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Probabilidades e Estatística III-59

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Tópicos: Tabelas da Distribuição F (continuação da página anterior) |


1) Tabelas da Distribuição F

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Nas tabelas abaixo, valores de x conforme Figura I-1 são dados para o valor de A indicado.

ν1: graus de liberdade da variável do numerador (primeira linha).

ν2: graus de liberdade da variável do denominador (primeira coluna à esquerda da tabela).

Distribuição F
Fig I-1

Tabela para A = 0,05 ou 5%
ν21 1 2 3 4 5 6 7 8 9 10 12 15 20 24 30 40 60 120
1 161,4 199,5 215,7 224,6 230,2 234,0 236,8 238,9 240,5 241,9 243,9 245,9 248,0 249,1 250,1 251,1 252,2 253,3 254,3
2 18,51 19,00 19,16 19,25 19,30 19,33 19,35 19,37 19,38 19,40 19,41 19,43 19,45 19,45 19,46 19,47 19,48 19,49 19,50
3 10,13 9,552 9,277 9,117 9,014 8,941 8,887 8,845 8,812 8,786 8,745 8,703 8,660 8,639 8,617 8,594 8,572 8,549 8,526
4 7,709 6,944 6,591 6,388 6,256 6,163 6,094 6,041 5,999 5,964 5,912 5,858 5,803 5,774 5,746 5,717 5,688 5,658 5,628
5 6,608 5,786 5,410 5,192 5,050 4,950 4,876 4,818 4,773 4,735 4,678 4,619 4,558 4,527 4,496 4,464 4,431 4,399 4,365
6 5,987 5,143 4,757 4,534 4,387 4,284 4,207 4,147 4,099 4,060 4,000 3,938 3,874 3,842 3,808 3,774 3,740 3,705 3,669
7 5,591 4,737 4,347 4,120 3,972 3,866 3,787 3,726 3,677 3,637 3,575 3,511 3,445 3,411 3,376 3,340 3,304 3,267 3,230
8 5,318 4,459 4,066 3,838 3,688 3,581 3,501 3,438 3,388 3,347 3,284 3,218 3,150 3,115 3,079 3,043 3,005 2,967 2,928
9 5,117 4,257 3,863 3,633 3,482 3,374 3,293 3,230 3,179 3,137 3,073 3,006 2,937 2,901 2,864 2,826 2,787 2,748 2,707
10 4,965 4,103 3,708 3,478 3,326 3,217 3,136 3,072 3,020 2,978 2,913 2,845 2,774 2,737 2,700 2,661 2,621 2,580 2,538
11 4,844 3,982 3,587 3,357 3,204 3,095 3,012 2,948 2,896 2,854 2,788 2,719 2,646 2,609 2,571 2,531 2,490 2,448 2,405
12 4,747 3,885 3,490 3,259 3,106 2,996 2,913 2,849 2,796 2,753 2,687 2,617 2,544 2,506 2,466 2,426 2,384 2,341 2,296
13 4,667 3,806 3,411 3,179 3,025 2,915 2,832 2,767 2,714 2,671 2,604 2,533 2,459 2,420 2,380 2,339 2,297 2,252 2,206
14 4,600 3,739 3,344 3,112 2,958 2,848 2,764 2,699 2,646 2,602 2,534 2,463 2,388 2,349 2,308 2,266 2,223 2,178 2,131
