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 0.05 и степеней свободы 10 и 12 находится на пересечении столбца со значением 10 (числитель) и строки со значением 12 (знаменатель): F(0.05, 10, 12) = 2.7534.
df1— число степеней свободы большей дисперсии
df2—число степеней свободы меньшей дисперсии
Уровень значимости a =0.05
|
df2/df1 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
12 |
15 |
20 |
24 |
30 |
40 |
60 |
120 |
INF |
|
1 |
161.4476 |
199.5000 |
215.7073 |
224.5832 |
230.1619 |
233.9860 |
236.7684 |
238.8827 |
240.5433 |
241.8817 |
243.9060 |
245.9499 |
248.0131 |
249.0518 |
250.0951 |
251.1432 |
252.1957 |
253.2529 |
254.3144 |
|
2 |
18.5128 |
19.0000 |
19.1643 |
19.2468 |
19.2964 |
19.3295 |
19.3532 |
19.3710 |
19.3848 |
19.3959 |
19.4125 |
19.4291 |
19.4458 |
19.4541 |
19.4624 |
19.4707 |
19.4791 |
19.4874 |
19.4957 |
|
3 |
10.1280 |
9.5521 |
9.2766 |
9.1172 |
9.0135 |
8.9406 |
8.8867 |
8.8452 |
8.8123 |
8.7855 |
8.7446 |
8.7029 |
8.6602 |
8.6385 |
8.6166 |
8.5944 |
8.5720 |
8.5494 |
8.5264 |
|
4 |
7.7086 |
6.9443 |
6.5914 |
6.3882 |
6.2561 |
6.1631 |
6.0942 |
6.0410 |
5.9988 |
5.9644 |
5.9117 |
5.8578 |
5.8025 |
5.7744 |
5.7459 |
5.7170 |
5.6877 |
5.6581 |
5.6281 |
|
5 |
6.6079 |
5.7861 |
5.4095 |
5.1922 |
5.0503 |
4.9503 |
4.8759 |
4.8183 |
4.7725 |
4.7351 |
4.6777 |
4.6188 |
4.5581 |
4.5272 |
4.4957 |
4.4638 |
4.4314 |
4.3985 |
4.3650 |
|
6 |
5.9874 |
5.1433 |
4.7571 |
4.5337 |
4.3874 |
4.2839 |
4.2067 |
4.1468 |
4.0990 |
4.0600 |
3.9999 |
3.9381 |
3.8742 |
3.8415 |
3.8082 |
3.7743 |
3.7398 |
3.7047 |
3.6689 |
|
7 |
5.5914 |
4.7374 |
4.3468 |
4.1203 |
3.9715 |
3.8660 |
3.7870 |
3.7257 |
3.6767 |
3.6365 |
3.5747 |
3.5107 |
3.4445 |
3.4105 |
3.3758 |
3.3404 |
3.3043 |
3.2674 |
3.2298 |
|
8 |
5.3177 |
4.4590 |
4.0662 |
3.8379 |
3.6875 |
3.5806 |
3.5005 |
3.4381 |
3.3881 |
3.3472 |
3.2839 |
3.2184 |
3.1503 |
3.1152 |
3.0794 |
3.0428 |
3.0053 |
2.9669 |
2.9276 |
|
9 |
5.1174 |
4.2565 |
3.8625 |
3.6331 |
3.4817 |
3.3738 |
3.2927 |
3.2296 |
3.1789 |
3.1373 |
3.0729 |
3.0061 |
2.9365 |
2.9005 |
2.8637 |
2.8259 |
2.7872 |
2.7475 |
2.7067 |
|
10 |
4.9646 |
4.1028 |
3.7083 |
3.4780 |
3.3258 |
3.2172 |
3.1355 |
3.0717 |
3.0204 |
2.9782 |
