(4)
должно подчиняться распределению Фишера.
В соответствии с критерием оценки статистической гипотезы необходимо величину (4) сопоставлять с табличным значением для заданного уровня значимости и чисел степеней свободы и соответственно.
При этом если
, (5)
то гипотезу линейности принимают.
Величины приведены в таблице для критерия значимости .
В числителе дисперсионного отношения (4) должна стоять большая из сравниваемых дисперсий. Как правило, . Число степеней свободы дисперсии равно .
Значения при
|
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
|
|
1 |
161,45 |
199,50 |
215,71 |
224,58 |
230,16 |
233,99 |
236,77 |
238,88 |
240,50 |
|
2 |
18,513 |
19,000 |
19,164 |
19,247 |
19,296 |
19,330 |
19,353 |
19,371 |
19,38 |
|
3 |
10,128 |
9,552 |
9,277 |
9,117 |
9,014 |
8,941 |
8,887 |
8,887 |
8,81 |
|
4 |
7,709 |
6,944 |
6,591 |
6,388 |
6,256 |
6,163 |
6,094 |
6,041 |
5,99 |
|
5 |
6,608 |
5,786 |
5,410 |
5,192 |
5,050 |
4,950 |
4,876 |
4,818 |
4,77 |
|
6 |
5,987 |
5,141 |
4,757 |
4,534 |
4,387 |
4,284 |
4,207 |
4,147 |
4,09 |
|
7 |
5,591 |
4,737 |
4,347 |
4,120 |
3,972 |
3,866 |
3,787 |
3,726 |
3,67 |
|
8 |
5,318 |
4,459 |
4,066 |
3,838 |
3,688 |
3,581 |
3,501 |
3,438 |
3,38 |
|
9 |
5,117 |
4,257 |
3,863 |
3,633 |
3,482 |
3,374 |
3,293 |
3,230 |
3,17 |
|
10 |
4,965 |
4,103 |
3,708 |
3,478 |
3,326 |
3,217 |
3,136 |
3,072 |
3,02 |
|
11 |
4,844 |
3,982 |
3,587 |
3,357 |
3,204 |
3,095 |
3,012 |
2,948 |
2,89 |
|
12 |
4,747 |
3,885 |
3,490 |
3,259 |
3,106 |
2,996 |
2,913 |
2,849 |
2,79 |
|
13 |
4,667 |
3,806 |
3,411 |
3,179 |
3,025 |
2,915 |
2,832 |
2,767 |
2,71 |
|
14 |
4,600 |
3,739 |
3,344 |
3,112 |
2,958 |
2,848 |
2,764 |
2,699 |
2,64 |
|
15 |
4,543 |
3,682 |
3,287 |
3,056 |
2,901 |
2,791 |
2,707 |
2,641 |
2,55 |
|
16 |
4,494 |
3,634 |
3,239 |
3,007 |
2,852 |
2,741 |
2,657 |
2,591 |
2,53 |
|
17 |
4,451 |
3,592 |
3,197 |
2,965 |
2,810 |
2,699 |
2,614 |
2,548 |
2,49 |
|
18 |
4,414 |
3,555 |
3,160 |
2,928 |
2,773 |
2,661 |
2,577 |
2,510 |
2,45 |
|
19 |
4,381 |
3,522 |
3,127 |
2,895 |
2,740 |
2,628 |
2,544 |
2,477 |
2,423 |
|
20 |
4,351 |
3,493 |
3,098 |
2,866 |
2,711 |
2,599 |
2,514 |
2,447 |
3,393 |
|
21 |
4,325 |
3,467 |
3,073 |
2,840 |
2,685 |
2,573 |
2,488 |
2,421 |
2,366 |
|
22 |
4,301 |
3,443 |
3,049 |
2,817 |
2,661 |
2,549 |
2,464 |
2,397 |
2,342 |
|
23 |
4,279 |
3,422 |
3,028 |
2,796 |
2,640 |
2,528 |
2,442 |
2,375 |
2,320 |
|
24 |
4,260 |
3,403 |
3,009 |
2,776 |
2,621 |
2,508 |
2,423 |
2,355 |
2,300 |
|
25 |
4,242 |
3,385 |
2,991 |
2,759 |
2,603 |
2,490 |
2,405 |
2,337 |
2,282 |
|
26 |
4,225 |
3,369 |
2,975 |
2,743 |
2,585 |
2,474 |
2,388 |
2,321 |
2,226 |
|
27 |
4,210 |
3,354 |
2,960 |
2,728 |
2,572 |
2,459 |
2,373 |
2,305 |
2,250 |
|
28 |
4,196 |
3,340 |
2,947 |
2,714 |
2,558 |
2,445 |
2,359 |
2,291 |
2,236 |
|
29 |
4,183 |
3,328 |
2,934 |
2,701 |
2,545 |
2,434 |
2,346 |
2,278 |
2,223 |
|
30 |
4,171 |
3,316 |
2,922 |
2,690 |
2,534 |
2,421 |
2,334 |
2,266 |
2,211 |
|
40 |
4,085 |
3,232 |
2,839 |
2,606 |
2,450 |
2,336 |
2,249 |
2,180 |
2,124 |
|
60 |
4,001 |
3,150 |
2,758 |
2,525 |
2,368 |
2,254 |
2,167 |
2,097 |
2,040 |
|
120 |
3,920 |
3,072 |
2,680 |
2,447 |
2,290 |
