Upper Percentiles of the F-distribution 1 For each N, D, P, the entry is the 100Pth Percentile for the F-distribution with N and D degrees of Freedom D P N1 N2 N3 N4 N5 N6 N7 N8 N9 N10 1 0.900 39.863 49.5 53.593 55.833 57.24 58.204 58.906 59.439 59.858 60.195 1 0.950 161.45 199.5 215.71 224.58 230.16 233.99 236.77 238.88 240.54 241.88 1 0.975 647.79 799.5 864.16 899.58 921.85 937.11 948.22 956.66 963.28 968.63 1 0.980 1012.5 1249.5 1350.5 1405.8 1440.6 1464.5 1481.8 1495 1505.3 1513.7 1 0.990 4052.2 4999.5 5403.4 5624.6 5763.6 5859 5928.4 5981.1 6022.5 6055.8 1 0.995 16211 20000 21615 22500 23056 23437 23715 23925 24091 24224 1 0.999 405284 499999 540379 562500 576405 585937 592873 598144 602284 605621 2 0.900 8.5263 9 9.1618 9.2434 9.2926 9.3255 9.3491 9.3668 9.3805 9.3916 2 0.950 18.513 19 19.164 19.247 19.296 19.33 19.353 19.371 19.385 19.396 2 0.975 38.506 39 39.165 39.248 39.298 39.331 39.355 39.373 39.387 39.398 2 0.980 48.505 49 49.166 49.249 49.299 49.332 49.356 49.373 49.387 49.398 2 0.990 98.503 99 99.166 99.249 99.299 99.333 99.356 99.374 99.388 99.399 2 0.995 198.5 199 199.17 199.25 199.3 199.33 199.36 199.37 199.39 199.4 2 0.999 998.5 999 999.17 999.25 999.3 999.33 999.36 999.37 999.39 999.4 3 0.900 5.5383 5.4624 5.3908 5.3426 5.3092 5.2847 5.2662 5.2517 5.24 5.2304 3 0.950 10.128 9.5521 9.2766 9.1172 9.0135 8.9406 8.8867 8.8452 8.8123 8.7855 3 0.975 17.443 16.044 15.439 15.101 14.885 14.735 14.624 14.54 14.473 14.419 3 0.980 20.618 18.858 18.11 17.694 17.429 17.245 17.11 17.007 16.926 16.86 3 0.990 34.116 30.817 29.457 28.71 28.237 27.911 27.672 27.489 27.345 27.229 3 0.995 55.552 49.799 47.467 46.195 45.392 44.838 44.434 44.126 43.882 43.686 3 0.999 167.03 148.5 141.11 137.1 134.58 132.85 131.58 130.62 129.86 129.25 4 0.900 4.5448 4.3246 4.1909 4.1072 4.0506 4.0097 3.979 3.9549 3.9357 3.9199 4 0.950 7.7086 6.9443 6.5914 6.3882 6.2561 6.1631 6.0942 6.041 5.9988 5.9644 4 0.975 12.218 10.649 9.9792 9.6045 9.3645 9.1973 9.0741 8.9796 8.9047 8.8439 4 0.980 14.04 12.142 11.344 10.899 10.616 10.419 10.274 10.162 10.074 10.003 4 0.990 21.198 18 16.694 15.977 15.522 15.207 14.976 14.799 14.659 14.546 4 0.995 31.333 26.284 24.259 23.155 22.456 21.975 21.622 21.352 21.139 20.967 4 0.999 74.137 61.246 56.177 53.436 51.712 50.525 49.658 48.996 48.475 48.053 5 0.900 4.0604 3.7797 3.6195 3.5202 3.453 3.4045 3.3679 3.3393 3.3163 3.2974 5 0.950 6.6079 5.7861 5.4095 5.1922 5.0503 4.9503 4.8759 4.8183 4.7725 4.7351 5 0.975 10.007 8.4336 7.7636 7.3879 7.1464 6.9777 6.8531 6.7572 6.6811 6.6192 5 0.980 11.323 9.4544 8.6702 8.233 7.9529 7.7577 7.6137 7.503 7.4152 7.3438 5 0.990 16.258 13.274 12.06 11.392 10.967 10.672 10.456 10.289 10.158 10.051 5 0.995 22.785 18.314 16.53 15.556 14.94 14.513 14.2 13.961 13.772 13.618 5 0.999 47.181 37.122 33.202 31.085 29.752 28.834 28.163 27.649 27.244 26.917 6 0.900 3.7759 3.4633 3.2888 3.1808 3.1075 3.0546 3.0145 2.983 2.9577 2.9369 6 0.950 5.9874 5.1433 4.7571 4.5337 4.3874 4.2839 4.2067 4.1468 4.099 4.06 6 0.975 8.8131 7.2599 6.5988 6.2272 5.9876 5.8198 5.6955 5.5996 5.5234 5.4613 6 0.980 9.8764 8.0521 7.287 6.8594 6.5847 6.3928 6.2508 6.1415 6.0546 5.9839 6 0.990 13.745 10.925 9.7795 9.1483 8.7459 8.4661 8.26 8.1017 7.9761 7.8741 6 0.995 18.635 14.544 12.917 12.028 11.464 11.073 10.786 10.566 10.391 10.25 6 0.999 35.507 27 23.703 21.924 20.803 20.03 19.463 19.03 18.688 18.411 7 0.900 3.5894 3.2574 3.0741 2.9605 2.8833 2.8274 2.7849 2.7516 2.7247 2.7025 7 0.950 5.5914 4.7374 4.3468 4.1203 3.9715 3.866 3.787 3.7257 3.6767 3.6365 7 0.975 8.0727 6.5415 5.8898 5.5226 5.2852 5.1186 4.9949 4.8993 4.8232 4.7611 7 0.980 8.9877 7.2026 6.4539 6.0347 5.7647 5.5756 5.4355 5.3273 5.2413 5.1711 7 0.990 12.246 9.5466 8.4513 7.8466 7.4604 7.1914 6.9928 6.84 6.7188 6.6201 7 0.995 16.236 12.404 10.882 10.05 9.5221 9.1553 8.8854 8.6781 8.5138 8.3803 7 0.999 29.245 21.689 18.772 17.198 16.206 15.521 15.019 14.634 14.33 14.083 8 0.900 3.4579 3.1131 2.9238 2.8064 2.7264 2.6683 2.6241 2.5893 2.5612 2.538 8 0.950 5.3177 4.459 4.0662 3.8379 3.6875 3.5806 3.5005 3.4381 3.3881 3.3472 Upper Percentiles of the F-distribution 2 For each N, D, P, the entry is the 100Pth Percentile for the F-distribution with N and D degrees of Freedom D P N1 N2 N3 N4 N5 N6 N7 N8 N9 N10 8 0.975 7.5709 6.0595 5.416 5.0526 4.8173 4.6517 4.5286 4.4333 4.3572 4.2951 8 0.980 8.3895 6.6366 5.9014 5.4889 5.2227 5.0359 4.8972 4.79 4.7046 4.6348 8 0.990 11.259 8.6491 7.591 7.0061 6.6318 6.3707 6.1776 6.0289 5.9106 5.8143 8 0.995 14.688 11.042 9.5965 8.8051 8.3018 7.952 7.6941 7.4959 7.3386 7.2106 8 0.999 25.415 18.494 15.829 14.392 13.485 12.858 12.398 12.046 11.767 11.54 9 0.900 3.3603 3.0065 2.8129 2.6927 2.6106 2.5509 2.5053 2.4694 2.4403 2.4163 9 0.950 5.1174 4.2565 3.8625 3.6331 3.4817 3.3738 3.2927 3.2296 3.1789 3.1373 9 0.975 7.2093 5.7147 5.0781 4.7181 