Национальный стандарт РФ ГОСТ Р 50779.21-2004 "Статистические методы. Правила определения и методы расчета статистических характеристик по выборочным данным. Часть 1. Нормальное распределение" (утв. постановлением Госстандарта РФ от 12 января 2004 г. N 3- стр. 8

  1. Документы
2 1
Пример - Для ню=14 требуется найти квантиль уровня альфа=0,988. Полагаем альфа_1=0,98, aльфа_2=0,99; находим по таблице В.1 хи(2)_0,98=26,873; хи(2)_0,99=29,141 и вычисляем для степеней свободы ню=14.
2 29,141 - 26,873
хи = (0,988 - 0,98) [-----------------] + 26,873 = 28,6874.
0,988 0,99 - 0,98

Таблица В.1 - Значения квантилей хи(2)_альфа распределения

+------------+-----------------------------------------------------------------------------------------------------------------------------------+
| мю | Значения квантилей хи(2)_альфа распределения с ню степенями свободы для уровня альфа |
| +---------+---------+---------+----------+----------+--------+---------+---------+---------+---------+---------+----------+---------+
| | 0,01 | 0,02 | 0,05 | 0,1 | 0,2 | 0,3 | 0,5 | 0,7 | 0,8 | 0,9 | 0,95 | 0,98 | 0,99 |
+------------+---------+---------+---------+----------+----------+--------+---------+---------+---------+---------+---------+----------+---------+
| 1 | 0,0157 | 0,0628 | 0,0393 | 0,0158 | 0,0642 | 0,148 | 0,455 | 1,074 | 1,642 | 2,706 | 3,841 | 5,412 | 6,635 |
| | | | | | | | | | | | | | |
| 2 | 0,0201 | 0,0404 | 0,103 | 0,211 | 0,446 | 0,713 | 1,386 | 2,408 | 3,219 | 4,605 | 5,991 | 7,824 | 9,210 |
| | | | | | | | | | | | | | |
| 3 | 0,115 | 0,185 | 0,352 | 0,584 | 1,005 | 1,424 | 2,366 | 3,665 | 4,642 | 6,251 | 7,815 | 9,837 | 11,345 |
| | | | | | | | | | | | | | |
| 4 | 0,297 | 0,429 | 0,711 | 1,064 | 1,649 | 2,195 | 3,357 | 4,878 | 5,989 | 7,779 | 9,488 | 11,668 | 13,277 |
| | | | | | | | | | | | | | |
| 5 | 0,554 | 0,752 | 1,145 | 1,160 | 2,343 | 3,000 | 4,351 | 6,064 | 7,289 | 9,233 | 11,070 | 13,388 | 15,086 |
+------------+---------+---------+---------+----------+----------+--------+---------+---------+---------+---------+---------+----------+---------+
| 6 | 0,872 | 1,134 | 1,635 | 2,204 | 3,070 | 3,828 | 5,348 | 7,231 | 8,558 | 10,645 | 12,592 | 15,033 | 16,812 |
| | | | | | | | | | | | | | |
| 7 | 1,239 | 1,564 | 2,167 | 2,833 | 3,822 | 4,671 | 6,346 | 8,383 | 9,803 | 12,017 | 14,067 | 16,622 | 18,475 |
| | | | | | | | | | | | | | |
| 8 | 1,646 | 2,032 | 2,733 | 3,490 | 4,594 | 5,527 | 7,344 | 9,524 | 11,030 | 13,362 | 15,507 | 18,168 | 20,090 |
| | | | | | | | | | | | | | |
| 9 | 2,088 | 2,532 | 3,325 | 4,168 | 5,380 | 6,393 | 8,343 | 10,656 | 12,242 | 14,684 | 16,919 | 19,679 | 21,666 |
| | | | | | | | | | | | | | |
| 10 | 2,358 | 3,059 | 3,940 | 4,865 | 6,179 | 7,267 | 9,342 | 11,781 | 13,442 | 15,987 | 18,307 | 21,161 | 23,209 |
+------------+---------+---------+---------+----------+----------+--------+---------+---------+---------+---------+---------+----------+---------+
| 11 | 3,053 | 3,609 | 4,575 | 5,578 | 6,989 | 8,148 | 10,341 | 12,899 | 14,631 | 17,275 | 19,675 | 22,618 | 24,725 |
| | | | | | | | | | | | | | |
| 12 | 3,571 | 4,178 | 5,226 | 6,304 | 7,807 | 9,034 | 11,340 | 14,011 | 15,821 | 18,549 | 21,026 | 24,054 | 26,217 |
| | | | | | | | | | | | | | |
| 13 | 4,107 | 4,765 | 5,892 | 7,042 | 8,634 | 9,926 | 12,340 | 15,119 | 16,985 | 19,812 | 22,362 | 25,472 | 27,688 |
| | | | | | | | | | | | | | |
| 14 | 5,660 | 5,368 | 6,571 | 7,790 | 9,467 | 10,821 | 13,339 | 16,222 | 18,151 | 21,064 | 23,996 | 26,873 | 29,141 |