2,175 |
2,087 |
2,016 |
1,959 |
|
|
3,842 |
2,996 |
2,605 |
2,372 |
2,214 |
2,099 |
2,010 |
1,938 |
1,880 |
Продолжение
|
10 |
12 |
15 |
20 |
24 |
30 |
40 |
60 |
120 |
||
|
1 |
241,88 |
243,91 |
245,95 |
248,01 |
249,05 |
250,09 |
251,14 |
252,20 |
253,25 |
254,32 |
|
2 |
19,396 |
19,413 |
19,429 |
19,446 |
19,454 |
19,462 |
19,471 |
19,479 |
19,487 |
19,496 |
|
3 |
8,786 |
8,745 |
8,703 |
8,660 |
8,639 |
8,617 |
8,594 |
8,572 |
8,549 |
8,257 |
|
4 |
5,964 |
5,912 |
5,858 |
5,803 |
5,774 |
5,746 |
5,717 |
5,688 |
5,658 |
5,628 |
|
5 |
4,735 |
4,678 |
4,619 |
4,558 |
4,527 |
4,496 |
4,464 |
4,431 |
4,398 |
4,365 |
|
6 |
4,060 |
4,000 |
3,938 |
3,874 |
3,842 |
3,808 |
3,774 |
3,740 |
3,705 |
3,669 |
|
7 |
3,637 |
3,575 |
3,511 |
3,445 |
3,411 |
3,376 |
3,430 |
3,304 |
3,267 |
3,230 |
|
8 |
3,347 |
3,284 |
3,218 |
3,150 |
3,115 |
3,079 |
3,043 |
3,005 |
2,967 |
2,928 |
|
9 |
3,137 |
3,073 |
3,006 |
2,937 |
2,901 |
2,864 |
2,826 |
2,787 |
2,748 |
2,707 |
|
10 |
2,978 |
2,913 |
2,845 |
2,774 |
2,737 |
2,700 |
2,661 |
2,621 |
2,580 |
2,588 |
|
11 |
2,854 |
2,788 |
2,719 |
2,646 |
2,609 |
2,571 |
2,531 |
2,490 |
2,448 |
2,405 |
|
12 |
2,753 |
2,687 |
2,617 |
2,544 |
2,506 |
2,466 |
2,426 |
2,384 |
2,341 |
2,296 |
|
13 |
2,671 |
2,604 |
2,533 |
2,459 |
2,420 |
2,380 |
2,330 |
2,297 |
2,252 |
2,206 |
|
14 |
2,602 |
2,534 |
2,463 |
2,388 |
2,349 |
2,308 |
2,266 |
2,223 |
2,178 |
2,131 |
|
15 |
2,544 |
2,475 |
2,404 |
2,328 |
2,288 |
2,247 |
2,204 |
2,160 |
2,114 |
2,066 |
|
16 |
2,494 |
2,425 |
2,352 |
2,276 |
2,235 |
2,194 |
2,151 |
2,106 |
2,059 |
2,010 |
|
17 |
2,450 |
2,381 |
2,308 |
2,230 |
2,190 |
2,148 |
2,104 |
2,058 |
2,011 |
1,960 |
|
18 |
2,412 |
2,342 |
2,269 |
2,191 |
2,150 |
2,107 |
2,063 |
2,017 |
1,968 |
1,913 |
|
19 |
2,378 |
2,308 |
2,234 |
2,156 |
2,114 |
2,071 |
2,026 |
1,980 |
1,930 |
1,878 |
|
20 |
2,348 |
2,278 |
2,203 |
2,124 |
2,083 |
2,039 |
1,994 |
1,946 |
1,896 |
1,843 |
|
21 |
2,321 |
2,250 |
2,178 |
2,096 |
2,054 |
2,010 |
1,965 |
1,917 |
1,876 |
1,812 |
|
22 |
2,297 |
2,226 |
2,151 |
2,071 |
2,028 |
1,984 |
1,938 |
1,890 |
1,838 |
1,783 |
|
23 |
2,275 |
2,204 |
2,128 |
2,048 |
2,005 |
1,961 |
1,914 |
1,865 |
1,813 |
1,757 |
|
24 |
2,255 |
2,183 |
2,108 |
2,027 |
1,984 |
1,939 |
1,892 |
1,842 |
1,790 |
1,733 |
|
25 |
2,237 |
2,165 |
2,089 |
2,008 |
1,964 |
1,919 |
1,872 |
1,822 |
1,768 |
1,711 |
|
26 |
2,220 |
2,148 |
2,072 |
1,990 |
1,946 |
1,901 |
1,853 |
1,803 |
1,749 |
1,691 |
|
27 |
2,204 |
2,132 |
2,056 |
1,974 |
1,930 |
1,884 |
1,836 |
1,785 |
1,731 |
1,672 |
|
28 |
2,190 |
2,118 |
2,041 |
1,959 |
1,915 |
1,869 |
1,820 |
1,769 |
1,714 |
1,654 |
|
29 |
2,177 |
2,105 |
2,028 |
1,945 |
1,901 |
1,854 |
1,806 |
1,754 |
1,698 |
1,638 |
|
30 |
1,165 |
2,092 |
2,015 |
1,932 |
1,887 |
1,841 |
1,792 |
1,740 |
1,684 |
1,622 |
|
40 |
2,077 |
2,004 |
1,925 |
1,839 |
1,793 |
1,744 |
1,693 |
1,637 |
1,577 |
1,509 |
|
60 |
1,993 |
1,917 |
1,836 |
1,748 |
1,700 |
1,649 |
1,594 |
1,534 |
1,467 |
1,389 |
|
120 |
1,911 |
1,834 |
1,751 |
1,659 |
1,608 |
1,554 |
1,495 |
1,429 |
1,352 |
1,254 |
|
1,831 |
1,752 |
1,666 |
1,571 |
1,517 |
1,459 |
1,394 |
1,318 |
1,221 |
1,000 |
|
