Приложения
ТАБЛИЦА 1 – Значения интегральной функции Лапласа
x |
F(x) |
x |
F(x) |
x |
F(x) |
x |
F(x) |
x |
F(x) |
0,01 |
0,003989 |
0,51 |
0,194974 |
1,01 |
0,343752 |
1,51 |
0,434478 |
2,01 |
0,477784 |
0,02 |
0,007978 |
0,52 |
0,198468 |
1,02 |
0,346136 |
1,52 |
0,435745 |
2,02 |
0,478308 |
0,03 |
0,011966 |
0,53 |
0,201944 |
1,03 |
0,348495 |
1,53 |
0,436992 |
2,03 |
0,478822 |
0,04 |
0,015953 |
0,54 |
0,205401 |
1,04 |
0,35083 |
1,54 |
0,43822 |
2,04 |
0,479325 |
0,05 |
0,019939 |
0,55 |
0,20884 |
1,05 |
0,353141 |
1,55 |
0,439429 |
2,05 |
0,479818 |
0,06 |
0,023922 |
0,56 |
0,21226 |
1,06 |
0,355428 |
1,56 |
0,44062 |
2,06 |
0,480301 |
0,07 |
0,027903 |
0,57 |
0,215661 |
1,07 |
0,35769 |
1,57 |
0,441792 |
2,07 |
0,480774 |
0,08 |
0,031881 |
0,58 |
0,219043 |
1,08 |
0,359929 |
1,58 |
0,442947 |
2,08 |
0,481237 |
0,09 |
0,035856 |
0,59 |
0,222405 |
1,09 |
0,362143 |
1,59 |
0,444083 |
2,09 |
0,481691 |
0,1 |
0,039828 |
0,6 |
0,225747 |
1,1 |
0,364334 |
1,6 |
0,445201 |
2,1 |
0,482136 |
0,11 |
0,043795 |
0,61 |
0,229069 |
1,11 |
0,3665 |
1,61 |
0,446301 |
2,11 |
0,482571 |
0,12 |
0,047758 |
0,62 |
0,232371 |
1,12 |
0,368643 |
1,62 |
0,447384 |
2,12 |
0,482997 |
0,13 |
0,051717 |
0,63 |
0,235653 |
1,13 |
0,370762 |
1,63 |
0,448449 |
2,13 |
0,483414 |
0,14 |
0,05567 |
0,64 |
0,238914 |
1,14 |
0,372857 |
1,64 |
0,449497 |
2,14 |
0,483823 |
0,15 |
0,059618 |
0,65 |
0,242154 |
1,15 |
0,374928 |
1,65 |
0,450529 |
2,15 |
0,484222 |
0,16 |
0,063559 |
0,66 |
0,245373 |
1,16 |
0,376976 |
1,66 |
0,451543 |
2,16 |
0,484614 |
0,17 |
0,067495 |
0,67 |
0,248571 |
1,17 |
0,379 |
1,67 |
0,45254 |
2,17 |
0,484997 |
0,18 |
0,071424 |
0,68 |
0,251748 |
1,18 |
0,381 |
1,68 |
0,453521 |
2,18 |
0,485371 |
0,19 |
0,075345 |
0,69 |
0,254903 |
1,19 |
0,382977 |
1,69 |
0,454486 |
2,19 |
0,485738 |
0,2 |
0,07926 |
0,7 |
0,258036 |
1,2 |
0,38493 |
1,7 |
0,455435 |
2,2 |
0,486097 |
0,21 |
0,083166 |
0,71 |
0,261148 |
1,21 |
0,386861 |
1,71 |
0,456367 |
2,21 |
0,486447 |
0,22 |
0,087064 |
0,72 |
0,264238 |
1,22 |
0,388768 |
1,72 |
0,457284 |
2,22 |
0,486791 |
0,23 |
0,090954 |
0,73 |
0,267305 |
1,23 |
0,390651 |
1,73 |
0,458185 |
2,23 |
0,487126 |
0,24 |
0,094835 |
0,74 |
0,27035 |
1,24 |
0,392512 |
1,74 |
0,45907 |
2,24 |
0,487455 |
0,25 |
0,098706 |
0,75 |
0,273373 |
1,25 |
0,39435 |
1,75 |
0,459941 |
2,25 |
0,487776 |
0,26 |
0,102568 |
0,76 |
0,276373 |
1,26 |
0,396165 |
1,76 |
0,460796 |
2,26 |
0,488089 |
0,27 |
0,10642 |
0,77 |
0,27935 |
1,27 |
0,397958 |
1,77 |
0,461636 |
2,27 |
0,488396 |
0,28 |
0,110261 |
0,78 |
0,282305 |
1,28 |
0,399727 |
1,78 |
0,462462 |
2,28 |
0,488696 |
0,29 |
0,114092 |
0,79 |
0,285236 |
1,29 |
0,401475 |
1,79 |
0,463273 |
2,29 |
0,488989 |
0,3 |
0,117911 |
0,8 |
0,288145 |
1,3 |
0,4032 |
1,8 |