| | | | | | | | | | | | | | |
| 15 | 5,229 | 5,985 | 7,261 | 8,547 | 10,307 | 11,721 | 14,339 | 17,322 | 19,311 | 22,307 | 24,996 | 28,259 | 30,578 |
+------------+---------+---------+---------+----------+----------+--------+---------+---------+---------+---------+---------+----------+---------+
| 16 | 5,812 | 6,614 | 7,962 | 9,312 | 11,152 | 12,624 | 15,333 | 18,418 | 20,465 | 23,542 | 26,296 | 29,633 | 32,000 |
| | | | | | | | | | | | | | |
| 17 | 6,408 | 7,255 | 8,672 | 10,035 | 12,002 | 13,531 | 16,338 | 19,511 | 21,615 | 24,769 | 27,587 | 30,995 | 33,409 |
| | | | | | | | | | | | | | |
| 18 | 7,015 | 7,906 | 9,390 | 10,865 | 12,857 | 14,440 | 17,338 | 20,601 | 22,760 | 25,989 | 28,869 | 32,346 | 34,805 |
| | | | | | | | | | | | | | |
| 19 | 7,633 | 8,567 | 10,117 | 11,651 | 13,716 | 15,352 | 18,338 | 21,689 | 23,900 | 27,204 | 30,144 | 33,687 | 36,191 |
| | | | | | | | | | | | | | |
| 20 | 8,260 | 9,237 | 10,851 | 12,443 | 14,578 | 16,266 | 19,337 | 22,775 | 25,038 | 28,412 | 31,410 | 35,020 | 37,566 |
+------------+---------+---------+---------+----------+----------+--------+---------+---------+---------+---------+---------+----------+---------+
| 21 | 8,897 | 9,915 | 11,591 | 13,240 | 15,445 | 17,182 | 20,337 | 23,858 | 26,171 | 29,615 | 32,671 | 36,343 | 38,932 |
| | | | | | | | | | | | | | |
| 22 | 9,542 | 10,600 | 12,338 | 14,041 | 16,314 | 18,101 | 21,337 | 24,939 | 27,301 | 30,813 | 33,924 | 37,659 | 40,289 |
| | | | | | | | | | | | | | |
| 23 | 10,196 | 11,293 | 13,091 | 14,848 | 17,187 | 19,021 | 22,337 | 26,018 | 28,429 | 32,007 | 35,172 | 38,968 | 41,638 |
| | | | | | | | | | | | | | |
| 24 | 10,856 | 11,992 | 13,848 | 15,659 | 18,062 | 19,943 | 23,337 | 27,096 | 29,553 | 33,196 | 36,415 | 40,270 | 42,980 |
| | | | | | | | | | | | | | |
| 25 | 11,524 | 12,697 | 14,611 | 16,473 | 18,940 | 20,867 | 24,337 | 28,172 | 30,675 | 34,382 | 37,652 | 41,566 | 44,314 |
+------------+---------+---------+---------+----------+----------+--------+---------+---------+---------+---------+---------+----------+---------+
| 26 | 12,198 | 13,409 | 15,379 | 17,292 | 19,820 | 21,792 | 25,336 | 29,246 | 31,795 | 35,563 | 38,885 | 42,856 | 45,642 |
| | | | | | | | | | | | | | |
| 27 | 12,879 | 14,125 | 16,151 | 18,114 | 20,703 | 22,719 | 26,336 | 30,319 | 32,912 | 36,741 | 40,113 | 44,140 | 46,963 |
| | | | | | | | | | | | | | |
| 28 | 13,565 | 14,847 | 16,928 | 18,939 | 21,588 | 23,647 | 27,336 | 31,391 | 34,027 | 37,916 | 41,337 | 45,419 | 48,278 |
| | | | | | | | | | | | | | |
| 29 | 14,256 | 15,574 | 17,708 | 19,768 | 22,475 | 24,577 | 28,336 | 32,461 | 35,139 | 39,087 | 42,557 | 46,693 | 49,588 |
| | | | | | | | | | | | | | |
| 30 | 14,953 | 16,306 | 18,493 | 20,599 | 23,364 | 25,508 | 29,336 | 33,530 | 36,250 | 40,256 | 43,773 | 47,962 | 50,892 |
+------------+---------+---------+---------+----------+----------+--------+---------+---------+---------+---------+---------+----------+---------+
+------------+-----------------------------------------------------------------------------------------------------------------------------------+
Приложение Г
(справочное)

Таблицы значений квантилей распределения Фишера

Г.1 В таблицах Г.1-Г.9 содержатся значения квантилей F_альфа(ню_1, ню_2) при заданных уровнях альфа для различных сочетаний степеней свободы ню_1 и ню_2. Каждая таблица соответствует одному уровню альфа, значение которого указано в заголовке таблицы, и различным значениям ню_1 и ню_2.