15 4,543 3,682 3,287 3,056 2,901 2,791 2,707 2,641 2,588 2,544 2,475 2,403 2,328 2,288 2,247 2,204 2,160 2,114 2,066
16 4,494 3,634 3,239 3,007 2,852 2,741 2,657 2,591 2,538 2,494 2,425 2,352 2,276 2,235 2,194 2,151 2,106 2,059 2,010
17 4,451 3,592 3,197 2,965 2,810 2,699 2,614 2,548 2,494 2,450 2,381 2,308 2,230 2,190 2,148 2,104 2,058 2,011 1,960
18 4,414 3,555 3,160 2,928 2,773 2,661 2,577 2,510 2,456 2,412 2,342 2,269 2,191 2,150 2,107 2,063 2,017 1,968 1,917
19 4,381 3,522 3,127 2,895 2,740 2,628 2,544 2,477 2,423 2,378 2,308 2,234 2,156 2,114 2,071 2,026 1,980 1,930 1,878
20 4,351 3,493 3,098 2,866 2,711 2,599 2,514 2,447 2,393 2,348 2,278 2,203 2,124 2,083 2,039 1,994 1,946 1,896 1,843
21 4,325 3,467 3,073 2,840 2,685 2,573 2,488 2,421 2,366 2,321 2,250 2,176 2,096 2,054 2,010 1,965 1,917 1,866 1,812
22 4,301 3,443 3,049 2,817 2,661 2,549 2,464 2,397 2,342 2,297 2,226 2,151 2,071 2,028 1,984 1,938 1,889 1,838 1,783
23 4,279 3,422 3,028 2,796 2,640 2,528 2,442 2,375 2,320 2,275 2,204 2,128 2,048 2,005 1,961 1,914 1,865 1,813 1,757
24 4,260 3,403 3,009 2,776 2,621 2,508 2,423 2,355 2,300 2,255 2,183 2,108 2,027 1,984 1,939 1,892 1,842 1,790 1,733
25 4,242 3,385 2,991 2,759 2,603 2,490 2,405 2,337 2,282 2,237 2,165 2,089 2,008 1,964 1,919 1,872 1,822 1,768 1,711
26 4,225 3,369 2,975 2,743 2,587 2,474 2,388 2,321 2,266 2,220 2,148 2,072 1,990 1,946 1,901 1,853 1,803 1,749 1,691
27 4,210 3,354 2,960 2,728 2,572 2,459 2,373 2,305 2,250 2,204 2,132 2,056 1,974 1,930 1,884 1,836 1,785 1,731 1,672
28 4,196 3,340 2,947 2,714 2,558 2,445 2,359 2,291 2,236 2,190 2,118 2,041 1,959 1,915 1,869 1,820 1,769 1,714 1,654
29 4,183 3,328 2,934 2,701 2,545 2,432 2,346 2,278 2,223 2,177 2,105 2,028 1,945 1,901 1,854 1,806 1,754 1,698 1,638
30 4,171 3,316 2,922 2,690 2,534 2,421 2,334 2,266 2,211 2,165 2,092 2,015 1,932 1,887 1,841 1,792 1,740 1,684 1,622
40 4,085 3,232 2,839 2,606 2,450 2,336 2,249 2,180 2,124 2,077 2,004 1,925 1,839 1,793 1,744 1,693 1,637 1,577 1,509
60 4,001 3,150 2,758 2,525 2,368 2,254 2,167 2,097 2,040 1,993 1,917 1,836 1,748 1,700 1,649 1,594 1,534 1,467 1,389
120 3,920 3,072 2,680 2,447 2,290 2,175 2,087 2,016 1,959 1,911 1,834 1,751 1,659 1,608 1,554 1,495 1,429 1,352 1,254
3,842 2,996 2,605 2,372 2,214 2,099 2,010 1,938 1,880 1,831 1,752 1,666 1,571 1,517 1,459 1,394 1,318 1,221 1,000