4.4844 4.3197 4.197 4.102 4.026 3.9639 9 0.980 7.9605 6.234 5.5097 5.1027 4.8395 4.6545 4.5169 4.4105 4.3255 4.2561 9 0.990 10.561 8.0215 6.9919 6.4221 6.0569 5.8018 5.6129 5.4671 5.3511 5.2565 9 0.995 13.614 10.107 8.7171 7.9559 7.4712 7.1339 6.8849 6.6933 6.5411 6.4172 9 0.999 22.857 16.387 13.902 12.56 11.714 11.128 10.698 10.368 10.107 9.8943 10 0.900 3.285 2.9245 2.7277 2.6053 2.5216 2.4606 2.414 2.3772 2.3473 2.3226 10 0.950 4.9646 4.1028 3.7083 3.478 3.3258 3.2172 3.1355 3.0717 3.0204 2.9782 10 0.975 6.9367 5.4564 4.8256 4.4683 4.2361 4.0721 3.9498 3.8549 3.779 3.7168 10 0.980 7.6384 5.9336 5.2182 4.8156 4.555 4.3714 4.2348 4.1288 4.0442 3.975 10 0.990 10.044 7.5594 6.5523 5.9943 5.6363 5.3858 5.2001 5.0567 4.9424 4.8491 10 0.995 12.826 9.427 8.0807 7.3428 6.8724 6.5446 6.3025 6.1159 5.9676 5.8467 10 0.999 21.04 14.905 12.553 11.283 10.481 9.9256 9.5175 9.2041 8.9558 8.7539 11 0.900 3.2252 2.8595 2.6602 2.5362 2.4512 2.3891 2.3416 2.304 2.2735 2.2482 11 0.950 4.8443 3.9823 3.5874 3.3567 3.2039 3.0946 3.0123 2.948 2.8962 2.8536 11 0.975 6.7241 5.2559 4.63 4.2751 4.044 3.8807 3.7586 3.6638 3.5879 3.5257 11 0.980 7.388 5.7012 4.9932 4.5943 4.3357 4.1533 4.0174 3.9119 3.8275 3.7584 11 0.990 9.646 7.2057 6.2167 5.6683 5.316 5.0692 4.8861 4.7445 4.6315 4.5393 11 0.995 12.226 8.9122 7.6004 6.8809 6.4217 6.1016 5.8648 5.6821 5.5368 5.4183 11 0.999 19.687 13.812 11.561 10.346 9.5784 9.0466 8.6553 8.3548 8.1163 7.9224 12 0.900 3.1765 2.8068 2.6055 2.4801 2.394 2.331 2.2828 2.2446 2.2135 2.1878 12 0.950 4.7472 3.8853 3.4903 3.2592 3.1059 2.9961 2.9134 2.8486 2.7964 2.7534 12 0.975 6.5538 5.0959 4.4742 4.1212 3.8911 3.7283 3.6065 3.5118 3.4358 3.3736 12 0.980 7.1878 5.5163 4.8145 4.4187 4.1617 3.9804 3.845 3.7398 3.6557 3.5867 12 0.990 9.3302 6.9266 5.9525 5.412 5.0643 4.8206 4.6395 4.4994 4.3875 4.2961 12 0.995 11.754 8.5096 7.2258 6.5211 6.0711 5.757 5.5245 5.3451 5.2021 5.0855 12 0.999 18.643 12.974 10.804 9.6327 8.8921 8.3788 8.0009 7.7104 7.4797 7.292 13 0.900 3.1362 2.7632 2.5603 2.4337 2.3467 2.283 2.2341 2.1953 2.1638 2.1376 13 0.950 4.6672 3.8056 3.4105 3.1791 3.0254 2.9153 2.8321 2.7669 2.7144 2.671 13 0.975 6.4143 4.9653 4.3472 3.9959 3.7667 3.6043 3.4827 3.388 3.312 3.2497 13 0.980 7.0241 5.3657 4.6692 4.276 4.0205 3.8399 3.705 3.6002 3.5161 3.4472 13 0.990 9.0738 6.701 5.7394 5.2053 4.8616 4.6204 4.441 4.3021 4.1911 4.1003 13 0.995 11.374 8.1865 6.9258 6.2335 5.791 5.4819 5.2529 5.0761 4.9351 4.8199 13 0.999 17.815 12.313 10.209 9.0727 8.3541 7.8557 7.4886 7.2061 6.9818 6.7992 14 0.900 3.1022 2.7265 2.5222 2.3947 2.3069 2.2426 2.1931 2.1539 2.122 2.0954 14 0.950 4.6001 3.7389 3.3439 3.1122 2.9582 2.8477 2.7642 2.6987 2.6458 2.6022 14 0.975 6.2979 4.8567 4.2417 3.8919 3.6634 3.5014 3.3799 3.2853 3.2093 3.1469 14 0.980 6.888 5.2408 4.5488 4.1579 3.9036 3.7237 3.5892 3.4845 3.4006 3.3317 14 0.990 8.8616 6.5149 5.5639 5.0354 4.695 4.4558 4.2779 4.1399 4.0297 3.9394 14 0.995 11.06 7.9216 6.6804 5.9984 5.5623 5.2574 5.0313 4.8566 4.7173 4.6034 14 0.999 17.143 11.779 9.7294 8.6223 7.9218 7.4358 7.0775 6.8017 6.5826 6.4041 15 0.900 3.0732 2.6952 2.4898 2.3614 2.273 2.2081 2.1582 2.1185 2.0862 2.0593 15 0.950 4.5431 3.6823 3.2874 3.0556 2.9013 2.7905 2.7066 2.6408 2.5876 2.5437 15 0.975 6.1995 4.765 4.1528 3.8043 3.5764 3.4147 3.2934 3.1987 3.1227 3.0602 15 0.980 6.7729 5.1354 4.4474 4.0584 3.8052 3.6259 3.4918 3.3873 3.3035 3.2346 Upper Percentiles of the F-distribution 3 For each N, D, P, the entry is the 100Pth Percentile for the F-distribution with N and D degrees of Freedom D P N1 N2 N3 N4 N5 N6 N7 N8 N9 N10 15 0.990 8.6831 6.3589 5.417 4.8932 4.5556 4.3183 4.1415 4.0045 3.8948 3.8049 15 0.995 10.798 7.7008 6.476 5.8029 5.3721 5.0708 4.8473 4.6744 4.5364 4.4235 15 0.999 16.587 11.339 9.3353 8.2527 7.5674 7.0917 6.7408 6.4707 6.2559 6.0808 16 0.900 3.0481 2.6682 2.4618 2.3327 2.2438 2.1783 2.128 2.088 2.0553 2.0281 16 0.950 4.494 3.6337 3.2389 3.0069 2.8524 2.7413 2.6572 2.5911 2.5377 2.4935 16 0.975 6.1151 4.6867 4.0768 3.7294 3.5021 3.3406 3.2194 3.1248 3.0488 2.9862 16 0.980 6.6744 5.0455 4.3609 3.9737 3.7214 3.5426 3.4087 3.3044 3.2206 3.1518 16 0.990 8.531 6.2262 5.2922 4.7726 4.4374 4.2016 4.0259 3.8896 3.7804 3.6909 16 0.995 10.575 7.5138 6.3034 5.6378 5.2117 4.9134 4.692 4.5207 4.3838 4.2719 16 0.999 16.12 10.971 9.0059 7.9442 7.2719 6.8049 6.4604 6.195 5.9839 5.8117 17 0.900 3.0262 2.6446 2.4374 2.3077 2.2183 2.1524 2.1017 2.0613 2.0284 2.0009 17 0.950 4.4513 3.5915 3.1968 2.9647 2.81 2.6987 2.6143 2.548 2.4943 2.4499 17 0.975 6.042 4.6189 4.0112 3.6648 3.4379 3.2767 3.1556 3.061 2.9849 2.9222 17 0.980 6.5892 4.9678 4.2863 3.9006 3.6491 3.4707 3.3371 3.2329 3.1492 3.0803 17 0.990 8.3997 6.1121 5.185 4.669 4.3359 4.1015 3.9267 3.791 3.6822 3.5931 17 0.995 10.384 7.3536 6.1556 5.4967 5.0746 4.7789 4.5594 4.3894 4.2535 4.1424 