Г.1.1 Для определения квантилей уровня альфа менее 0,5 следует использовать соотношение:
1
F (ню , ню ) = ------------------ .
альфа 1 2 F (ню , ню )
1-альфа 2 1
Г.1.2 Для промежуточных значений альфа, лежащих между двумя соседними табличными значениями альфа_1 и альфа_2:
альфа < альфа < альфа
1 2
значение квантиля F_альфа может быть вычислено приближенно по формуле (метод линейной интерполяции):
F - F
альфа2 альфа1
F = (альфа - альфа )[----------------] + F .
альфа 1 альфа - альфа альфа1
2 1
Г.1.3 Для промежуточных значений ню_1 и ню_2, лежащих между двумя соседними табличными значениями ню_1' и ню_1" и или ню_2' и ню_2", т.е.
ню' < ню < ню" или ню' < ню < ню" ,
1 1 1 2 2 2
значения квантилей F_альфа (ню_1), F_альфа(ню_2) могут быть приближенно вычислены по формулам:
F (ню") - F (ню')
альфа 1 альфа 1
F (ню ) = (ню - ню') ------------------------- + F (ню');
альфа 1 1 1 ню" - ню' альфа 1
1 1
F (ню") - F (ню')
альфа 2 альфа 2
F (ню ) = (ню - ню') ------------------------- + F (ню').
альфа 2 2 2 ню" - ню' альфа 2
2 2

Таблица Г.1 - Значения квантилей F-распределения уровня альфа=0,5

+-----------+-----------------------------------------------------------------------------------------------+
| ню_2 | Значения квантилей F-распределения уровня альфа=0,5 для степеней свободы ню_1 |
| +-----------+---------+----------+---------+----------+---------+----------+----------+---------+
| | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
+-----------+-----------+---------+----------+---------+----------+---------+----------+----------+---------+
| 1 | 1,0000 | 1,5000 | 1,7092 | 1,8227 | 1,8937 | 1,9422 | 1,9774 | 2,0041 | 2,0250 |
| | | | | | | | | | |
| 2 | 0,66667 | 1,0000 | 1,1349 | 1,2071 | 1,2519 | 1,2824 | 1,3045 | 1,3213 | 1,3344 |
| | | | | | | | | | |
| 3 | 0,58506 | 0,88110 | 1,0000 | 1,0632 | 1,1024 | 1,1289 | 1,1482 | 1,1627 | 1,1741 |
| | | | | | | | | | |
| 4 | 0,54863 | 0,82843 | 0,94054 | 1,0000 | 1,0367 | 1,0617 | 1,0797 | 1,0933 | 1,1040 |
+-----------+-----------+---------+----------+---------+----------+---------+----------+----------+---------+
| 5 | 0,52807 | 0,79877 | 0,90715 | 0,96456 | 1,0000 | 1,0240 | 1,0414 | 1,0545 | 1,0648 |
| | | | | | | | | | |
| 6 | 0,51489 | 0,77976 | 0,88578 | 0,94191 | 0,97654 | 1,0000 | 1,0169 | 1,0298 | 1,0398 |
| | | | | | | | | | |
| 7 | 0,50572 | 0,76655 | 0,87095 | 0,92619 | 0,96026 | 0,98334 | 1,0000 | 1,0126 | 1,0224 |
| | | | | | | | | | |
| 8 | 0,49898 | 0,75683 | 0,86004 | 0,91464 | 0,93831 | 0,97111 | 0,98757 | 1,0000 | 1,0097 |
| | | | | | | | | | |
| 9 | 0,49382 | 0,74938 | 0,85168 | 0,90580 | 0,93916 | 0,96175 | 0,97805 | 0,99037 | 1,0000 |
+-----------+-----------+---------+----------+---------+----------+---------+----------+----------+---------+
| 10 | 0,48973 | 0,74349 | 0,84508 | 0,89882 | 0,93193 | 0,95436 | 0,97054 | 0,98276 | 0,99232 |
