |
10.672 |
10.456 |
10.289 |
10.158 |
10.051 |
9.888 |
9.722 |
9.553 |
9.466 |
9.379 |
9.291 |
9.202 |
9.112 |
9.020 |
|
6 |
13.745 |
10.925 |
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 |
6.880 |
|
7 |
12.246 |
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 |
5.650 |
|
8 |
11.259 |
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 |
4.859 |
|
9 |
10.561 |
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 |
4.311 |
|
10 |
10.044 |
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 |
3.909 |
|
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 |
3.602 |
|
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 |
3.361 |
|
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 |
3.165 |
|
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 |
3.004 |
|
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 |
2.868 |
|
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 |
2.753 |
|
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 |
2.653 |
|
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 |
2.566 |
|
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 |
2.489 |
|
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 |
2.421 |
|
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 |
2.360 |
|
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 |
2.305 |
|
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 |
2.256 |
|
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 |
2.211 |
|
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 |
2.169 |
|
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 |
2.131 |
|
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 |
2.097 |
|
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 |
2.064 |
|
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 |
2.034 |
|
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 |
2.006 |
|
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 |
1.805 |
|
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 |
1.601 |
|
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 |
1.381 |
|
inf |
6.635 |
4.605 |
3.782 |
3.319 |
3.017 |
2.802 |
2.639 |
2.511 |
2.407 |
2.321 |
2.185 |
2.039 |
1.878 |
1.791 |
1.696 |
1.592 |
1.473 |
1.325 |
1,000 |
Вернуться Статистические таблицы