0,46407 |
2,3 |
0,489276 |
0,31 |
0,12172 |
0,81 |
0,29103 |
1,31 |
0,404902 |
1,81 |
0,464852 |
2,31 |
0,489556 |
0,32 |
0,125516 |
0,82 |
0,293892 |
1,32 |
0,406582 |
1,82 |
0,46562 |
2,32 |
0,48983 |
0,33 |
0,1293 |
0,83 |
0,296731 |
1,33 |
0,408241 |
1,83 |
0,466375 |
2,33 |
0,490097 |
0,34 |
0,133072 |
0,84 |
0,299546 |
1,34 |
0,409877 |
1,84 |
0,467116 |
2,34 |
0,490358 |
0,35 |
0,136831 |
0,85 |
0,302337 |
1,35 |
0,411492 |
1,85 |
0,467843 |
2,35 |
0,490613 |
0,36 |
0,140576 |
0,86 |
0,305105 |
1,36 |
0,413085 |
1,86 |
0,468557 |
2,36 |
0,490863 |
0,37 |
0,144309 |
0,87 |
0,30785 |
1,37 |
0,414657 |
1,87 |
0,469258 |
2,37 |
0,491106 |
0,38 |
0,148027 |
0,88 |
0,31057 |
1,38 |
0,416207 |
1,88 |
0,469946 |
2,38 |
0,491344 |
0,39 |
0,151732 |
0,89 |
0,313267 |
1,39 |
0,417736 |
1,89 |
0,470621 |
2,39 |
0,491576 |
0,4 |
0,155422 |
0,9 |
0,31594 |
1,4 |
0,419243 |
1,9 |
0,471283 |
2,4 |
0,491802 |
0,41 |
0,159097 |
0,91 |
0,318589 |
1,41 |
0,42073 |
1,91 |
0,471933 |
2,41 |
0,492024 |
0,42 |
0,162757 |
0,92 |
0,321214 |
1,42 |
0,422196 |
1,92 |
0,472571 |
2,42 |
0,49224 |
0,43 |
0,166402 |
0,93 |
0,323814 |
1,43 |
0,423641 |
1,93 |
0,473197 |
2,43 |
0,492451 |
0,44 |
0,170031 |
0,94 |
0,326391 |
1,44 |
0,425066 |
1,94 |
0,47381 |
2,44 |
0,492656 |
0,45 |
0,173645 |
0,95 |
0,328944 |
1,45 |
0,426471 |
1,95 |
0,474412 |
2,45 |
0,492857 |
0,46 |
0,177242 |
0,96 |
0,331472 |
1,46 |
0,427855 |
1,96 |
0,475002 |
2,46 |
0,493053 |
0,47 |
0,180822 |
0,97 |
0,333977 |
1,47 |
0,429219 |
1,97 |
0,475581 |
2,47 |
0,493244 |
0,48 |
0,184386 |
0,98 |
0,336457 |
1,48 |
0,430563 |
1,98 |
0,476148 |
2,48 |
0,493431 |
0,49 |
0,187933 |
0,99 |
0,338913 |
1,49 |
0,431888 |
1,99 |
0,476705 |
2,49 |
0,493613 |
0,5 |
0,191462 |
1 |
0,341345 |
1,5 |
0,433193 |
2 |
0,47725 |
2,5 |
0,49379 |
ТАБЛИЦА 1 – Значения интегральной функции Лапласа
x |
F(x) |
x |
F(x) |
x |
F(x) |
x |
F(x) |
x |
F(x) |
2,51 |
0,493963 |
3,01 |
0,498694 |
3,51 |
0,499776 |
4,01 |
0,49997 |
4,51 |
0,499997 |
2,52 |
0,494132 |
3,02 |
0,498736 |
3,52 |
0,499784 |
4,02 |
0,499971 |
4,52 |
0,499997 |
2,53 |
0,494297 |
3,03 |
0,498777 |
3,53 |
0,499792 |
4,03 |
0,499972 |
4,53 |
0,499997 |
2,54 |
0,494457 |
3,04 |
0,498817 |
3,54 |
0,4998 |
4,04 |
0,499973 |
4,54 |
0,499997 |
2,55 |
0,494614 |
3,05 |
0,498856 |
3,55 |
0,499807 |
4,05 |
0,499974 |
4,55 |
0,499997 |
2,56 |
0,494766 |
3,06 |
0,498893 |
3,56 |
0,499815 |
4,06 |
0,499975 |
4,56 |
0,499997 |
2,57 |
0,494915 |
3,07 |
0,49893 |
3,57 |
0,499822 |
4,07 |
0,499976 |
4,57 |
0,499998 |
2,58 |
0,49506 |
3,08 |
0,498965 |
3,58 |
0,499828 |
4,08 |
0,499977 |
4,58 |
0,499998 |
2,59 |
0,495201 |
3,09 |
0,498999 |
3,59 |
0,499835 |
4,09 |
0,499978 |
4,59 |
0,499998 |
2,6 |
0,495339 |
3,1 |
0,499032 |
3,6 |