| | | | | | | | | | |
| 11 | 0,48644 | 0,73872 | 0,83973 | 0,89316 | 0,92608 | 0,94837 | 0,96445 | 0,97661 | 0,98610 |
| | | | | | | | | | |
| 12 | 0,48369 | 0,73477 | 0,83530 | 0,88848 | 0,92124 | 0,94342 | 0,95943 | 0,97152 | 0,98097 |
| | | | | | | | | | |
| 13 | 0,48141 | 0,73145 | 0,83159 | 0,88454 | 0,91718 | 0,93926 | 0,95520 | 0,96724 | 0,97665 |
| | | | | | | | | | |
| 14 | 0,47944 | 0,72862 | 0,82842 | 0,88119 | 0,91371 | 0,93573 | 0,95161 | 0,96360 | 0,97298 |
+-----------+-----------+---------+----------+---------+----------+---------+----------+----------+---------+
| 15 | 0,47775 | 0,72619 | 0,82569 | 0,87830 | 0,91073 | 0,93627 | 0,94850 | 0,96046 | 0,96981 |
| | | | | | | | | | |
| 16 | 0,47628 | 0,72406 | 0,82330 | 0,87578 | 0,90812 | 0,93001 | 0,94580 | 0,95773 | 0,96705 |
| | | | | | | | | | |
| 17 | 0,47499 | 0,72219 | 0,82121 | 0,87357 | 0,90584 | 0,92767 | 0,94342 | 0,95532 | 0,96462 |
| | | | | | | | | | |
| 18 | 0,47385 | 0,72053 | 0,81936 | 0,87161 | 0,90381 | 0,92560 | 0,94132 | 0,95319 | 0,96247 |
| | | | | | | | | | |
| 19 | 0,47284 | 0,71906 | 0,81771 | 0,86987 | 0,90200 | 0,92375 | 0,93944 | 0,95129 | 0,96056 |
+-----------+-----------+---------+----------+---------+----------+---------+----------+----------+---------+
| 20 | 0,47192 | 0,71773 | 0,81621 | 0,86830 | 0,90038 | 0,92210 | 0,93776 | 0,94959 | 0,95884 |
| | | | | | | | | | |
| 21 | 0,47108 | 0,71653 | 0,81487 | 0,86688 | 0,89891 | 0,92060 | 0,93624 | 0,94805 | 0,95728 |
| | | | | | | | | | |
| 22 | 0,47033 | 0,71545 | 0,81365 | 0,86559 | 0,89759 | 0,91924 | 0,93436 | 0,94665 | 0,95588 |
| | | | | | | | | | |
| 23 | 0,46965 | 0,71446 | 0,81255 | 0,86442 | 0,89638 | 0,91800 | 0,93360 | 0,94538 | 0,95459 |
| | | | | | | | | | |
| 24 | 0,46902 | 0,71356 | 0,81153 | 0,86335 | 0,89527 | 0,91687 | 0,93245 | 0,94422 | 0,95342 |
+-----------+-----------+---------+----------+---------+----------+---------+----------+----------+---------+
| 25 | 0,46844 | 0,71272 | 0,81061 | 0,86236 | 0,89425 | 0,91583 | 0,93140 | 0,94315 | 0,95234 |
| | | | | | | | | | |
| 26 | 0,46793 | 0,71195 | 0,80975 | 0,86145 | 0,89331 | 0,91487 | 0,93042 | 0,94217 | 0,95135 |
| | | | | | | | | | |
| 27 | 0,46744 | 0,71124 | 0,80894 | 0,86061 | 0,89244 | 0,91399 | 0,92952 | 0,94126 | 0,95044 |
| | | | | | | | | | |
| 28 | 0,46697 | 0,71059 | 0,80820 | 0,85983 | 0,89164 | 0,91317 | 0,92869 | 0,94041 | 0,94958 |
| | | | | | | | | | |
| 29 | 0,46654 | 0,70999 | 0,80753 | 0,85911 | 0,89089 | 0,91241 | 0,92791 | 0,93963 | 0,94879 |
+-----------+-----------+---------+----------+---------+----------+---------+----------+----------+---------+
| 30 | 0,46616 | 0,70941 | 0,80689 | 0,85844 | 0,89019 | 0,91169 | 0,92719 | 0,93889 | 0,94805 |
| | | | | | | | | | |