17 0.999 15.722 10.658 8.7269 7.6831 7.0219 6.5625 6.2234 5.962 5.7541 5.5844 18 0.900 3.007 2.6239 2.416 2.2858 2.1958 2.1296 2.0785 2.0379 2.0047 1.977 18 0.950 4.4139 3.5546 3.1599 2.9277 2.7729 2.6613 2.5767 2.5102 2.4563 2.4117 18 0.975 5.9781 4.5597 3.9539 3.6083 3.382 3.2209 3.0999 3.0053 2.9291 2.8664 18 0.980 6.5146 4.9001 4.2213 3.8369 3.5861 3.4081 3.2747 3.1706 3.0869 3.018 18 0.990 8.2854 6.0129 5.0919 4.579 4.2479 4.0146 3.8406 3.7054 3.5971 3.5082 18 0.995 10.218 7.2148 6.0278 5.3746 4.956 4.6627 4.4448 4.2759 4.141 4.0305 18 0.999 15.379 10.39 8.4875 7.4593 6.8078 6.355 6.0206 5.7628 5.5575 5.39 19 0.900 2.9899 2.6056 2.397 2.2663 2.176 2.1094 2.058 2.0171 1.9836 1.9557 19 0.950 4.3807 3.5219 3.1274 2.8951 2.7401 2.6283 2.5435 2.4768 2.4227 2.3779 19 0.975 5.9216 4.5075 3.9034 3.5587 3.3327 3.1718 3.0509 2.9563 2.8801 2.8172 19 0.980 6.449 4.8404 4.1641 3.7809 3.5307 3.3531 3.2199 3.1159 3.0322 2.9633 19 0.990 8.1849 5.9259 5.0103 4.5003 4.1708 3.9386 3.7653 3.6305 3.5225 3.4338 19 0.995 10.073 7.0935 5.9161 5.2681 4.8526 4.5614 4.3448 4.177 4.0428 3.9329 19 0.999 15.081 10.157 8.2799 7.2655 6.6225 6.1754 5.8452 5.5904 5.3876 5.2219 20 0.900 2.9747 2.5893 2.3801 2.2489 2.1582 2.0913 2.0397 1.9985 1.9649 1.9367 20 0.950 4.3512 3.4928 3.0984 2.8661 2.7109 2.599 2.514 2.4471 2.3928 2.3479 20 0.975 5.8715 4.4613 3.8587 3.5147 3.2891 3.1283 3.0074 2.9128 2.8365 2.7737 20 0.980 6.3907 4.7876 4.1134 3.7313 3.4817 3.3044 3.1713 3.0674 2.9837 2.9148 20 0.990 8.096 5.8489 4.9382 4.4307 4.1027 3.8714 3.6987 3.5644 3.4567 3.3682 20 0.995 9.9439 6.9865 5.8177 5.1743 4.7616 4.4721 4.2569 4.09 3.9564 3.847 20 0.999 14.819 9.9526 8.0984 7.096 6.4606 6.0186 5.692 5.44 5.2392 5.0752 21 0.900 2.961 2.5746 2.3649 2.2333 2.1423 2.0751 2.0233 1.9819 1.948 1.9197 21 0.950 4.3248 3.4668 3.0725 2.8401 2.6848 2.5727 2.4876 2.4205 2.366 2.321 21 0.975 5.8266 4.4199 3.8188 3.4754 3.2501 3.0895 2.9686 2.874 2.7977 2.7348 21 0.980 6.3386 4.7404 4.0682 3.687 3.4379 3.261 3.128 3.0241 2.9405 2.8716 21 0.990 8.0166 5.7804 4.874 4.3688 4.0421 3.8117 3.6396 3.5056 3.3981 3.3098 21 0.995 9.8295 6.8914 5.7304 5.0911 4.6809 4.3931 4.1789 4.0128 3.8799 3.7709 21 0.999 14.587 9.7723 7.9383 6.9467 6.3179 5.8805 5.5571 5.3076 5.1087 4.9462 22 0.900 2.9486 2.5613 2.3512 2.2193 2.1279 2.0605 2.0084 1.9668 1.9327 1.9043 22 0.950 4.3009 3.4434 3.0491 2.8167 2.6613 2.5491 2.4638 2.3965 2.3419 2.2967 22 0.975 5.7863 4.3828 3.7829 3.4401 3.2151 3.0546 2.9338 2.8392 2.7628 2.6998 22 0.980 6.2917 4.698 4.0276 3.6473 3.3987 3.222 3.0892 2.9853 2.9017 2.8328 22 0.990 7.9454 5.719 4.8166 4.3134 3.988 3.7583 3.5867 3.453 3.3458 3.2576 22 0.995 9.7271 6.8064 5.6524 5.0168 4.6088 4.3225 4.1094 3.944 3.8116 3.703 Upper Percentiles of the F-distribution 4 For each N, D, P, the entry is the 100Pth Percentile for the F-distribution with N and D degrees of Freedom D P N1 N2 N3 N4 N5 N6 N7 N8 N9 N10 22 0.999 14.38 9.612 7.796 6.8142 6.1914 5.758 5.4376 5.1901 4.9929 4.8317 23 0.900 2.9374 2.5493 2.3387 2.2065 2.1149 2.0472 1.9949 1.9531 1.9189 1.8903 23 0.950 4.2793 3.4221 3.028 2.7955 2.64 2.5277 2.4422 2.3748 2.3201 2.2747 23 0.975 5.7498 4.3492 3.7505 3.4083 3.1835 3.0232 2.9023 2.8077 2.7313 2.6682 23 0.980 6.2493 4.6597 3.991 3.6115 3.3633 3.1868 3.0541 2.9503 2.8667 2.7977 23 0.990 7.8811 5.6637 4.7649 4.2636 3.9392 3.7102 3.539 3.4057 3.2986 3.2106 23 0.995 9.6348 6.73 5.5823 4.95 4.5441 4.2591 4.0469 3.8822 3.7502 3.642 23 0.999 14.195 9.4685 7.6688 6.6957 6.0783 5.6486 5.3308 5.0853 4.8896 4.7296 24 0.900 2.9271 2.5383 2.3274 2.1949 2.103 2.0351 1.9826 1.9407 1.9063 1.8775 24 0.950 4.2597 3.4028 3.0088 2.7763 2.6207 2.5082 2.4226 2.3551 2.3002 2.2547 24 0.975 5.7166 4.3187 3.7211 3.3794 3.1548 2.9946 2.8738 2.7791 2.7027 2.6396 24 0.980 6.2109 4.625 3.9578 3.579 3.3312 3.1549 3.0223 2.9186 2.835 2.766 24 0.990 7.8229 5.6136 4.7181 4.2184 3.8951 3.6667 3.4959 3.3629 3.256 3.1681 24 0.995 9.5513 6.6609 5.519 4.8898 4.4857 4.2019 3.9905 3.8264 3.6949 3.587 24 0.999 14.028 9.3394 7.5545 6.5892 5.9768 5.5504 5.2349 4.9912 4.7968 4.6379 25 0.900 2.9177 2.5283 2.317 2.1842 2.0922 2.0241 1.9714 1.9292 1.8947 1.8658 25 0.950 4.2417 3.3852 2.9912 2.7587 2.603 2.4904 2.4047 2.3371 2.2821 2.2365 25 0.975 5.6864 4.2909 3.6943 3.353 3.1287 2.9685 2.8478 2.7531 2.6766 2.6135 25 0.980 6.1758 4.5934 3.9275 3.5494 3.302 3.1259 2.9934 2.8897 2.806 2.737 25 0.990 7.7698 5.568 4.6755 4.1774 3.855 3.6272 3.4568 3.3239 3.2172 3.1294 25 0.995 9.4753 6.5982 5.4615 4.8351 4.4327 4.15 3.9394 3.7758 3.6447 3.537 25 0.999 13.877 9.2225 7.4511 6.4931 5.8851 5.4617 5.1484 4.9063 4.7131 4.5551 30 0.900 2.8807 2.4887 2.2761 2.1422 2.0492 1.9803 1.9269 1.8841 1.849 1.8195 30 0.950 4.1709 3.3158 2.9223 2.6896 2.5336 2.4205 2.3343 2.2662 2.2107 2.1646 30 0.975 5.5675 4.1821 3.5894 3.2499 3.0265 2.8667 2.746 