0,499841 |
4,1 |
0,499979 |
4,6 |
0,499998 |
2,61 |
0,495473 |
3,11 |
0,499065 |
3,61 |
0,499847 |
4,11 |
0,49998 |
4,61 |
0,499998 |
2,62 |
0,495604 |
3,12 |
0,499096 |
3,62 |
0,499853 |
4,12 |
0,499981 |
4,62 |
0,499998 |
2,63 |
0,495731 |
3,13 |
0,499126 |
3,63 |
0,499858 |
4,13 |
0,499982 |
4,63 |
0,499998 |
2,64 |
0,495855 |
3,14 |
0,499155 |
3,64 |
0,499864 |
4,14 |
0,499983 |
4,64 |
0,499998 |
2,65 |
0,495975 |
3,15 |
0,499184 |
3,65 |
0,499869 |
4,15 |
0,499983 |
4,65 |
0,499998 |
2,66 |
0,496093 |
3,16 |
0,499211 |
3,66 |
0,499874 |
4,16 |
0,499984 |
4,66 |
0,499998 |
2,67 |
0,496207 |
3,17 |
0,499238 |
3,67 |
0,499879 |
4,17 |
0,499985 |
4,67 |
0,499998 |
2,68 |
0,496319 |
3,18 |
0,499264 |
3,68 |
0,499883 |
4,18 |
0,499985 |
4,68 |
0,499999 |
2,69 |
0,496427 |
3,19 |
0,499289 |
3,69 |
0,499888 |
4,19 |
0,499986 |
4,69 |
0,499999 |
2,7 |
0,496533 |
3,2 |
0,499313 |
3,7 |
0,499892 |
4,2 |
0,499987 |
4,7 |
0,499999 |
2,71 |
0,496636 |
3,21 |
0,499336 |
3,71 |
0,499896 |
4,21 |
0,499987 |
4,71 |
0,499999 |
2,72 |
0,496736 |
3,22 |
0,499359 |
3,72 |
0,4999 |
4,22 |
0,499988 |
4,72 |
0,499999 |
2,73 |
0,496833 |
3,23 |
0,499381 |
3,73 |
0,499904 |
4,23 |
0,499988 |
4,73 |
0,499999 |
2,74 |
0,496928 |
3,24 |
0,499402 |
3,74 |
0,499908 |
4,24 |
0,499989 |
4,74 |
0,499999 |
2,75 |
0,49702 |
3,25 |
0,499423 |
3,75 |
0,499912 |
4,25 |
0,499989 |
4,75 |
0,499999 |
2,76 |
0,49711 |
3,26 |
0,499443 |
3,76 |
0,499915 |
4,26 |
0,49999 |
4,76 |
0,499999 |
2,77 |
0,497197 |
3,27 |
0,499462 |
3,77 |
0,499918 |
4,27 |
0,49999 |
4,77 |
0,499999 |
2,78 |
0,497282 |
3,28 |
0,499481 |
3,78 |
0,499922 |
4,28 |
0,499991 |
4,78 |
0,499999 |
2,79 |
0,497365 |
3,29 |
0,499499 |
3,79 |
0,499925 |
4,29 |
0,499991 |
4,79 |
0,499999 |
2,8 |
0,497445 |
3,3 |
0,499517 |
3,8 |
0,499928 |
4,3 |
0,499991 |
4,8 |
0,499999 |
2,81 |
0,497523 |
3,31 |
0,499534 |
3,81 |
0,499931 |
4,31 |
0,499992 |
4,81 |
0,499999 |
2,82 |
0,497599 |
3,32 |
0,49955 |
3,82 |
0,499933 |
4,32 |
0,499992 |
4,82 |
0,499999 |
2,83 |
0,497673 |
3,33 |
0,499566 |
3,83 |
0,499936 |
4,33 |
0,499993 |
4,83 |
0,499999 |
2,84 |
0,497744 |
3,34 |
0,499581 |
3,84 |
0,499938 |
4,34 |
0,499993 |
4,84 |
0,499999 |
2,85 |
0,497814 |
3,35 |
0,499596 |
3,85 |
0,499941 |
4,35 |
0,499993 |
4,85 |
0,499999 |
2,86 |
0,497882 |
3,36 |
0,49961 |
3,86 |
0,499943 |
4,36 |
0,499993 |
4,86 |
0,499999 |
2,87 |
0,497948 |
3,37 |
0,499624 |
3,87 |
0,499946 |
4,37 |
0,499994 |
4,87 |
0,499999 |
2,88 |
0,498012 |
3,38 |
0,499638 |
3,88 |
0,499948 |
4,38 |
0,499994 |
4,88 |
0,499999 |
2,89 |
0,498074 |
3,39 |
0,499651 |
3,89 |
0,49995 |
4,39 |
0,499994 |
4,89 |
0,499999 |
2,9 |
0,498134 |
3,4 |
0,499663 |
3,9 |
0,499952 |
4,4 |
0,499995 |
4,9 |
0,5 |
2,91 |
0,498193 |
3,41 |
0,499675 |