| 40 | 0,46330 | 0,70531 | 0,80228 | 0,85357 | 0,88516 | 0,90654 | 0,92197 | 0,93361 | 0,94272 |
| | | | | | | | | | |
| 60 | 0,46053 | 0,70122 | 0,79770 | 0,84873 | 0,88017 | 0,90144 | 0,91679 | 0,92838 | 0,93743 |
| | | | | | | | | | |
| 120 | 0,45774 | 0,69717 | 0,79314 | 0,84392 | 0,87521 | 0,89637 | 0,91164 | 0,92318 | 0,93218 |
| | | | | | | | | | |
| бесконеч- | 0,45494 | 0,69315 | 0,78866 | 0,83918 | 0,87029 | 0,89135 | 0,90654 | 0,91802 | 0,92698 |
| ность | | | | | | | | | |
+-----------+-----------+---------+----------+---------+----------+---------+----------+----------+---------+
+-----------+-----------------------------------------------------------------------------------------------+
Продолжение таблицы
+----------+------------------------------------------------------------------------------------------------+
| ню_2 | Значения квантилей F-распределения уровня альфа=0,5 для степеней свободы ню_1 |
| +----------+--------+---------+----------+--------+---------+--------+--------+--------+---------+
| | 10 | 12 | 15 | 20 | 24 | 30 | 40 | 60 | 120 |бесконеч-|
| | | | | | | | | | | ность |
+----------+----------+--------+---------+----------+--------+---------+--------+--------+--------+---------+
| 1 | 2,0419 | 2,0674 | 2,0931 | 2,1190 | 2,1321 | 2,1452 | 2,1584 | 2,1716 | 2,1848 | 2,1981 |
| | | | | | | | | | | |
| 2 | 1,3450 | 1,3610 | 1,3771 | 1,3933 | 1,4014 | 1,4096 | 1,4178 | 1,4261 | 1,4344 | 1,4427 |
| | | | | | | | | | | |
| 3 | 1,1833 | 1,1972 | 1,2111 | 1,2252 | 1,2322 | 1,2393 | 1,2464 | 1,2536 | 1,2608 | 1,2680 |
| | | | | | | | | | | |
| 4 | 1,1126 | 1,1255 | 1,1386 | 1,1517 | 1,1583 | 1,1649 | 1,1716 | 1,1782 | 1,1849 | 1,1916 |
+----------+----------+--------+---------+----------+--------+---------+--------+--------+--------+---------+
| 5 | 1,0730 | 1,0855 | 1,0980 | 1,1106 | 1,1170 | 1,1234 | 1,1297 | 1,1361 | 1,1426 | 1,1490 |
| | | | | | | | | | | |
| 6 | 1,0478 | 1,0600 | 1,0722 | 1,0845 | 1,0907 | 1,0969 | 1,1031 | 1,1093 | 1,1156 | 1,1219 |
| | | | | | | | | | | |
| 7 | 1,0304 | 1,0423 | 1,0543 | 1,0664 | 1,0724 | 1,0785 | 1,0846 | 1,0908 | 1,0969 | 1,1031 |
| | | | | | | | | | | |
| 8 | 1,0175 | 1,0293 | 1,0412 | 1,0531 | 1,0591 | 1,0651 | 1,0711 | 1,0771 | 1,0832 | 1,0893 |
| | | | | | | | | | | |
| 9 | 1,0077 | 1,0194 | 1,0311 | 1,0429 | 1,0489 | 1,0548 | 1,0608 | 1,0667 | 1,0727 | 1,0788 |
+----------+----------+--------+---------+----------+--------+---------+--------+--------+--------+---------+
| 10 | 1,0000 | 1,0116 | 1,0232 | 1,0349 | 1,0408 | 1,0467 | 1,0526 | 1,0585 | 1,0645 | 1,0705 |
| | | | | | | | | | | |
| 11 | 0,99373 | 1,0052 | 1,0168 | 1,0284 | 1,0343 | 1,0401 | 1,0460 | 1,0519 | 1,0578 | 1,0637 |
| | | | | | | | | | | |
| 12 | 0,98856 | 1,0000 | 1,0115 | 1,0231 | 1,0289 | 1,0347 | 1,0405 | 1,0464 | 1,0523 | 1,0582 |