Tabela para A = 0,025 ou 2,5%
ν21 1 2 3 4 5 6 7 8 9 10 12 15 20 24 30 40 60 120
1 647,8 799,5 864,2 899,6 921,8 937,1 948,2 956,7 963,3 968,6 976,7 984,9 993,1 997,2 1001 1006 1010 1014 1018
2 38,51 39,00 39,17 39,25 39,30 39,33 39,36 39,37 39,39 39,40 39,41 39,43 39,45 39,46 39,47 39,47 39,48 39,49 39,50
3 17,44 16,04 15,44 15,10 14,88 14,73 14,62 14,54 14,47 14,42 14,34 14,25 14,17 14,12 14,08 14,04 13,99 13,95 13,90
4 12,22 10,65 9,979 9,605 9,365 9,197 9,074 8,980 8,905 8,844 8,751 8,657 8,560 8,511 8,461 8,411 8,360 8,309 8,257
5 10,01 8,434 7,764 7,388 7,146 6,978 6,853 6,757 6,681 6,619 6,525 6,428 6,329 6,278 6,227 6,175 6,123 6,069 6,015
6 8,813 7,260 6,599 6,227 5,988 5,820 5,696 5,600 5,523 5,461 5,366 5,269 5,168 5,117 5,065 5,012 4,959 4,904 4,849
7 8,073 6,542 5,890 5,523 5,285 5,119 4,995 4,899 4,823 4,761 4,666 4,568 4,467 4,415 4,362 4,309 4,254 4,199 4,142
8 7,571 6,060 5,416 5,053 4,817 4,652 4,529 4,433 4,357 4,295 4,200 4,101 4,000 3,947 3,894 3,840 3,784 3,728 3,670
9 7,209 5,715 5,078 4,718 4,484 4,320 4,197 4,102 4,026 3,964 3,868 3,769 3,667 3,614 3,560 3,505 3,449 3,392 3,333
10 6,937 5,456 4,826 4,468 4,236 4,072 3,950 3,855 3,779 3,717 3,621 3,522 3,419 3,365 3,311 3,255 3,198 3,140 3,080
11 6,724 5,256 4,630 4,275 4,044 3,881 3,759 3,664 3,588 3,526 3,430 3,330 3,226 3,173 3,118 3,061 3,004 2,944 2,883
12 6,554 5,096 4,474 4,121 3,891 3,728 3,607 3,512 3,436 3,374 3,277 3,177 3,073 3,019 2,963 2,906 2,848 2,787 2,725
13 6,414 4,965 4,347 3,996 3,767 3,604 3,483 3,388 3,312 3,250 3,153 3,053 2,948 2,893 2,837 2,780 2,720 2,659 2,595
14 6,298 4,857 4,242 3,892 3,663 3,501 3,380 3,285 3,209 3,147 3,050 2,949 2,844 2,789 2,732 2,674 2,614 2,552 2,487
15 6,200 4,765 4,153 3,804 3,576 3,415 3,293 3,199 3,123 3,060 2,963 2,862 2,756 2,701 2,644 2,585 2,524 2,461 2,395
16 6,115 4,687 4,077 3,729 3,502 3,341 3,219 3,125 3,049 2,986 2,889 2,788 2,681 2,625 2,568 2,509 2,447 2,383 2,316
17 6,042 4,619 4,011 3,665 3,438 3,277 3,156 3,061 2,985 2,922 2,825 2,723 2,616 2,560 2,502 2,442 2,380 2,315 2,247
18 5,978 4,560 3,954 3,608 3,382 3,221 3,100 3,005 2,929 2,866 2,769 2,667 2,559 2,503 2,445 2,384 2,321 2,256 2,187
19 5,922 4,508 3,903 3,559 3,333 3,172 3,051 2,956 2,880 2,817 2,720 2,617 2,509 2,452 2,394 2,333 2,270 2,203 2,133
20 5,872 4,461 3,859 3,515 3,289 3,128 3,007 2,913 2,837 2,774 2,676 2,573 2,465 2,408 2,349 2,287 2,223 2,156 2,085
21 5,827 4,420 3,819 3,475 3,250 3,090 2,969 2,874 2,798 2,735 2,637 2,534 2,425 2,368 2,308 2,246 2,182 2,114 2,042
22 5,786 4,383 3,783 3,440 3,215 3,055 2,934 2,839 2,763 2,700 2,602 2,498 2,389 2,332 2,272 2,210 2,145 2,076 2,003
23 5,750 4,349 3,751 3,408 3,184 3,023 2,902 2,808 2,731 2,668 2,570 2,467 2,357 2,299 2,239 2,176 2,111 2,041 1,968
24 5,717 4,319 3,721 3,379 3,155 2,995 2,874 2,779 2,703 2,640 2,541 2,437 2,327 2,269 2,209 2,146 2,080 2,010 1,935
25 5,686 4,291 3,694 3,353 3,129 2,969 2,848 2,753 2,677 2,614 2,515 2,411 2,301 2,242 2,182 2,118 2,052 1,981 1,906
26 5,659 4,266 3,670 3,329 3,105 2,945 2,824 2,729 2,653 2,590 2,491 2,387 2,276 2,217 2,157 2,093 2,026 1,954 1,878
27 5,633 4,242 3,647 3,307 3,083 2,923 2,802 2,707 2,631 2,568 2,469 2,364 2,253 2,195 2,133 2,069 2,002 1,930 1,853
28 5,610 4,221 3,626 3,286 3,063 2,903 2,782 2,687 2,611 2,547 2,448 2,344 2,232 2,174 2,112 2,048 1,980 1,907 1,829
29 5,588 4,201 3,607 3,267 3,044 2,884 2,763 2,669 2,592 2,529 2,430 2,325 2,213 2,154 2,092 2,028 1,959 1,886 1,807
30 5,568 4,182 3,589 3,250 3,027 2,867 2,746 2,651 2,575 2,511 2,412 2,307 2,195 2,136 2,074 2,009 1,940 1,866 1,787
40 5,424 4,051 3,463 3,126 2,904 2,744 2,624 2,529 2,452 2,388 2,288 2,182 2,068 2,007 1,943 1,875 1,803 1,724 1,637
60 5,286 3,925 3,343 3,008 2,786 2,627 2,507 2,412 2,334 2,270 2,169 2,061 1,945 1,882 1,815 1,744 1,667 1,581 1,482
120 5,152 3,805 3,227 2,894 2,674 2,515 2,395 2,299 2,222 2,157 2,055 1,945 1,825 1,760 1,690 1,614 1,530 1,433 1,310
5,024 3,689 3,116 2,786 2,567 2,408 2,288 2,192 2,114 2,048 1,945 1,833 1,709 1,640 1,566 1,484 1,388 1,268 1,000