3,91 |
0,499954 |
4,41 |
0,499995 |
4,91 |
0,5 |
2,92 |
0,49825 |
3,42 |
0,499687 |
3,92 |
0,499956 |
4,42 |
0,499995 |
4,92 |
0,5 |
2,93 |
0,498305 |
3,43 |
0,499698 |
3,93 |
0,499958 |
4,43 |
0,499995 |
4,93 |
0,5 |
2,94 |
0,498359 |
3,44 |
0,499709 |
3,94 |
0,499959 |
4,44 |
0,499996 |
4,94 |
0,5 |
2,95 |
0,498411 |
3,45 |
0,49972 |
3,95 |
0,499961 |
4,45 |
0,499996 |
4,95 |
0,5 |
2,96 |
0,498462 |
3,46 |
0,49973 |
3,96 |
0,499963 |
4,46 |
0,499996 |
4,96 |
0,5 |
2,97 |
0,498511 |
3,47 |
0,49974 |
3,97 |
0,499964 |
4,47 |
0,499996 |
4,97 |
0,5 |
2,98 |
0,498559 |
3,48 |
0,499749 |
3,98 |
0,499966 |
4,48 |
0,499996 |
4,98 |
0,5 |
2,99 |
0,498605 |
3,49 |
0,499758 |
3,99 |
0,499967 |
4,49 |
0,499996 |
4,99 |
0,5 |
3 |
0,49865 |
3,5 |
0,499767 |
4 |
0,499968 |
4,5 |
0,499997 |
5 |
0,5 |
ТАБЛИЦА 2 – Значения коэффициента Стьюдента
n |
γ=0,9 |
γ=0,95 |
γ=0,99 |
γ=0,999 |
n |
γ=0,95 |
γ=0,9 |
γ=0,99 |
γ=0,999 |
5 |
2,131847 |
2,776445 |
4,604095 |
8,610302 |
55 |
1,673565 |
2,004879 |
2,669985 |
3,480016 |
6 |
2,015048 |
2,570582 |
4,032143 |
6,868827 |
56 |
1,673034 |
2,004045 |
2,668216 |
3,476398 |
7 |
1,94318 |
2,446912 |
3,707428 |
5,958816 |
58 |
1,672029 |
2,002465 |
2,66487 |
3,469562 |
8 |
1,894579 |
2,364624 |
3,499483 |
5,407883 |
60 |
1,671093 |
2,000995 |
2,661759 |
3,46321 |
9 |
1,859548 |
2,306004 |
3,355387 |
5,041305 |
62 |
1,670219 |
1,999624 |
2,658857 |
3,457294 |
10 |
1,833113 |
2,262157 |
3,249836 |
4,780913 |
64 |
1,669402 |
1,998341 |
2,656145 |
3,451769 |
11 |
1,812461 |
2,228139 |
3,169273 |
4,586894 |
66 |
1,668636 |
1,997138 |
2,653604 |
3,446598 |
12 |
1,795885 |
2,200985 |
3,105807 |
4,436979 |
68 |
1,667916 |
1,996008 |
2,65122 |
3,441749 |
13 |
1,782288 |
2,178813 |
3,05454 |
4,317791 |
70 |
1,667239 |
1,994945 |
2,648977 |
3,437192 |
14 |
1,770933 |
2,160369 |
3,012276 |
4,220832 |
72 |
1,6666 |
1,993943 |
2,646863 |
3,432901 |
15 |
1,76131 |
2,144787 |
2,976843 |
4,140454 |
74 |
1,665996 |
1,992997 |
2,644869 |
3,428854 |
16 |
1,75305 |
2,13145 |
2,946713 |
4,072765 |
76 |
1,665425 |
1,992102 |
2,642983 |
3,425031 |
17 |
1,745884 |
2,119905 |
2,920782 |
4,014996 |
78 |
1,664885 |
1,991254 |
2,641198 |
3,421413 |
18 |
1,739607 |
2,109816 |
2,898231 |
3,965126 |
80 |
1,664371 |
1,99045 |
2,639505 |
3,417985 |
19 |
1,734064 |
2,100922 |
2,87844 |
3,921646 |
82 |
1,663884 |
1,989686 |
2,637897 |
3,414732 |
20 |
1,729133 |
2,093024 |
2,860935 |
3,883406 |
84 |
1,66342 |
1,98896 |
2,636369 |
3,411641 |
21 |
1,724718 |
2,085963 |
2,84534 |
3,849516 |
86 |
1,662978 |
1,988268 |
2,634914 |
3,408699 |
22 |
1,720743 |
2,079614 |
2,83136 |
3,819277 |
88 |
1,662557 |
1,987608 |
2,633527 |
3,405897 |
23 |
1,717144 |
2,073873 |
2,818756 |
3,792131 |
90 |
1,662155 |
1,986979 |
2,632204 |