| | | | | | | | | | | |
| 13 | 0,98421 |0,99560 | 1,0071 | 1,0186 | 1,0243 | 1,0301 | 1,0360 | 1,0418 | 1,0476 | 1,0535 |
| | | | | | | | | | | |
| 14 | 0,98051 |0,99186 | 1,0033 | 1,0147 | 1,0205 | 1,0263 | 1,0321 | 1,0379 | 1,0437 | 1,0495 |
+----------+----------+--------+---------+----------+--------+---------+--------+--------+--------+---------+
| 15 | 0,97732 |0,98863 | 1,0000 | 1,0114 | 1,0172 | 1,0229 | 1,0287 | 1,0345 | 1,0403 | 1,0461 |
| | | | | | | | | | | |
| 16 | 0,97454 |0,98582 | 0,99716 | 1,0086 | 1,0143 | 1,0200 | 1,0258 | 1,0315 | 1,0373 | 1,0431 |
| | | | | | | | | | | |
| 17 | 0,97203 |0,98334 | 0,99466 | 1,0060 | 1,0117 | 1,0174 | 1,0232 | 1,0289 | 1,0347 | 1,0405 |
| | | | | | | | | | | |
| 18 | 0,96993 |0,98116 | 0,99245 | 1,0038 | 1,0095 | 1,0152 | 1,0209 | 1,0267 | 1,0324 | 1,0382 |
| | | | | | | | | | | |
| 19 | 0,96800 |0,97920 | 0,99047 | 1,0018 | 1,0075 | 1,0132 | 1,0189 | 1,0246 | 1,0304 | 1,0361 |
+----------+----------+--------+---------+----------+--------+---------+--------+--------+--------+---------+
| 20 | 0,96626 |0,97746 | 0,98870 | 1,0000 | 1,0057 | 1,0114 | 1,0171 | 1,0228 | 1,0285 | 1,0343 |
| | | | | | | | | | | |
| 21 | 0,96470 |0,97587 | 0,98710 | 0,99838 | 1,0040 | 1,0097 | 1,0154 | 1,0211 | 1,0268 | 1,0326 |
| | | | | | | | | | | |
| 22 | 0,96328 |0,97444 | 0,98565 | 0,99692 | 1,0026 | 1,0082 | 1,0139 | 1,0196 | 1,0253 | 1,0311 |
| | | | | | | | | | | |
| 23 | 0,96199 |0,97313 | 0,98433 | 0,99558 | 1,0012 | 1,0069 | 1,0126 | 1,0183 | 1,0240 | 1,0297 |
| | | | | | | | | | | |
| 24 | 0,96081 |0,97194 | 0,98312 | 0,99436 | 1,0000 | 1,0057 | 1,0113 | 1,0170 | 1,0227 | 1,0284 |
+----------+----------+--------+---------+----------+--------+---------+--------+--------+--------+---------+
| 25 | 0,95972 |0,97084 | 0,98201 | 0,99324 |0,99887 | 1,0045 | 1,0102 | 1,0159 | 1,0215 | 1,0273 |
| | | | | | | | | | | |
| 26 | 0,95872 |0,96983 | 0,98099 | 0,99220 |0,99783 | 1,0035 | 1,0091 | 1,0148 | 1,0205 | 1,0262 |
| | | | | | | | | | | |
| 27 | 0,95779 |0,96889 | 0,98004 | 0,99125 |0,99687 | 1,0025 | 1,0082 | 1,0138 | 1,0195 | 1,0252 |
| | | | | | | | | | | |
| 28 | 0,95694 |0,96802 | 0,97917 | 0,99036 |0,99598 | 1,0016 | 1,0073 | 1,0129 | 1,0186 | 1,0243 |
| | | | | | | | | | | |
| 29 | 0,95614 |0,96722 | 0,97835 | 0,98954 |0,99515 | 1,0008 | 1,0064 | 1,0121 | 1,0177 | 1,0234 |
+----------+----------+--------+---------+----------+--------+---------+--------+--------+--------+---------+
| 30 | 0,95540 |0,96647 | 0,97759 | 0,98877 |0,99438 | 1,0000 | 1,0056 | 1,0113 | 1,0170 | 1,0226 |
| | | | | | | | | | | |
| 40 | 0,95003 |0,96104 | 0,97211 | 0,98323 |0,98880 | 0,99440 | 1,0000 | 1,0056 | 1,0113 | 1,0169 |
| | | | | | | | | | | |
| 60 | 0,94471 |0,95566 | 0,96667 | 0,97773 |0,98328 | 0,98884 |0,99411 | 1,0000 | 1,0056 | 1,0112 |