2.9130 |
2.8450 |
2.7740 |
2.7372 |
2.6996 |
2.6609 |
2.6211 |
2.5801 |
2.5379 |
|
11 |
4.8443 |
3.9823 |
3.5874 |
3.3567 |
3.2039 |
3.0946 |
3.0123 |
2.9480 |
2.8962 |
2.8536 |
2.7876 |
2.7186 |
2.6464 |
2.6090 |
2.5705 |
2.5309 |
2.4901 |
2.4480 |
2.4045 |
|
12 |
4.7472 |
3.8853 |
3.4903 |
3.2592 |
3.1059 |
2.9961 |
2.9134 |
2.8486 |
2.7964 |
2.7534 |
2.6866 |
2.6169 |
2.5436 |
2.5055 |
2.4663 |
2.4259 |
2.3842 |
2.3410 |
2.2962 |
|
13 |
4.6672 |
3.8056 |
3.4105 |
3.1791 |
3.0254 |
2.9153 |
2.8321 |
2.7669 |
2.7144 |
2.6710 |
2.6037 |
2.5331 |
2.4589 |
2.4202 |
2.3803 |
2.3392 |
2.2966 |
2.2524 |
2.2064 |
|
14 |
4.6001 |
3.7389 |
3.3439 |
3.1122 |
2.9582 |
2.8477 |
2.7642 |
2.6987 |
2.6458 |
2.6022 |
2.5342 |
2.4630 |
2.3879 |
2.3487 |
2.3082 |
2.2664 |
2.2229 |
2.1778 |
2.1307 |
|
15 |
4.5431 |
3.6823 |
3.2874 |
3.0556 |
2.9013 |
2.7905 |
2.7066 |
2.6408 |
2.5876 |
2.5437 |
2.4753 |
2.4034 |
2.3275 |
2.2878 |
2.2468 |
2.2043 |
2.1601 |
2.1141 |
2.0658 |
|
16 |
4.4940 |
3.6337 |
3.2389 |
3.0069 |
2.8524 |
2.7413 |
2.6572 |
2.5911 |
2.5377 |
2.4935 |
2.4247 |
2.3522 |
2.2756 |
2.2354 |
2.1938 |
2.1507 |
2.1058 |
2.0589 |
2.0096 |
|
17 |
4.4513 |
3.5915 |
3.1968 |
2.9647 |
2.8100 |
2.6987 |
2.6143 |
2.5480 |
2.4943 |
2.4499 |
2.3807 |
2.3077 |
2.2304 |
2.1898 |
2.1477 |
2.1040 |
2.0584 |
2.0107 |
1.9604 |
|
18 |
4.4139 |
3.5546 |
3.1599 |
2.9277 |
2.7729 |
2.6613 |
2.5767 |
2.5102 |
2.4563 |
2.4117 |
2.3421 |
2.2686 |
2.1906 |
2.1497 |
2.1071 |
2.0629 |
2.0166 |
1.9681 |
1.9168 |
|
19 |
4.3807 |
3.5219 |
3.1274 |
2.8951 |
2.7401 |
2.6283 |
2.5435 |
2.4768 |
2.4227 |
2.3779 |
2.3080 |
2.2341 |
2.1555 |
2.1141 |
2.0712 |
2.0264 |
1.9795 |
1.9302 |
1.8780 |
|
20 |
4.3512 |
3.4928 |
3.0984 |
2.8661 |
2.7109 |
2.5990 |
2.5140 |
2.4471 |
2.3928 |
2.3479 |
2.2776 |
2.2033 |
2.1242 |
2.0825 |
2.0391 |
1.9938 |
1.9464 |
1.8963 |
1.8432 |
|
21 |
4.3248 |
3.4668 |
3.0725 |
2.8401 |
2.6848 |
2.5727 |
2.4876 |
2.4205 |
2.3660 |
2.3210 |
2.2504 |
2.1757 |
2.0960 |
2.0540 |
2.0102 |
1.9645 |
1.9165 |
1.8657 |
1.8117 |
|
22 |
4.3009 |
3.4434 |
3.0491 |
2.8167 |
2.6613 |
2.5491 |
2.4638 |
2.3965 |
2.3419 |
2.2967 |
2.2258 |
2.1508 |
2.0707 |
2.0283 |
1.9842 |
1.9380 |
1.8894 |