Tabela para A = 0,01 ou 1%
ν21 1 2 3 4 5 6 7 8 9 10 12 15 20 24 30 40 60 120
1 4052 5000 5403 5625 5764 5859 5928 5981 6022 6056 6106 6157 6209 6235 6261 6287 6313 6339 6366
2 98,50 99,00 99,17 99,25 99,30 99,33 99,36 99,37 99,39 99,40 99,42 99,43 99,45 99,46 99,47 99,47 99,48 99,49 99,50
3 34,12 30,82 29,46 28,71 28,24 27,91 27,67 27,49 27,35 27,23 27,05 26,87 26,69 26,60 26,51 26,41 26,32 26,22 26,13
4 21,20 18,00 16,69 15,98 15,52 15,21 14,98 14,80 14,66 14,55 14,37 14,20 14,02 13,93 13,84 13,75 13,65 13,56 13,46
5 16,26 13,27 12,06 11,39 10,97 10,67 10,46 10,29 10,16 10,05 9,888 9,722 9,553 9,466 9,379 9,291 9,202 9,112 9,020
6 13,75 10,93 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 12,25 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 11,26 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 10,56 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 10,04 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
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
Referências
APOSTOL, Tom M. Calculus. USA: Blaisdell, 1969.
GRINSTEAD, Charles M. SNELL, J. Laurie. Introduction to Probability.
NIST/SEMATECH e-Handbook of Statistical Methods. http://www.itl.nist.gov/div898/handbook/.

Topo | Rev: Mar/2018