| | | | | | | | | | | |
| 120 | 0,93943 |0,95032 | 0,96128 | 0,97228 |0,97780 | 0,98333 |0,98887 |0,99443 | 1,0000 | 1,0056 |
| | | | | | | | | | | |
| бесконеч-| 0,93418 |0,94503 | 0,95593 | 0,96687 |0,97236 | 0,97787 |0,98339 |0,98891 |0,99445 | 1,0000 |
| ность | | | | | | | | | | |
+----------+----------+--------+---------+----------+--------+---------+--------+--------+--------+---------+
+----------+------------------------------------------------------------------------------------------------+

Таблица Г.2 - Значения квантилей F-распределения уровня альфа=0,75

+-----------+-----------------------------------------------------------------------------------------------+
| ню_2 | Значения квантилей F-распределения уровня альфа=0,75 для степеней свободы ню_1 |
| +----------+----------+----------+---------+----------+----------+----------+---------+---------+
| | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
+-----------+----------+----------+----------+---------+----------+----------+----------+---------+---------+
| 1 | 5,8285 | 7,5000 | 8,1999 | 8,5810 | 8,8198 | 8,9833 | 9,1021 | 9,1922 | 9,2631 |
| | | | | | | | | | |
| 2 | 2,5714 | 3,0000 | 3,1534 | 3,2320 | 3,2799 | 3,3121 | 3,3352 | 3,3526 | 3,3661 |
| | | | | | | | | | |
| 3 | 2,0239 | 2,2798 | 2,3555 | 2,3901 | 2,4095 | 2,4218 | 2,4302 | 2,4364 | 2,4410 |
| | | | | | | | | | |
| 4 | 1,8074 | 2,0000 | 2,0467 | 2,0642 | 2,0723 | 2,0766 | 2,0790 | 2,0805 | 2,0814 |
+-----------+----------+----------+----------+---------+----------+----------+----------+---------+---------+
| 5 | 1,6925 | 1,8528 | 1,8843 | 1,8927 | 1,8947 | 1,8945 | 1,8935 | 1,8923 | 1,8911 |
| | | | | | | | | | |
| 6 | 1,6214 | 1,7622 | 1,7844 | 1,7872 | 1,7852 | 1,7821 | 1,7789 | 1,7760 | 1,7733 |
| | | | | | | | | | |
| 7 | 1,5732 | 1,7010 | 1,7169 | 1,7157 | 1,7111 | 1,7059 | 1,7011 | 1,6969 | 1,6931 |
| | | | | | | | | | |
| 8 | 1,5384 | 1,6569 | 1,6683 | 1,6642 | 1,6575 | 1,6508 | 1,6448 | 1,6396 | 1,6350 |
| | | | | | | | | | |
| 9 | 1,5121 | 1,6236 | 1,6315 | 1,6253 | 1,6170 | 1,6091 | 1,6022 | 1,5961 | 1,5909 |
+-----------+----------+----------+----------+---------+----------+----------+----------+---------+---------+
| 10 | 1,4915 | 1,5975 | 1,6028 | 1,5949 | 1,5863 | 1,5765 | 1,5688 | 1,5621 | 1,5563 |
| | | | | | | | | | |
| 11 | 1,4749 | 1,5767 | 1,5798 | 1,5794 | 1,5598 | 1,5502 | 1,5418 | 1,5346 | 1,5284 |
| | | | | | | | | | |
| 12 | 1,4613 | 1,5595 | 1,5609 | 1,5503 | 1,5389 | 1,5286 | 1,5197 | 1,5120 | 1,5054 |
| | | | | | | | | | |
| 13 | 1,4500 | 1,5452 | 1,5451 | 1,5336 | 1,5214 | 1,5105 | 1,5011 | 1,4931 | 1,4861 |
| | | | | | | | | | |
| 14 | 1,4403 | 1,5331 | 1,5317 | 1,5194 | 1,5066 | 1,4952 | 1,4854 | 1,4770 | 1,4697 |
+-----------+----------+----------+----------+---------+----------+----------+----------+---------+---------+