2.6513 2.5746 2.5112 30 0.980 6.0381 4.4696 3.8092 3.4338 3.1878 3.0124 2.8803 2.7767 2.693 2.6239 30 0.990 7.5625 5.3903 4.5097 4.0179 3.699 3.4735 3.3045 3.1726 3.0665 2.9791 30 0.995 9.1797 6.3547 5.2388 4.6234 4.2276 3.9492 3.7416 3.5801 3.4505 3.344 30 0.999 13.293 8.7734 7.0545 6.1245 5.5339 5.1223 4.8173 4.5814 4.393 4.2388 35 0.900 2.8547 2.4609 2.2474 2.1128 2.0191 1.9496 1.8957 1.8524 1.8168 1.7869 35 0.950 4.1213 3.2674 2.8742 2.6415 2.4851 2.3718 2.2852 2.2167 2.1608 2.1143 35 0.975 5.4848 4.1065 3.5166 3.1785 2.9557 2.7961 2.6755 2.5807 2.5039 2.4403 35 0.980 5.9425 4.3838 3.7274 3.3539 3.1089 2.934 2.8021 2.6986 2.6149 2.5456 35 0.990 7.4191 5.2679 4.3957 3.9082 3.5919 3.3679 3.2 3.0687 2.963 2.8758 35 0.995 8.9763 6.1878 5.0865 4.4788 4.0876 3.8123 3.6066 3.4466 3.318 3.2123 35 0.999 12.896 8.4697 6.787 5.8764 5.2978 4.8942 4.595 4.3634 4.1782 4.0265 40 0.900 2.8354 2.4404 2.2261 2.0909 1.9968 1.9269 1.8725 1.8289 1.7929 1.7627 40 0.950 4.0847 3.2317 2.8387 2.606 2.4495 2.3359 2.249 2.1802 2.124 2.0772 40 0.975 5.4239 4.051 3.4633 3.1261 2.9037 2.7444 2.6238 2.5289 2.4519 2.3882 40 0.980 5.8722 4.3208 3.6674 3.2954 3.0511 2.8766 2.7448 2.6413 2.5576 2.4882 40 0.990 7.3141 5.1785 4.3126 3.8283 3.5138 3.291 3.1238 2.993 2.8876 2.8005 40 0.995 8.8279 6.0664 4.9758 4.3738 3.986 3.7129 3.5088 3.3498 3.222 3.1167 40 0.999 12.609 8.2508 6.5945 5.6981 5.1283 4.7306 4.4355 4.207 4.0243 3.8744 45 0.900 2.8205 2.4245 2.2097 2.0742 1.9796 1.9094 1.8547 1.8107 1.7745 1.744 45 0.950 4.0566 3.2043 2.8115 2.5787 2.4221 2.3083 2.2212 2.1521 2.0958 2.0487 45 0.975 5.3773 4.0085 3.4224 3.086 2.864 2.7048 2.5842 2.4892 2.4122 2.3483 45 0.980 5.8183 4.2727 3.6216 3.2506 3.0069 2.8327 2.7011 2.5976 2.5138 2.4444 45 0.990 7.2339 5.1103 4.2492 3.7674 3.4544 3.2325 3.0658 2.9353 2.8301 2.7432 45 0.995 8.7148 5.9741 4.8918 4.2941 3.909 3.6376 3.4346 3.2764 3.1492 3.0443 45 0.999 12.392 8.0855 6.4495 5.5639 5.0007 4.6075 4.3157 4.0895 3.9086 3.7601 50 0.900 2.8087 2.412 2.1967 2.0608 1.966 1.8954 1.8405 1.7963 1.7598 1.7291 Upper Percentiles of the F-distribution 5 For each N, D, P, the entry is the 100Pth Percentile for the F-distribution with N and D degrees of Freedom D P N1 N2 N3 N4 N5 N6 N7 N8 N9 N10 50 0.950 4.0343 3.1826 2.79 2.5572 2.4004 2.2864 2.1992 2.1299 2.0734 2.0261 50 0.975 5.3403 3.9749 3.3902 3.0544 2.8327 2.6736 2.553 2.4579 2.3808 2.3168 50 0.980 5.7757 4.2347 3.5854 3.2154 2.9721 2.7981 2.6666 2.5631 2.4793 2.4098 50 0.990 7.1706 5.0566 4.1993 3.7195 3.4077 3.1864 3.0202 2.89 2.785 2.6981 50 0.995 8.6258 5.9016 4.8259 4.2316 3.8486 3.5785 3.3765 3.2189 3.092 2.9875 50 0.999 12.222 7.9564 6.3364 5.4593 4.9013 4.5117 4.2224 3.998 3.8185 3.6711 60 0.900 2.7911 2.3933 2.1774 2.041 1.9457 1.8747 1.8194 1.7748 1.738 1.707 60 0.950 4.0012 3.1504 2.7581 2.5252 2.3683 2.2541 2.1665 2.097 2.0401 1.9926 60 0.975 5.2856 3.9253 3.3425 3.0077 2.7863 2.6274 2.5068 2.4117 2.3344 2.2702 60 0.980 5.7127 4.1785 3.532 3.1633 2.9207 2.747 2.6156 2.5122 2.4283 2.3586 60 0.990 7.0771 4.9774 4.1259 3.649 3.3389 3.1187 2.953 2.8233 2.7185 2.6318 60 0.995 8.4946 5.795 4.729 4.1399 3.7599 3.4918 3.2911 3.1344 3.0083 2.9042 60 0.999 11.973 7.7678 6.1712 5.3067 4.7565 4.3721 4.0864 3.8648 3.6873 3.5415 70 0.900 2.7786 2.38 2.1637 2.0269 1.9313 1.86 1.8044 1.7596 1.7225 1.6913 70 0.950 3.9778 3.1277 2.7355 2.5027 2.3456 2.2312 2.1435 2.0737 2.0166 1.9689 70 0.975 5.247 3.8903 3.309 2.9748 2.7537 2.5949 2.4743 2.3791 2.3017 2.2374 70 0.980 5.6682 4.139 3.4944 3.1267 2.8845 2.7111 2.5798 2.4763 2.3924 2.3226 70 0.990 7.0114 4.9219 4.0744 3.5996 3.2907 3.0712 2.906 2.7765 2.6719 2.5852 70 0.995 8.4027 5.7204 4.6613 4.0758 3.698 3.4313 3.2315 3.0755 2.9498 2.846 70 0.999 11.799 7.6366 6.0566 5.2008 4.6561 4.2753 3.9922 3.7725 3.5964 3.4517 80 0.900 2.7693 2.3701 2.1535 2.0165 1.9206 1.8491 1.7933 1.7483 1.711 1.6796 80 0.950 3.9604 3.1108 2.7188 2.4859 2.3287 2.2142 2.1263 2.0564 1.9991 1.9512 80 0.975 5.2184 3.8643 3.2841 2.9504 2.7295 2.5708 2.4502 2.3549 2.2775 2.213 80 0.980 5.6353 4.1097 3.4666 3.0995 2.8578 2.6845 2.5533 2.4498 2.3658 2.296 80 0.990 6.9627 4.8807 4.0363 3.5631 3.255 3.0361 2.8713 2.742 2.6374 2.5508 80 0.995 8.3346 5.6652 4.6113 4.0285 3.6524 3.3867 3.1876 3.032 2.9066 2.8031 80 0.999 11.671 7.5401 5.9723 5.1231 4.5824 4.2043 3.9232 3.7049 3.5298 3.3859 90 0.900 2.7621 2.3625 2.1457 2.0084 1.9123 1.8406 1.7846 1.7395 1.7021 1.6705 90 0.950 3.9469 3.0977 2.7058 2.4729 2.3157 2.2011 2.1131 2.043 1.9856 1.9376 90 0.975 5.1962 3.8443 3.2649 2.9315 2.7109 2.5522 2.4316 2.3363 2.2588 2.1942 90 0.980 5.6098 4.0871 3.4451 3.0786 2.8371 2.664 2.5328 2.4293 2.3453 2.2754 90 0.990 6.9251 4.8491 4.007 3.535 3.2276 3.0091 2.8445 2.7154 2.6109 2.5243 90 0.995 8.2822 5.6228 4.5728 3.9922 3.6173 3.3524 3.1538 2.9986 2.8735 2.7701 90 0.999 11.573 7.4661 