3,403225 |
24 |
1,713872 |
2,068658 |
2,807336 |
3,767627 |
92 |
1,661771 |
1,986377 |
2,63094 |
3,400674 |
25 |
1,710882 |
2,063899 |
2,79694 |
3,745399 |
94 |
1,661404 |
1,985802 |
2,629732 |
3,398236 |
26 |
1,708141 |
2,059539 |
2,787436 |
3,725144 |
96 |
1,661052 |
1,985251 |
2,628576 |
3,395904 |
27 |
1,705618 |
2,055529 |
2,778715 |
3,706612 |
98 |
1,660715 |
1,984723 |
2,627468 |
3,39367 |
28 |
1,703288 |
2,051831 |
2,770683 |
3,689592 |
100 |
1,660391 |
1,984217 |
2,626405 |
3,391529 |
29 |
1,701131 |
2,048407 |
2,763262 |
3,673906 |
102 |
1,660081 |
1,983731 |
2,625386 |
3,389475 |
30 |
1,699127 |
2,04523 |
2,756386 |
3,659405 |
104 |
1,659782 |
1,983264 |
2,624407 |
3,387503 |
31 |
1,697261 |
2,042272 |
2,749996 |
3,645959 |
106 |
1,659495 |
1,982815 |
2,623465 |
3,385608 |
32 |
1,695519 |
2,039513 |
2,744042 |
3,633456 |
108 |
1,659219 |
1,982383 |
2,62256 |
3,383785 |
33 |
1,693889 |
2,036933 |
2,738481 |
3,621802 |
110 |
1,658953 |
1,981967 |
2,621688 |
3,382032 |
34 |
1,69236 |
2,034515 |
2,733277 |
3,610913 |
112 |
1,658697 |
1,981567 |
2,620849 |
3,380342 |
35 |
1,690924 |
2,032245 |
2,728394 |
3,600716 |
114 |
1,65845 |
1,98118 |
2,620039 |
3,378714 |
36 |
1,689572 |
2,030108 |
2,723806 |
3,591147 |
116 |
1,658212 |
1,980808 |
2,619258 |
3,377145 |
37 |
1,688298 |
2,028094 |
2,719485 |
3,58215 |
118 |
1,657982 |
1,980448 |
2,618504 |
3,375629 |
38 |
1,687094 |
2,026192 |
2,715409 |
3,573675 |
120 |
1,657759 |
1,9801 |
2,617776 |
3,374167 |
39 |
1,685954 |
2,024394 |
2,711558 |
3,565678 |
122 |
1,657544 |
1,979764 |
2,617072 |
3,372753 |
40 |
1,684875 |
2,022691 |
2,707913 |
3,55812 |
124 |
1,657336 |
1,979439 |
2,616392 |
3,371387 |
41 |
1,683851 |
2,021075 |
2,704459 |
3,550966 |
126 |
1,657135 |
1,979124 |
2,615733 |
3,370065 |
42 |
1,682878 |
2,019541 |
2,701181 |
3,544184 |
128 |
1,65694 |
1,97882 |
2,615096 |
3,368785 |
43 |
1,681952 |
2,018082 |
2,698066 |
3,537745 |
130 |
1,656752 |
1,978524 |
2,614479 |
3,367546 |
44 |
1,681071 |
2,016692 |
2,695102 |
3,531626 |
132 |
1,656569 |
1,978239 |
2,61388 |
3,366346 |
45 |
1,68023 |
2,015368 |
2,692278 |
3,525801 |
134 |
1,656391 |
1,977961 |
2,6133 |
3,365183 |
46 |
1,679427 |
2,014103 |
2,689585 |
3,520251 |
136 |
1,656219 |
1,977692 |
2,612738 |
3,364055 |
47 |
1,67866 |
2,012896 |
2,687013 |
3,514957 |
138 |
1,656052 |
1,977431 |
2,612192 |
3,36296 |
48 |
1,677927 |
2,011741 |
2,684556 |
3,509901 |
140 |
1,65589 |
1,977178 |
2,611662 |
3,361897 |
49 |
1,677224 |
2,010635 |
2,682204 |
3,505068 |
142 |
1,655732 |
1,976931 |
2,611147 |
3,360866 |
50 |
1,676551 |
2,009575 |
2,679952 |
3,500443 |
144 |
1,655579 |
1,976692 |
2,610647 |
3,359863 |
51 |
1,675905 |
2,008559 |
2,677793 |
3,496013 |
146 |
1,65543 |
1,97646 |
2,610161 |