| 15 | 1,4321 | 1,5227 | 1,5202 | 1,5071 | 1,4938 | 1,4820 | 1,4718 | 1,4631 | 1,4556 |
| | | | | | | | | | |
| 16 | 1,4249 | 1,5137 | 1,5103 | 1,4965 | 1,4827 | 1,4705 | 14601 | 1,4511 | 1,4433 |
| | | | | | | | | | |
| 17 | 1,4186 | 1,5057 | 1,5015 | 1,4873 | 1,4730 | 1,4605 | 1,4497 | 1,4405 | 1,4325 |
| | | | | | | | | | |
| 18 | 1,4130 | 1,4988 | 1,4938 | 1,4790 | 1,4644 | 1,4516 | 1,4406 | 1,4312 | 1,4230 |
| | | | | | | | | | |
| 19 | 1,4081 | 1,4925 | 1,4870 | 1,4717 | 1,4568 | 1,4437 | 1,4325 | 1,4228 | 1,4145 |
+-----------+----------+----------+----------+---------+----------+----------+----------+---------+---------+
| 20 | 1,4037 | 1,4870 | 1,4808 | 1,4652 | 1,4500 | 1,4366 | 1,4252 | 1,4153 | 1,4069 |
| | | | | | | | | | |
| 21 | 1,3997 | 1,4820 | 1,4573 | 1,4593 | 1,4438 | 1,4302 | 1,4186 | 1,4086 | 1,4000 |
| | | | | | | | | | |
| 22 | 1,3961 | 1,4774 | 1,4703 | 1,4540 | 1,4382 | 1,4244 | 1,4126 | 1,4025 | 1,3937 |
| | | | | | | | | | |
| 23 | 1,3928 | 1,4733 | 1,4657 | 1,4491 | 1,4331 | 1,4191 | 1,4072 | 1,3969 | 1,3880 |
| | | | | | | | | | |
| 24 | 1,3898 | 1,4695 | 1,4615 | 1,4447 | 1,4285 | 1,4143 | 1,4022 | 1,3918 | 1,3828 |
+-----------+----------+----------+----------+---------+----------+----------+----------+---------+---------+
| 25 | 1,3870 | 1,4661 | 1,4577 | 1,4406 | 1,4242 | 1,4099 | 1,3976 | 1,3871 | 1,3780 |
| | | | | | | | | | |
| 26 | 1,3845 | 1,4629 | 1,4542 | 1,4368 | 1,4203 | 1,4058 | 1,3935 | 1,3828 | 1,3737 |
| | | | | | | | | | |
| 27 | 1,3822 | 1,4600 | 1,4510 | 1,4334 | 1,4166 | 1,4021 | 1,3896 | 1,3788 | 1,3696 |
| | | | | | | | | | |
| 28 | 1,3800 | 1,4573 | 1,4480 | 1,4302 | 1,4133 | 1,3986 | 1,3860 | 1,3752 | 1,3658 |
| | | | | | | | | | |
| 29 | 1,3780 | 1,4547 | 1,4452 | 1,4272 | 1,4102 | 1,3953 | 1,3826 | 1,3717 | 1,3623 |
+-----------+----------+----------+----------+---------+----------+----------+----------+---------+---------+
| 30 | 1,3761 | 1,4524 | 1,4426 | 1,4244 | 1,4073 | 1,3923 | 1,3795 | 1,3685 | 1,3590 |
| | | | | | | | | | |
| 40 | 1,3626 | 1,4355 | 1,4239 | 1,4045 | 1,3863 | 1,3706 | 1,3571 | 1,3455 | 1,3354 |
| | | | | | | | | | |
| 60 | 1,3493 | 1,4188 | 1,4055 | 1,3848 | 1,3657 | 1,3491 | 1,3349 | 1,3226 | 1,3119 |
| | | | | | | | | | |
| 120 | 1,3362 | 1,4024 | 1,3873 | 1,3654 | 1,3453 | 1,3278 | 1,3128 | 1,2999 | 1,2886 |
| | | | | | | | | | |
| бесконеч- | 1,3233 | 1,3863 | 1,3694 | 1,3463 | 1,3251 | 1,3068 | 1,2910 | 1,2774 | 1,2654 |
| ность | | | | | | | | | |
+-----------+----------+----------+----------+---------+----------+----------+----------+---------+---------+
+-----------+-----------------------------------------------------------------------------------------------+
Продолжение таблицы
Содержание
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