Tablas y Fórmulas Estadísticas 12 TABLA 7. DISTRIBUCION F Grados de libertad del denominador 0.05 Grados de libertad del numerador 4 5 6 7 224.58 230.16 233.99 236.77 19.247 19.296 19.330 19.353 9.1172 9.0135 8.9406 8.8867 6.3882 6.2561 6.1631 6.0942 5.1922 5.0503 4.9503 4.8759 1 2 3 4 5 1 161.45 18.513 10.128 7.7086 6.6079 2 199.50 19.000 9.5521 6.9443 5.7861 3 215.71 19.164 9.2766 6.5914 5.4095 6 7 8 9 10 5.9874 5.5914 5.3177 5.1174 4.9646 5.1433 4.7374 4.4590 4.2565 4.1028 4.7571 4.3468 4.0662 3.8625 3.7083 4.5337 4.1203 3.8379 3.6331 3.4780 4.3874 3.9715 3.6875 3.4817 3.3258 4.2839 3.8660 3.5806 3.3738 3.2172 11 12 13 14 15 4.8443 4.7472 4.6672 4.6001 4.5431 3.9823 3.8853 3.8056 3.7389 3.6823 3.5874 3.4903 3.4105 3.3439 3.2874 3.3567 3.2592 3.1791 3.1122 3.0556 3.2039 3.1059 3.0254 2.9582 2.9013 16 17 18 19 20 4.4940 4.4513 4.4139 4.3807 4.3512 3.6337 3.5915 3.5546 3.5219 3.4928 3.2389 3.1968 3.1599 3.1274 3.0984 3.0069 2.9647 2.9277 2.8951 2.8661 21 22 23 24 25 4.3248 4.3009 4.2793 4.2597 4.2417 3.4668 3.4434 3.4221 3.4028 3.3852 3.0725 3.0491 3.0280 3.0088 2.9912 26 27 28 29 30 4.2252 4.2100 4.1960 4.1830 4.1709 3.3690 3.3541 3.3404 3.3277 3.3158 40 50 60 4.0847 4.0343 4.0012 3.9201 3.2317 3.1826 3.1504 3.0718 120 ∞ 8 238.88 19.371 8.8452 6.0410 4.8183 9 240.54 19.385 8.8123 5.9988 4.7725 10 241.88 19.396 8.7855 5.9644 4.7351 12 243.91 19.413 8.7446 5.9117 4.6777 4.2067 3.7870 3.5005 3.2927 3.1355 4.1468 3.7257 3.4381 3.2296 3.0717 4.0990 3.6767 3.3881 3.1789 3.0204 4.0600 3.6365 3.3472 3.1373 2.9782 3.9999 3.5747 3.2839 3.0729 2.9130 3.0946 2.9961 2.9153 2.8477 2.7905 3.0123 2.9134 2.8321 2.7642 2.7066 2.9480 2.8486 2.7669 2.6987 2.6408 2.8962 2.7964 2.7144 2.6458 2.5876 2.8536 2.7534 2.6710 2.6022 2.5437 2.7876 2.6866 2.6037 2.5342 2.4753 2.8524 2.8100 2.7729 2.7401 2.7109 2.7413 2.6987 2.6613 2.6283 2.5990 2.6572 2.6143 2.5767 2.5435 2.5140 2.5911 2.5480 2.5102 2.4768 2.4471 2.5377 2.4943 2.4563 2.4227 2.3928 2.4935 2.4499 2.4117 2.3779 2.3479 2.4247 2.3807 2.3421 2.3080 2.2776 2.8401 2.8167 2.7955 2.7763 2.7587 2.6848 2.6613 2.6400 2.6207 2.6030 2.5727 2.5491 2.5277 2.5082 2.4904 2.4876 2.4638 2.4422 2.4226 2.4047 2.4205 2.3965 2.3748 2.3551 2.3371 2.3660 2.3419 2.3201 2.3002 2.2821 2.3210 2.2967 2.2747 2.2547 2.2365 2.2504 2.2258 2.2036 2.1834 2.1649 2.9752 2.9604 2.9467 2.9340 2.9223 2.7426 2.7278 2.7141 2.7014 2.6896 2.5868 2.5719 2.5581 2.5454 2.5336 2.4741 2.4591 2.4453 2.4324 2.4205 2.3883 2.3732 2.3593 2.3463 2.3343 2.3205 2.3053 2.2913 2.2783 2.2662 2.2655 2.2501 2.2360 2.2229 2.2107 2.2197 2.2043 2.1900 2.1768 2.1646 2.1479 2.1323 2.1179 2.1045 2.0921 2.8387 2.7900 2.7581 2.6802 2.6060 2.5572 2.5252 2.4472 2.4495 2.4004 2.3683 2.2899 2.3359 2.2864 2.2541 2.1750 2.2490 2.1992 2.1665 2.0868 2.1802 2.1299 2.0970 2.0164 2.1240 2.0734 2.0401 1.9588 2.0772 2.0261 1.9926 1.9105 2.0035 1.9515 1.9174 1.8337 3.8841 3.0369 2.6456 2.4127 2.2551 2.1400 2.0514 1.9807 1.9226 