5.9078 5.0636 4.526 4.15 3.8703 3.6531 3.4789 3.3356 100 0.900 2.7564 2.3564 2.1394 2.0019 1.9057 1.8339 1.7778 1.7324 1.6949 1.6632 100 0.950 3.9361 3.0873 2.6955 2.4626 2.3053 2.1906 2.1025 2.0323 1.9748 1.9267 100 0.975 5.1786 3.8284 3.2496 2.9166 2.6961 2.5374 2.4168 2.3215 2.2439 2.1793 100 0.980 5.5895 4.0691 3.4281 3.062 2.8207 2.6477 2.5165 2.413 2.329 2.259 100 0.990 6.8953 4.8239 3.9837 3.5127 3.2059 2.9877 2.8233 2.6943 2.5898 2.5033 100 0.995 8.2406 5.5892 4.5424 3.9634 3.5895 3.3252 3.1271 2.9722 2.8472 2.744 100 0.999 11.495 7.4077 5.8568 5.0167 4.4815 4.1071 3.8286 3.6123 3.4387 3.2959 110 0.900 2.7517 2.3515 2.1343 1.9967 1.9004 1.8284 1.7721 1.7267 1.6891 1.6573 110 0.950 3.9274 3.0788 2.6871 2.4542 2.2969 2.1821 2.0939 2.0236 1.9661 1.9178 110 0.975 5.1642 3.8154 3.2372 2.9044 2.684 2.5254 2.4048 2.3094 2.2318 2.1671 110 0.980 5.573 4.0545 3.4142 3.0485 2.8074 2.6344 2.5033 2.3998 2.3157 2.2457 110 0.990 6.871 4.8035 3.9648 3.4946 3.1882 2.9703 2.8061 2.6771 2.5727 2.4862 110 0.995 8.2068 5.5619 4.5177 3.94 3.5669 3.3032 3.1054 2.9507 2.8259 2.7228 110 0.999 11.432 7.3603 5.8155 4.9786 4.4455 4.0724 3.7949 3.5792 3.4061 3.2637 120 0.900 2.7478 2.3473 2.13 1.9923 1.8959 1.8238 1.7675 1.722 1.6842 1.6524 120 0.950 3.9201 3.0718 2.6802 2.4472 2.2899 2.175 2.0868 2.0164 1.9588 1.9105 120 0.975 5.1523 3.8046 3.2269 2.8943 2.674 2.5154 2.3948 2.2994 2.2217 2.157 Upper Percentiles of the F-distribution 6 For each N, D, P, the entry is the 100Pth Percentile for the F-distribution with N and D degrees of Freedom D P N1 N2 N3 N4 N5 N6 N7 N8 N9 N10 120 0.980 5.5593 4.0424 3.4027 3.0372 2.7963 2.6235 2.4923 2.3888 2.3047 2.2347 120 0.990 6.8509 4.7865 3.9491 3.4795 3.1735 2.9559 2.7918 2.6629 2.5586 2.4721 120 0.995 8.1788 5.5393 4.4972 3.9207 3.5482 3.2849 3.0874 2.933 2.8083 2.7052 120 0.999 11.38 7.3211 5.7814 4.9472 4.4157 4.0437 3.767 3.5519 3.3792 3.2372 1000000 0.900 2.7055 2.3026 2.0838 1.9449 1.8473 1.7741 1.7167 1.6702 1.6315 1.5987 1000000 0.950 3.8415 2.9957 2.6049 2.3719 2.2141 2.0986 2.0096 1.9384 1.8799 1.8307 1000000 0.975 5.0239 3.6889 3.1161 2.7858 2.5665 2.4082 2.2876 2.1918 2.1137 2.0483 1000000 0.980 5.4119 3.912 3.2792 2.917 2.6777 2.5055 2.3746 2.271 2.1866 2.1161 1000000 0.990 6.6349 4.6052 3.7816 3.3192 3.0173 2.802 2.6393 2.5113 2.4074 2.3209 1000000 0.995 7.8795 5.2983 4.2794 3.7151 3.3499 3.0913 2.8968 2.7444 2.6211 2.5188 1000000 0.999 10.828 6.9078 5.4221 4.6167 4.103 3.743 3.4746 3.2656 3.0975 2.9589 Upper Percentiles of the F-distribution 7 For each N, D, P, the entry is the 100Pth Percentile for the F-distribution with N and D degrees of Freedom D P N11 N12 N13 N14 N15 N16 N17 N18 N19 N20 1 0.900 60.473 60.705 60.903 61.073 61.22 61.35 61.464 61.566 62.416 61.74 1 0.950 242.98 243.91 244.69 245.36 245.95 246.46 246.92 247.32 250.69 248.01 1 0.975 973.03 976.71 979.84 982.53 984.87 986.92 988.73 990.35 1003.8 993.1 1 0.980 1520.6 1526.3 1531.2 1535.4 1539.1 1542.3 1545.1 1547.6 1568.6 1551.9 1 0.990 6083.3 6106.3 6125.9 6142.7 6157.3 6170.1 6181.4 6191.5 6275.6 6208.7 1 0.995 24334 24426 24505 24572 24630 24681 24727 24767 25103 24836 1 0.999 608368 610668 612622 614303 615764 617045 618178 619188 627591 620908 2 0.900 9.4006 9.4081 9.4145 9.42 9.4247 9.4289 9.4325 9.4358 9.4627 9.4413 2 0.950 19.405 19.413 19.419 19.424 19.429 19.433 19.437 19.44 19.467 19.446 2 0.975 39.407 39.415 39.421 39.427 39.431 39.435 39.439 39.442 39.469 39.448 2 0.980 49.407 49.415 49.421 49.427 49.432 49.436 49.44 49.443 49.47 49.448 2 0.990 99.408 99.416 99.422 99.428 99.433 99.437 99.44 99.444 99.471 99.449 2 0.995 199.41 199.42 199.42 199.43 199.43 199.44 199.44 199.44 199.47 199.45 2 0.999 999.41 999.42 999.42 999.43 999.43 999.44 999.44 999.44 999.47 999.45 3 0.900 5.2224 5.2156 5.2098 5.2047 5.2003 5.1964 5.1929 5.1898 5.1633 5.1845 3 0.950 8.7633 8.7446 8.7287 8.7149 8.7029 8.6923 8.6829 8.6745 8.6039 8.6602 3 0.975 14.374 14.337 14.304 14.277 14.253 14.232 14.213 14.196 14.055 14.167 3 0.980 16.805 16.759 16.72 16.686 16.657 16.631 16.608 16.588 16.417 16.553 3 0.990 27.133 27.052 26.983 26.924 26.872 26.827 26.787 26.751 26.451 26.69 3 0.995 43.524 43.387 43.271 43.172 43.085 43.008 42.941 42.88 42.376 42.778 3 0.999 128.74 128.32 127.96 127.64 127.37 127.14 126.93 126.74 125.17 126.42 4 0.900 3.9067 3.8955 3.8859 3.8776 3.8704 3.8639 3.8582 3.8531 3.8096 3.8443 4 0.950 5.9358 5.9117 5.8911 5.8733 5.8578 5.8441 5.832 5.8211 5.7294 5.8025 4 0.975 8.7935 8.7512 8.715 8.6838 8.6565 8.6326 8.6113 8.5924 8.4327 8.5599 4 0.980 9.9436 9.8939 9.8514 9.8148 9.7828 9.7547 9.7298 9.7076 9.5205 9.6696 4 0.990 14.452 14.374 14.307 14.249 14.198 14.154 14.115 14.08 13.785 14.02 4 0.995 20.824 20.705 20.603 20.515 20.438 20.371 20.311 20.258 19.812 20.167 4 0.999 47.704 47.412 47.163 46.948 46.761 46.597 46.451 46.322 45.235 