3,358889 |
52 |
1,675285 |
2,007584 |
2,675722 |
3,491766 |
148 |
1,655285 |
1,976233 |
2,609688 |
3,357942 |
53 |
1,674689 |
2,006647 |
2,673734 |
3,487691 |
150 |
1,655145 |
1,976013 |
2,609228 |
3,35702 |
54 |
1,674116 |
2,005746 |
2,671823 |
3,483777 |
∞ |
1,644855 |
1,959966 |
2,575834 |
3,290536 |
ТАБЛИЦА 3 – Значения коэффициента q
ТАБЛИЦА 4 – Значения критических точек распределения Фишера-Снедикора
k1 – число степеней свободы меньшей дисперсии
k2 – число степеней свободы большей дисперсии
α=0,05
k2 k1 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
1 |
161 |
200 |
216 |
225 |
230 |
234 |
237 |
239 |
241 |
242 |
243 |
244 |
2 |
18,51 |
19,00 |
19,16 |
19,25 |
19,30 |
19,33 |
19,35 |
19,37 |
19,38 |
19,40 |
19,40 |
19,41 |
3 |
10,128 |
9,552 |
9,277 |
9,117 |
9,013 |
8,941 |
8,887 |
8,845 |
8,812 |
8,786 |
8,763 |
8,745 |
4 |
7,709 |
6,944 |
6,591 |
6,388 |
6,256 |
6,163 |
6,094 |
6,041 |
5,999 |
5,964 |
5,936 |
5,912 |
5 |
6,608 |
5,786 |
5,409 |
5,192 |
5,050 |
4,950 |
4,876 |
4,818 |
4,772 |
4,735 |
4,704 |
4,678 |
6 |
5,987 |
5,143 |
4,757 |
4,534 |
4,387 |
4,284 |
4,207 |
4,147 |
4,099 |
4,060 |
4,027 |
4,000 |
7 |
5,591 |
4,737 |
4,347 |
4,120 |
3,972 |
3,866 |
3,787 |
3,726 |
3,677 |
3,637 |
3,603 |
3,575 |
8 |
5,318 |
4,459 |
4,066 |
3,838 |
3,687 |
3,581 |
3,500 |
3,438 |
3,388 |
3,347 |
3,313 |
3,284 |
9 |
5,117 |
4,256 |
3,863 |
3,633 |
3,482 |
3,374 |
3,293 |
3,230 |
3,179 |
3,137 |
3,102 |
3,073 |
10 |
4,965 |
4,103 |
3,708 |
3,478 |
3,326 |
3,217 |
3,135 |
3,072 |
3,020 |
2,978 |
2,943 |
2,913 |
11 |
4,844 |
3,982 |
3,587 |
3,357 |
3,204 |
3,095 |
3,012 |
2,948 |
2,896 |
2,854 |
2,818 |
2,788 |
12 |
4,747 |
3,885 |
3,490 |
3,259 |
3,106 |
2,996 |
2,913 |
2,849 |
2,796 |
2,753 |
2,717 |
2,687 |
13 |
4,667 |
3,806 |
3,411 |
3,179 |
3,025 |
2,915 |
2,832 |
2,767 |
2,714 |
2,671 |
2,635 |
2,604 |
14 |
4,600 |
3,739 |
3,344 |
3,112 |
2,958 |
2,848 |
2,764 |
2,699 |
2,646 |
2,602 |
2,565 |
2,534 |
15 |
4,543 |
3,682 |
3,287 |
3,056 |
2,901 |
2,790 |
2,707 |
2,641 |
2,588 |
2,544 |
2,507 |
2,475 |
16 |
4,494 |
3,634 |
3,239 |
3,007 |
2,852 |
2,741 |
2,657 |
2,591 |
2,538 |
2,494 |
2,456 |
2,425 |
17 |
4,451 |
3,592 |
3,197 |
2,965 |
2,810 |
2,699 |
2,614 |
2,548 |
2,494 |
2,450 |
2,413 |
2,381 |
18 |
4,414 |
3,555 |
3,160 |
2,928 |
2,773 |
2,661 |
2,577 |
2,510 |
2,456 |
2,412 |
2,374 |
2,342 |
19 |
4,381 |
3,522 |
3,127 |
2,895 |
2,740 |
2,628 |
2,544 |
2,477 |
2,423 |
2,378 |
2,340 |
2,308 |
20 |
4,351 |
3,493 |
3,098 |
2,866 |
2,711 |
2,599 |
2,514 |
2,447 |
2,393 |
2,348 |
2,310 |
2,278 |
α=0,01
k2 k1 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
1 |
4052 |
5000 |
5403 |
5625 |
5764 |
5859 |
5928 |
5981 |
6022 |
6056 |
6083 |
6106 |
2 |
98,50 |
99,00 |
99,17 |
99,25 |