1.8739 1.7964 Tablas y Fórmulas Estadísticas 13 Grados de libertad del denominador 0.01 1 2 3 4 5 1 4052.2 98.503 34.116 21.198 16.258 2 4999.5 99.000 30.817 18.000 13.274 3 5403.4 99.166 29.457 16.694 12.060 Grados de libertad del numerador 4 5 6 7 5624.6 5763.6 5859.0 5928.4 99.249 99.299 99.333 99.356 28.710 28.237 27.911 27.672 15.977 15.522 15.207 14.976 11.392 10.967 10.672 10.456 8 5981.1 99.374 27.489 14.799 10.289 9 6022.5 99.388 27.345 14.659 10.158 10 6055.8 99.399 27.229 14.546 10.051 12 6106.3 99.416 27.052 14.374 9.8883 6 7 8 9 10 13.745 12.246 11.259 10.561 10.044 10.925 9.5466 8.6491 8.0215 7.5594 9.7795 8.4513 7.5910 6.9919 6.5523 9.1483 7.8466 7.0061 6.4221 5.9943 8.7459 7.4604 6.6318 6.0569 5.6363 8.4661 7.1914 6.3707 5.8018 5.3858 8.2600 6.9928 6.1776 5.6129 5.2001 8.1017 6.8400 6.0289 5.4671 5.0567 7.9761 6.7188 5.9106 5.3511 4.9424 7.8741 6.6201 5.8143 5.2565 4.8491 7.7183 6.4691 5.6667 5.1114 4.7059 11 12 13 14 15 9.6460 9.3302 9.0738 8.8616 8.6831 7.2057 6.9266 6.7010 6.5149 6.3589 6.2167 5.9525 5.7394 5.5639 5.4170 5.6683 5.4120 5.2053 5.0354 4.8932 5.3160 5.0643 4.8616 4.6950 4.5556 5.0692 4.8206 4.6204 4.4558 4.3183 4.8861 4.6395 4.4410 4.2779 4.1415 4.7445 4.4994 4.3021 4.1399 4.0045 4.6315 4.3875 4.1911 4.0297 3.8948 4.5393 4.2961 4.1003 3.9394 3.8049 4.3974 4.1553 3.9603 3.8001 3.6662 16 17 18 19 20 8.5310 8.3997 8.2854 8.1849 8.0960 6.2262 6.1121 6.0129 5.9259 5.8489 5.2922 5.1850 5.0919 5.0103 4.9382 4.7726 4.6690 4.5790 4.5003 4.4307 4.4374 4.3359 4.2479 4.1708 4.1027 4.2016 4.1015 4.0146 3.9386 3.8714 4.0259 3.9267 3.8406 3.7653 3.6987 3.8896 3.7910 3.7054 3.6305 3.5644 3.7804 3.6822 3.5971 3.5225 3.4567 3.6909 3.5931 3.5082 3.4338 3.3682 3.5527 3.4552 3.3706 3.2965 3.2311 21 22 23 24 25 8.0166 7.9454 7.8811 7.8229 7.7698 5.7804 5.7190 5.6637 5.6136 5.5680 4.8740 4.8166 4.7649 4.7181 4.6755 4.3688 4.3134 4.2636 4.2184 4.1774 4.0421 3.9880 3.9392 3.8951 3.8550 3.8117 3.7583 3.7102 3.6667 3.6272 3.6396 3.5867 3.5390 3.4959 3.4568 3.5056 3.4530 3.4057 3.3629 3.3239 3.3981 3.3458 3.2986 3.2560 3.2172 3.3098 3.2576 3.2106 3.1681 3.1294 3.1730 3.1209 3.0740 3.0316 2.9931 26 27 28 29 30 7.7213 7.6767 7.6356 7.5977 7.5625 5.5263 5.4881 5.4529 5.4204 5.3903 4.6366 4.6009 4.5681 4.5378 4.5097 4.1400 4.1056 4.0740 4.0449 4.0179 3.8183 3.7848 3.7539 3.7254 3.6990 3.5911 3.5580 3.5276 3.4995 3.4735 3.4210 3.3882 3.3581 3.3303 3.3045 3.2884 3.2558 3.2259 3.1982 3.1726 3.1818 3.1494 3.1195 3.0920 3.0665 3.0941 3.0618 3.0320 3.0045 2.9791 2.9578 2.9256 2.8959 2.8685 2.8431 40 50 60 120 7.3141 7.1706 7.0771 6.8509 5.1785 5.0566 4.9774 4.7865 4.3126 4.1993 4.1259 3.9491 3.8283 3.7195 3.6490 3.4795 3.5138 3.4077 3.3389 3.1735 3.2910 3.1864 3.1187 2.9559 3.1238 3.0202 2.9530 2.7918 2.9930 2.8900 2.8233 2.6629 2.8876 2.7850 2.7185 2.5586 2.8005 2.6981 2.6318 2.4721 2.6648 2.5625 2.4961 2.3363 ∞ 6.7515 4.7029 3.8719 3.4055 3.1014 2.8848 2.7214 2.5929 2.4888 2.4023 2.2664