46.1 5 0.900 3.2816 3.2682 3.2567 3.2468 3.238 3.2303 3.2234 3.2172 3.1645 3.2067 5 0.950 4.704 4.6777 4.6552 4.6358 4.6188 4.6038 4.5904 4.5785 4.4775 4.5581 5 0.975 6.5678 6.5245 6.4876 6.4556 6.4277 6.4032 6.3814 6.3619 6.1973 6.3286 5 0.980 7.2847 7.2348 7.1923 7.1555 7.1234 7.0952 7.0701 7.0477 6.8587 7.0094 5 0.990 9.9626 9.8883 9.8248 9.77 9.7222 9.6802 9.6429 9.6096 9.3291 9.5526 5 0.995 13.491 13.384 13.293 13.215 13.146 13.086 13.033 12.985 12.584 12.903 5 0.999 26.646 26.418 26.224 26.057 25.911 25.783 25.669 25.568 24.717 25.395 6 0.900 2.9195 2.9047 2.892 2.8809 2.8712 2.8626 2.855 2.8481 2.7893 2.8363 6 0.950 4.0274 3.9999 3.9764 3.9559 3.9381 3.9223 3.9083 3.8957 3.7889 3.8742 6 0.975 5.4098 5.3662 5.329 5.2968 5.2687 5.2439 5.2218 5.2021 5.0352 5.1684 6 0.980 5.9252 5.8757 5.8334 5.7968 5.7648 5.7366 5.7116 5.6892 5.4998 5.6509 6 0.990 7.7896 7.7183 7.6575 7.6049 7.559 7.5186 7.4827 7.4507 7.1799 7.3958 6 0.995 10.133 10.034 9.9501 9.8774 9.814 9.7582 9.7086 9.6644 9.2913 9.5888 6 0.999 18.182 17.989 17.824 17.682 17.559 17.45 17.353 17.267 16.542 17.12 7 0.900 2.6839 2.6681 2.6545 2.6426 2.6322 2.623 2.6148 2.6074 2.5439 2.5947 7 0.950 3.603 3.5747 3.5503 3.5292 3.5107 3.4944 3.4799 3.4669 3.3557 3.4445 7 0.975 4.7095 4.6658 4.6285 4.5961 4.5678 4.5428 4.5206 4.5008 4.3319 4.4667 7 0.980 5.1128 5.0636 5.0215 4.985 4.9531 4.9249 4.8999 4.8776 4.6877 4.8393 7 0.990 6.5382 6.4691 6.41 6.359 6.3143 6.275 6.2401 6.2089 5.9444 6.1554 7 0.995 8.2697 8.1764 8.0967 8.0279 7.9678 7.9148 7.8678 7.8258 7.4707 7.754 7 0.999 13.879 13.707 13.561 13.434 13.324 13.226 13.14 13.063 12.414 12.932 8 0.900 2.5186 2.502 2.4876 2.4752 2.4642 2.4545 2.4458 2.438 2.3707 2.4246 8 0.950 3.313 3.2839 3.259 3.2374 3.2184 3.2016 3.1867 3.1733 3.0586 3.1503 Upper Percentiles of the F-distribution 8 For each N, D, P, the entry is the 100Pth Percentile for the F-distribution with N and D degrees of Freedom D P N11 N12 N13 N14 N15 N16 N17 N18 N19 N20 8 0.975 4.2434 4.1997 4.1622 4.1297 4.1012 4.0761 4.0538 4.0338 3.8632 3.9995 8 0.980 4.5768 4.5278 4.4857 4.4493 4.4174 4.3893 4.3643 4.342 4.1513 4.3036 8 0.990 5.7343 5.6667 5.6089 5.5589 5.5151 5.4766 5.4423 5.4116 5.1512 5.3591 8 0.995 7.1045 7.0149 6.9384 6.8721 6.8143 6.7633 6.718 6.6775 6.3343 6.6082 8 0.999 11.352 11.194 11.06 10.943 10.841 10.752 10.672 10.601 10.001 10.48 9 0.900 2.3961 2.3789 2.364 2.351 2.3396 2.3295 2.3205 2.3123 2.2418 2.2983 9 0.950 3.1025 3.0729 3.0475 3.0255 3.0061 2.989 2.9737 2.96 2.8422 2.9365 9 0.975 3.9121 3.8682 3.8306 3.798 3.7694 3.7441 3.7216 3.7015 3.5292 3.6669 9 0.980 4.1982 4.1493 4.1073 4.0709 4.039 4.0109 3.9858 3.9634 3.7718 3.9249 9 0.990 5.1779 5.1114 5.0545 5.0052 4.9621 4.924 4.8902 4.8599 4.602 4.808 9 0.995 6.3142 6.2274 6.153 6.0887 6.0325 5.9829 5.9388 5.8994 5.5643 5.8318 9 0.999 9.7183 9.57 9.4433 9.3337 9.2381 9.1538 9.079 9.0121 8.4456 8.8976 10 0.900 2.3018 2.2841 2.2687 2.2553 2.2435 2.233 2.2237 2.2153 2.142 2.2007 10 0.950 2.943 2.913 2.8872 2.8647 2.845 2.8276 2.812 2.798 2.6776 2.774 10 0.975 3.6649 3.6209 3.5832 3.5504 3.5217 3.4963 3.4737 3.4534 3.2794 3.4185 10 0.980 3.9172 3.8684 3.8264 3.79 3.7581 3.7299 3.7048 3.6823 3.4895 3.6437 10 0.990 4.7715 4.7059 4.6496 4.6008 4.5581 4.5204 4.4869 4.4569 4.2005 4.4054 10 0.995 5.7462 5.6613 5.5887 5.5257 5.4707 5.4221 5.3789 5.3403 5.011 5.274 10 0.999 8.5864 8.4452 8.3245 8.22 8.1288 8.0484 7.977 7.9131 7.3711 7.8037 11 0.900 2.2269 2.2087 2.193 2.1792 2.1671 2.1563 2.1467 2.138 2.0623 2.123 11 0.950 2.8179 2.7876 2.7614 2.7386 2.7186 2.7009 2.6851 2.6709 2.548 2.6464 11 0.975 3.4737 3.4296 3.3917 3.3588 3.3299 3.3044 3.2816 3.2612 3.0856 3.2261 11 0.980 3.7008 3.6519 3.6099 3.5735 3.5415 3.5132 3.4881 3.4655 3.2716 3.4267 11 0.990 4.4624 4.3974 4.3416 4.2932 4.2509 4.2134 4.1801 4.1503 3.8948 4.099 11 0.995 5.3197 5.2363 5.1649 5.1031 5.0489 5.0011 4.9586 4.9205 4.5955 4.8552 11 0.999 7.7614 7.6256 7.5094 7.4089 7.321 7.2435 7.1747 7.1131 6.5894 7.0076 12 0.900 2.166 2.1474 2.1313 2.1173 2.1049 2.0938 2.0839 2.075 1.9971 2.0597 12 0.950 2.7173 2.6866 2.6602 2.6371 2.6169 2.5989 2.5828 2.5684 2.4433 2.5436 12 0.975 3.3215 3.2773 3.2393 3.2062 3.1772 3.1515 3.1286 3.1081 2.9309 3.0728 12 0.980 3.5291 3.4802 3.4382 3.4016 3.3696 3.3413 3.316 3.2934 3.0982 3.2544 12 0.990 4.2198 4.1553 4.0999 4.0518 4.0096 3.9724 3.9392 3.9095 3.6544 3.8584 12 0.995 4.9884 4.9062 4.8358 4.7748 4.7213 4.6741 4.6321 4.5945 4.2725 4.5299 12 0.999 7.1362 7.0046 6.892 6.7945 6.7092 6.634 6.5672 6.5074 5.9976 6.4048 13 0.900 2.1155 2.0966 2.0802 2.0658 2.0532 2.0419 2.0318 2.0227 1.9428 2.007 13 0.950 2.6347 2.6037 2.5769 2.5536 2.5331 2.5149 2.4987 2.4841 2.357 2.4589 13 0.975 3.1975 3.1532 3.115 3.0819 3.0527 3.0269 3.0039 2.9832 2.8046 2.9477 13 0.980 3.3896 3.3407 3.2986 3.262 3.2299 3.2015 3.1762 3.1534 2.9571 