99,30 |
99,33 |
99,36 |
99,37 |
99,39 |
99,40 |
99,41 |
99,42 |
3 |
34,12 |
30,82 |
29,46 |
28,71 |
28,24 |
27,91 |
27,67 |
27,49 |
27,35 |
27,23 |
27,13 |
27,05 |
4 |
21,20 |
18,00 |
16,69 |
15,98 |
15,52 |
15,21 |
14,98 |
14,80 |
14,66 |
14,55 |
14,45 |
14,37 |
5 |
16,26 |
13,27 |
12,06 |
11,39 |
10,97 |
10,67 |
10,46 |
10,29 |
10,16 |
10,05 |
9,96 |
9,89 |
6 |
13,745 |
10,925 |
9,780 |
9,148 |
8,746 |
8,466 |
8,260 |
8,102 |
7,976 |
7,874 |
7,790 |
7,718 |
7 |
12,246 |
9,547 |
8,451 |
7,847 |
7,460 |
7,191 |
6,993 |
6,840 |
6,719 |
6,620 |
6,538 |
6,469 |
8 |
11,259 |
8,649 |
7,591 |
7,006 |
6,632 |
6,371 |
6,178 |
6,029 |
5,911 |
5,814 |
5,734 |
5,667 |
9 |
10,561 |
8,022 |
6,992 |
6,422 |
6,057 |
5,802 |
5,613 |
5,467 |
5,351 |
5,257 |
5,178 |
5,111 |
10 |
10,044 |
7,559 |
6,552 |
5,994 |
5,636 |
5,386 |
5,200 |
5,057 |
4,942 |
4,849 |
4,772 |
4,706 |
11 |
9,646 |
7,206 |
6,217 |
5,668 |
5,316 |
5,069 |
4,886 |
4,744 |
4,632 |
4,539 |
4,462 |
4,397 |
12 |
9,330 |
6,927 |
5,953 |
5,412 |
5,064 |
4,821 |
4,640 |
4,499 |
4,388 |
4,296 |
4,220 |
4,155 |
13 |
9,074 |
6,701 |
5,739 |
5,205 |
4,862 |
4,620 |
4,441 |
4,302 |
4,191 |
4,100 |
4,025 |
3,960 |
14 |
8,862 |
6,515 |
5,564 |
5,035 |
4,695 |
4,456 |
4,278 |
4,140 |
4,030 |
3,939 |
3,864 |
3,800 |
15 |
8,683 |
6,359 |
5,417 |
4,893 |
4,556 |
4,318 |
4,142 |
4,004 |
3,895 |
3,805 |
3,730 |
3,666 |
16 |
8,531 |
6,226 |
5,292 |
4,773 |
4,437 |
4,202 |
4,026 |
3,890 |
3,780 |
3,691 |
3,616 |
3,553 |
17 |
8,400 |
6,112 |
5,185 |
4,669 |
4,336 |
4,102 |
3,927 |
3,791 |
3,682 |
3,593 |
3,519 |
3,455 |
18 |
8,285 |
6,013 |
5,092 |
4,579 |
4,248 |
4,015 |
3,841 |
3,705 |
3,597 |
3,508 |
3,434 |
3,371 |
19 |
8,185 |
5,926 |
5,010 |
4,500 |
4,171 |
3,939 |
3,765 |
3,631 |
3,523 |
3,434 |
3,360 |
3,297 |
20 |
8,096 |
5,849 |
4,938 |
4,431 |
4,103 |
3,871 |
3,699 |
3,564 |
3,457 |
3,368 |
3,294 |
3,231 |
ТАБЛИЦА 5 – Значения критических точек распределения χ2
n |
α=0,01 |
α=0,05 |
α=0,1 |
α=0,9 |
α=0,95 |
α=0,99 |
1 |
6,634897 |
3,841459 |
2,705543 |
0,015791 |
0,003932 |
0,000157 |
2 |
9,21034 |
5,991465 |
4,60517 |
0,210721 |
0,102587 |
0,020101 |
3 |
11,34487 |
7,814728 |
6,251389 |
0,584374 |
0,351846 |
0,114832 |
4 |
13,2767 |
9,487729 |
7,77944 |
1,063623 |
0,710723 |
0,297109 |
5 |
15,08627 |
11,0705 |
9,236357 |
1,610308 |
1,145476 |
0,554298 |
6 |
16,81189 |
12,59159 |
10,64464 |
2,204131 |
1,635383 |
0,87209 |
7 |
18,47531 |
14,06714 |
12,01704 |
2,833107 |
2,16735 |
1,239042 |
8 |
20,09024 |
15,50731 |
13,36157 |
3,489539 |
2,732637 |
1,646497 |
9 |
21,66599 |
16,91898 |
14,68366 |
4,168159 |
3,325113 |
2,087901 |
10 |
23,20925 |
18,30704 |
15,98718 |
4,865182 |
3,940299 |
2,558212 |
11 |
24,72497 |
19,67514 |
17,27501 |
5,577785 |
4,574813 |
3,053484 |