1.8380 |
1.7831 |
|
23 |
4.2793 |
3.4221 |
3.0280 |
2.7955 |
2.6400 |
2.5277 |
2.4422 |
2.3748 |
2.3201 |
2.2747 |
2.2036 |
2.1282 |
2.0476 |
2.0050 |
1.9605 |
1.9139 |
1.8648 |
1.8128 |
1.7570 |
|
24 |
4.2597 |
3.4028 |
3.0088 |
2.7763 |
2.6207 |
2.5082 |
2.4226 |
2.3551 |
2.3002 |
2.2547 |
2.1834 |
2.1077 |
2.0267 |
1.9838 |
1.9390 |
1.8920 |
1.8424 |
1.7896 |
1.7330 |
|
25 |
4.2417 |
3.3852 |
2.9912 |
2.7587 |
2.6030 |
2.4904 |
2.4047 |
2.3371 |
2.2821 |
2.2365 |
2.1649 |
2.0889 |
2.0075 |
1.9643 |
1.9192 |
1.8718 |
1.8217 |
1.7684 |
1.7110 |
|
26 |
4.2252 |
3.3690 |
2.9752 |
2.7426 |
2.5868 |
2.4741 |
2.3883 |
2.3205 |
2.2655 |
2.2197 |
2.1479 |
2.0716 |
1.9898 |
1.9464 |
1.9010 |
1.8533 |
1.8027 |
1.7488 |
1.6906 |
|
27 |
4.2100 |
3.3541 |
2.9604 |
2.7278 |
2.5719 |
2.4591 |
2.3732 |
2.3053 |
2.2501 |
2.2043 |
2.1323 |
2.0558 |
1.9736 |
1.9299 |
1.8842 |
1.8361 |
1.7851 |
1.7306 |
1.6717 |
|
28 |
4.1960 |
3.3404 |
2.9467 |
2.7141 |
2.5581 |
2.4453 |
2.3593 |
2.2913 |
2.2360 |
2.1900 |
2.1179 |
2.0411 |
1.9586 |
1.9147 |
1.8687 |
1.8203 |
1.7689 |
1.7138 |
1.6541 |
|
29 |
4.1830 |
3.3277 |
2.9340 |
2.7014 |
2.5454 |
2.4324 |
2.3463 |
2.2783 |
2.2229 |
2.1768 |
2.1045 |
2.0275 |
1.9446 |
1.9005 |
1.8543 |
1.8055 |
1.7537 |
1.6981 |
1.6376 |
|
30 |
4.1709 |
3.3158 |
2.9223 |
2.6896 |
2.5336 |
2.4205 |
2.3343 |
2.2662 |
2.2107 |
2.1646 |
2.0921 |
2.0148 |
1.9317 |
1.8874 |
1.8409 |
1.7918 |
1.7396 |
1.6835 |
1.6223 |
|
40 |
4.0847 |
3.2317 |
2.8387 |
2.6060 |
2.4495 |
2.3359 |
2.2490 |
2.1802 |
2.1240 |
2.0772 |
2.0035 |
1.9245 |
1.8389 |
1.7929 |
1.7444 |
1.6928 |
1.6373 |
1.5766 |
1.5089 |
|
60 |
4.0012 |
3.1504 |
2.7581 |
2.5252 |
2.3683 |
2.2541 |
2.1665 |
2.0970 |
2.0401 |
1.9926 |
1.9174 |
1.8364 |
1.7480 |
1.7001 |
1.6491 |
1.5943 |
1.5343 |
1.4673 |
1.3893 |
|
120 |
3.9201 |
3.0718 |
2.6802 |
2.4472 |
2.2899 |
2.1750 |
2.0868 |
2.0164 |
1.9588 |
1.9105 |
1.8337 |
1.7505 |
1.6587 |
1.6084 |
1.5543 |
1.4952 |
1.4290 |
1.3519 |
1.2539 |
|
inf |
3.8415 |
2.9957 |
2.6049 |
2.3719 |
2.2141 |
2.0986 |
2.0096 |
1.9384 |
1.8799 |
1.8307 |
1.7522 |
1.6664 |
1.5705 |
1.5173 |
1.4591 |
1.3940 |
1.3180 |
1.2214 |
1.0000 |
Вернуться Статистические таблицы