3.1143 13 0.990 4.0245 3.9603 3.9052 3.8573 3.8154 3.7783 3.7452 3.7156 3.4606 3.6646 13 0.995 4.724 4.6429 4.5733 4.5129 4.46 4.4132 4.3716 4.3344 4.0146 4.2703 13 0.999 6.6474 6.5192 6.4094 6.3144 6.2312 6.1578 6.0926 6.0342 5.5355 5.934 14 0.900 2.0729 2.0537 2.037 2.0224 2.0095 1.9981 1.9878 1.9785 1.8968 1.9625 14 0.950 2.5655 2.5342 2.5073 2.4837 2.463 2.4446 2.4282 2.4134 2.2845 2.3879 14 0.975 3.0946 3.0502 3.0119 2.9786 2.9493 2.9234 2.9003 2.8795 2.6994 2.8437 14 0.980 3.2741 3.2251 3.183 3.1464 3.1142 3.0857 3.0603 3.0374 2.8399 2.9981 14 0.990 3.864 3.8001 3.7452 3.6975 3.6557 3.6187 3.5857 3.5561 3.301 3.5052 14 0.995 4.5085 4.4281 4.3591 4.2993 4.2468 4.2005 4.1592 4.1221 3.804 4.0585 14 0.999 6.2556 6.1302 6.0228 5.9297 5.8483 5.7764 5.7124 5.6551 5.1653 5.5568 15 0.900 2.0366 2.0171 2.0001 1.9853 1.9722 1.9605 1.9501 1.9407 1.8573 1.9243 15 0.950 2.5068 2.4753 2.4481 2.4244 2.4034 2.3849 2.3683 2.3533 2.2227 2.3275 15 0.975 3.0078 2.9633 2.9249 2.8915 2.8621 2.836 2.8128 2.7919 2.6104 2.7559 15 0.980 3.1769 3.1279 3.0858 3.049 3.0168 2.9882 2.9627 2.9398 2.741 2.9003 Upper Percentiles of the F-distribution 9 For each N, D, P, the entry is the 100Pth Percentile for the F-distribution with N and D degrees of Freedom D P N11 N12 N13 N14 N15 N16 N17 N18 N19 N20 15 0.990 3.7299 3.6662 3.6115 3.5639 3.5222 3.4852 3.4523 3.4228 3.1674 3.3719 15 0.995 4.3295 4.2497 4.1813 4.1219 4.0698 4.0237 3.9827 3.9459 3.6289 3.8826 15 0.999 5.9352 5.8121 5.7066 5.6151 5.5351 5.4644 5.4015 5.3452 4.8625 5.2484 16 0.900 2.0051 1.9854 1.9682 1.9532 1.9399 1.9281 1.9175 1.9079 1.823 1.8913 16 0.950 2.4564 2.4247 2.3973 2.3733 2.3522 2.3335 2.3167 2.3016 2.1694 2.2756 16 0.975 2.9337 2.889 2.8506 2.817 2.7875 2.7614 2.738 2.717 2.5342 2.6808 16 0.980 3.0941 3.045 3.0028 2.966 2.9336 2.905 2.8794 2.8564 2.6565 2.8167 16 0.990 3.6162 3.5527 3.4981 3.4506 3.4089 3.372 3.3391 3.3096 3.0539 3.2587 16 0.995 4.1785 4.0994 4.0314 3.9723 3.9205 3.8747 3.8338 3.7972 3.4811 3.7342 16 0.999 5.6684 5.5473 5.4434 5.3533 5.2745 5.2048 5.1428 5.0872 4.6105 4.9918 17 0.900 1.9777 1.9577 1.9404 1.9252 1.9117 1.8997 1.8889 1.8792 1.7929 1.8624 17 0.950 2.4126 2.3807 2.3531 2.329 2.3077 2.2888 2.2719 2.2567 2.1229 2.2304 17 0.975 2.8696 2.8249 2.7863 2.7526 2.723 2.6968 2.6733 2.6522 2.4681 2.6158 17 0.980 3.0226 2.9735 2.9312 2.8943 2.8619 2.8331 2.8074 2.7844 2.5834 2.7446 17 0.990 3.5185 3.4552 3.4007 3.3533 3.3117 3.2748 3.2419 3.2124 2.9563 3.1615 17 0.995 4.0496 3.9709 3.9033 3.8445 3.7929 3.7473 3.7066 3.6701 3.3547 3.6073 17 0.999 5.4431 5.3237 5.2212 5.1323 5.0544 4.9856 4.9244 4.8695 4.3976 4.7751 18 0.900 1.9535 1.9333 1.9158 1.9004 1.8868 1.8747 1.8638 1.8539 1.7663 1.8368 18 0.950 2.3742 2.3421 2.3143 2.29 2.2686 2.2496 2.2325 2.2172 2.0821 2.1906 18 0.975 2.8137 2.7689 2.7302 2.6964 2.6667 2.6404 2.6168 2.5956 2.4103 2.559 18 0.980 2.9603 2.9111 2.8688 2.8318 2.7993 2.7705 2.7447 2.7216 2.5195 2.6816 18 0.990 3.4338 3.3706 3.3162 3.2689 3.2273 3.1904 3.1575 3.128 2.8714 3.0771 18 0.995 3.9382 3.8599 3.7926 3.7341 3.6827 3.6373 3.5967 3.5603 3.2453 3.4977 18 0.999 5.2505 5.1324 5.0312 4.9433 4.8663 4.7982 4.7376 4.6833 4.2156 4.5899 19 0.900 1.9321 1.9117 1.894 1.8785 1.8647 1.8524 1.8414 1.8314 1.7426 1.8142 19 0.950 2.3402 2.308 2.28 2.2556 2.2341 2.2149 2.1977 2.1823 2.0458 2.1555 19 0.975 2.7645 2.7196 2.6808 2.6469 2.6171 2.5907 2.567 2.5457 2.3593 2.5089 19 0.980 2.9055 2.8563 2.8139 2.7769 2.7443 2.7154 2.6895 2.6663 2.4632 2.6262 19 0.990 3.3596 3.2965 3.2422 3.1949 3.1533 3.1165 3.0836 3.0541 2.7969 3.0031 19 0.995 3.841 3.7631 3.6961 3.6378 3.5866 3.5412 3.5008 3.4645 3.1498 3.402 19 0.999 5.084 4.9672 4.8669 4.7799 4.7037 4.6362 4.5762 4.5223 4.0581 4.4297 20 0.900 1.9129 1.8924 1.8745 1.8588 1.8449 1.8325 1.8214 1.8113 1.7213 1.7938 20 0.950 2.31 2.2776 2.2495 2.225 2.2033 2.184 2.1667 2.1511 2.0135 2.1242 20 0.975 2.7209 2.6758 2.6369 2.603 2.5731 2.5465 2.5228 2.5014 2.3139 2.4645 20 0.980 2.857 2.8077 2.7652 2.7281 2.6955 2.6665 2.6406 2.6173 2.4131 2.577 20 0.990 3.2941 3.2311 3.1769 3.1296 3.088 3.0512 3.0183 2.9887 2.731 2.9377 20 0.995 3.7555 3.6779 3.6111 3.553 3.502 3.4568 3.4164 3.3802 3.0656 3.3178 20 0.999 4.9386 4.8229 4.7236 4.6374 4.5618 4.4949 4.4353 4.3819 3.9207 4.29 21 0.900 1.8956 1.875 1.857 1.8412 1.8271 1.8146 1.8034 1.7932 1.7021 1.7756 21 0.950 2.2829 2.2504 2.2222 2.1975 2.1757 2.1563 2.1389 2.1232 1.9844 2.096 21 0.975 2.6819 2.6368 2.5978 2.5638 2.5338 2.5071 2.4833 2.4618 2.2733 2.4247 21 0.980 2.8137 2.7644 2.7218 2.6847 2.6519 2.6229 2.5969 2.5735 2.3684 2.5331 21 0.990 3.2359 3.173 3.1187 3.0715 3.03 2.9931 2.9602 2.9306 2.6723 2.8796 21 0.995 3.6798 3.6024 3.5358 3.4779 3.427 3.3818 3.3416 3.3054 2.9909 3.2431 21 0.999 4.8107 4.696 4.5975 4.5119 4.4369 4.3705 4.3114 4.2583 3.7996 4.167 22 0.900 1.8801 