12 |
26,21697 |
21,02607 |
18,54935 |
6,303796 |
5,226029 |
3,570569 |
13 |
27,68825 |
22,36203 |
19,81193 |
7,041505 |
5,891864 |
4,106915 |
14 |
29,14124 |
23,68479 |
21,06414 |
7,789534 |
6,570631 |
4,660425 |
15 |
30,57791 |
24,99579 |
22,30713 |
8,546756 |
7,260944 |
5,229349 |
16 |
31,99993 |
26,29623 |
23,54183 |
9,312236 |
7,961646 |
5,812212 |
17 |
33,40866 |
27,58711 |
24,76904 |
10,08519 |
8,67176 |
6,40776 |
18 |
34,80531 |
28,8693 |
25,98942 |
10,86494 |
9,390455 |
7,014911 |
19 |
36,19087 |
30,14353 |
27,20357 |
11,65091 |
10,11701 |
7,63273 |
20 |
37,56623 |
31,41043 |
28,41198 |
12,44261 |
10,85081 |
8,260398 |
21 |
38,93217 |
32,67057 |
29,61509 |
13,2396 |
11,59131 |
8,897198 |
22 |
40,28936 |
33,92444 |
30,81328 |
14,04149 |
12,33801 |
9,542492 |
23 |
41,6384 |
35,17246 |
32,0069 |
14,84796 |
13,09051 |
10,19572 |
24 |
42,97982 |
36,41503 |
33,19624 |
15,65868 |
13,84843 |
10,85636 |
25 |
44,3141 |
37,65248 |
34,38159 |
16,47341 |
14,61141 |
11,52398 |
26 |
45,64168 |
38,88514 |
35,56317 |
17,29188 |
15,37916 |
12,19815 |
27 |
46,96294 |
40,11327 |
36,74122 |
18,1139 |
16,1514 |
12,8785 |
28 |
48,27824 |
41,33714 |
37,91592 |
18,93924 |
16,92788 |
13,56471 |
29 |
49,58788 |
42,55697 |
39,08747 |
19,76774 |
17,70837 |
14,25645 |
30 |
50,89218 |
43,77297 |
40,25602 |
20,59923 |
18,49266 |
14,95346 |
31 |
52,19139 |
44,98534 |
41,42174 |
21,43356 |
19,28057 |
15,65546 |
32 |
53,48577 |
46,19426 |
42,58475 |
22,27059 |
20,07191 |
16,36222 |
33 |
54,77554 |
47,39988 |
43,74518 |
23,1102 |
20,86653 |
17,07351 |
34 |
56,06091 |
48,60237 |
44,90316 |
23,95225 |
21,66428 |
17,78915 |
35 |
57,34207 |
49,80185 |
46,05879 |
24,79665 |
22,46502 |
18,50893 |
36 |
58,61921 |
50,99846 |
47,21217 |
25,6433 |
23,26861 |
19,23268 |
37 |
59,8925 |
52,19232 |
48,36341 |
26,49209 |
24,07494 |
19,96023 |
38 |
61,16209 |
53,38354 |
49,51258 |
27,34295 |
24,8839 |
20,69144 |
39 |
62,42812 |
54,57223 |
50,65977 |
28,19579 |
25,69539 |
21,42616 |
40 |
63,69074 |
55,75848 |
51,80506 |
29,05052 |
26,5093 |
22,16426 |
41 |
64,95007 |
56,94239 |
52,94851 |
29,90709 |
27,32555 |
22,90561 |
42 |
66,20624 |
58,12404 |
54,0902 |
30,76542 |
28,14405 |
23,65009 |
43 |
67,45935 |
59,30351 |
55,23019 |
31,62545 |
28,96472 |
24,3976 |
44 |
68,70951 |
60,48089 |
56,36854 |
32,48713 |
29,78748 |
25,14803 |
45 |
69,95683 |
61,65623 |
57,5053 |
33,35038 |
30,61226 |
25,90127 |
46 |
71,2014 |
62,82962 |
58,64054 |
34,21517 |
31,439 |
26,65724 |
47 |
72,44331 |
64,00111 |
59,77429 |
35,08143 |
32,26762 |
27,41585 |
48 |
73,68264 |
65,17077 |
60,90661 |
35,94913 |
33,09808 |
28,17701 |
49 |
74,91947 |
66,33865 |
62,03754 |
36,81822 |
33,93031 |
28,94065 |
50 |
76,15389 |
67,50481 |
63,16712 |
37,68865 |
34,76425 |
29,70668 |