1.8593 1.8411 1.8252 1.8111 1.7984 1.7871 1.7768 1.6847 1.759 22 0.950 2.2585 2.2258 2.1975 2.1727 2.1508 2.1313 2.1138 2.098 1.9581 2.0707 22 0.975 2.6469 2.6017 2.5626 2.5285 2.4984 2.4717 2.4478 2.4262 2.2366 2.389 22 0.980 2.7749 2.7255 2.6828 2.6456 2.6128 2.5837 2.5576 2.5342 2.3282 2.4937 22 0.990 3.1837 3.1209 3.0667 3.0195 2.9779 2.9411 2.9082 2.8786 2.6197 2.8274 22 0.995 3.6122 3.535 3.4686 3.4108 3.36 3.315 3.2748 3.2387 2.9241 3.1764 Upper Percentiles of the F-distribution 10 For each N, D, P, the entry is the 100Pth Percentile for the F-distribution with N and D degrees of Freedom D P N11 N12 N13 N14 N15 N16 N17 N18 N19 N20 22 0.999 4.6973 4.5835 4.4857 4.4007 4.3262 4.2602 4.2015 4.1487 3.6923 4.0579 23 0.900 1.8659 1.845 1.8267 1.8107 1.7964 1.7837 1.7723 1.7619 1.6689 1.7439 23 0.950 2.2364 2.2036 2.1752 2.1502 2.1282 2.1086 2.091 2.0751 1.9342 2.0476 23 0.975 2.6152 2.5699 2.5308 2.4966 2.4665 2.4396 2.4157 2.394 2.2035 2.3567 23 0.980 2.7398 2.6904 2.6477 2.6104 2.5775 2.5483 2.5222 2.4987 2.2918 2.458 23 0.990 3.1368 3.074 3.0199 2.9727 2.9311 2.8943 2.8613 2.8317 2.5722 2.7805 23 0.995 3.5515 3.4745 3.4083 3.3506 3.2999 3.2549 3.2148 3.1787 2.8641 3.1165 23 0.999 4.5962 4.4831 4.3859 4.3015 4.2274 4.1618 4.1034 4.0509 3.5964 3.9606 24 0.900 1.853 1.8319 1.8136 1.7974 1.7831 1.7703 1.7587 1.7483 1.6544 1.7302 24 0.950 2.2163 2.1834 2.1548 2.1298 2.1077 2.088 2.0703 2.0543 1.9124 2.0267 24 0.975 2.5865 2.5411 2.5019 2.4677 2.4374 2.4105 2.3865 2.3648 2.1733 2.3273 24 0.980 2.708 2.6585 2.6157 2.5784 2.5455 2.5162 2.49 2.4665 2.2587 2.4257 24 0.990 3.0944 3.0316 2.9775 2.9303 2.8887 2.8519 2.8189 2.7892 2.5292 2.738 24 0.995 3.4967 3.4199 3.3538 3.2962 3.2456 3.2007 3.1606 3.1246 2.8098 3.0624 24 0.999 4.5053 4.3929 4.2963 4.2124 4.1387 4.0735 4.0154 3.9631 3.5103 3.8732 25 0.900 1.8412 1.82 1.8015 1.7853 1.7708 1.7579 1.7463 1.7358 1.641 1.7175 25 0.950 2.1979 2.1649 2.1362 2.1111 2.0889 2.0691 2.0513 2.0353 1.8924 2.0075 25 0.975 2.5603 2.5149 2.4756 2.4413 2.411 2.384 2.3599 2.3381 2.1458 2.3005 25 0.980 2.679 2.6295 2.5867 2.5493 2.5163 2.487 2.4607 2.4371 2.2284 2.3962 25 0.990 3.0558 2.9931 2.9389 2.8917 2.8502 2.8133 2.7803 2.7506 2.49 2.6993 25 0.995 3.447 3.3704 3.3044 3.2469 3.1963 3.1515 3.1114 3.0754 2.7605 3.0133 25 0.999 4.4233 4.3116 4.2155 4.132 4.0587 3.9938 3.9359 3.8839 3.4325 3.7944 30 0.900 1.7944 1.7727 1.7538 1.7371 1.7223 1.709 1.697 1.6862 1.5877 1.6673 30 0.950 2.1256 2.0921 2.063 2.0374 2.0148 1.9946 1.9765 1.9601 1.8132 1.9317 30 0.975 2.4577 2.412 2.3724 2.3378 2.3072 2.2799 2.2554 2.2334 2.0372 2.1952 30 0.980 2.5657 2.5159 2.4729 2.4352 2.402 2.3724 2.3459 2.3219 2.1096 2.2805 30 0.990 2.9057 2.8431 2.789 2.7418 2.7002 2.6632 2.6301 2.6003 2.3369 2.5487 30 0.995 3.2547 3.1787 3.1132 3.056 3.0057 2.9611 2.9211 2.8852 2.5691 2.823 30 0.999 4.11 4.0006 3.9065 3.8247 3.7527 3.689 3.6321 3.581 3.1347 3.4928 35 0.900 1.7614 1.7394 1.7201 1.7031 1.688 1.6744 1.6622 1.6511 1.5497 1.6317 35 0.950 2.075 2.0411 2.0117 1.9858 1.9629 1.9424 1.924 1.9073 1.7571 1.8784 35 0.975 2.3866 2.3406 2.3008 2.2659 2.235 2.2075 2.1828 2.1605 1.9611 2.1218 35 0.980 2.4872 2.4373 2.3941 2.3562 2.3227 2.2929 2.2661 2.242 2.0266 2.2001 35 0.990 2.8026 2.74 2.6859 2.6387 2.597 2.5599 2.5266 2.4967 2.2309 2.4448 35 0.995 3.1236 3.048 2.9827 2.9258 2.8756 2.831 2.7911 2.7551 2.4377 2.693 35 0.999 3.8997 3.792 3.6992 3.6185 3.5474 3.4845 3.4282 3.3776 2.9341 3.2903 40 0.900 1.7369 1.7146 1.695 1.6778 1.6624 1.6486 1.6362 1.6249 1.5211 1.6052 40 0.950 2.0376 2.0035 1.9738 1.9476 1.9245 1.9037 1.8851 1.8682 1.7154 1.8389 40 0.975 2.3343 2.2882 2.2481 2.213 2.1819 2.1542 2.1293 2.1068 1.9047 2.0677 40 0.980 2.4297 2.3796 2.3362 2.2982 2.2645 2.2345 2.2076 2.1832 1.9653 2.141 40 0.990 2.7274 2.6648 2.6107 2.5634 2.5216 2.4844 2.4511 2.421 2.1531 2.3689 40 0.995 3.0284 2.9531 2.888 2.8312 2.7811 2.7365 2.6966 2.6607 2.3418 2.5984 40 0.999 3.749 3.6425 3.5507 3.4707 3.4003 3.3378 3.282 3.2318 2.7899 3.145 45 0.900 1.718 1.6954 1.6757 1.6582 1.6426 1.6287 1.6161 1.6046 1.4989 1.5846 45 0.950 2.0088 1.9745 1.9446 1.9182 1.8949 1.874 1.8551 1.8381 1.683 1.8084 45 0.975 2.2943 2.248 2.2078 2.1725 2.1412 2.1133 2.0883 2.0656 1.8613 2.0262 45 0.980 2.3858 2.3355 2.292 2.2538 2.2199 2.1898 2.1627 2.1382 1.918 2.0957 45 0.990 2.6701 2.6076 2.5534 2.506 2.4642 2.4269 2.3935 2.3633 2.0934 2.3109 45 0.995 2.9563 2.8811 2.8162 2.7595 2.7094 2.6648 2.6249 2.5889 2.2687 2.5266 45 0.999 3.6358 3.5301 3.439 3.3596 3.2897 3.2276 3.1721 3.1221 2.6812 3.0357 50 0.900 1.7029 1.6802 1.6602 1.6426 1.6269 1.6128 1.6 1.5884 1.481 1.5681 Upper Percentiles of the F-distribution 11 For each N, D, P, the entry is the 100Pth Percentile for the F-distribution with N and D degrees of Freedom D P N11 N12 N13 N14 N15 N16 N17 N18 N19 N20 50 0.950 1.9861 1.9515 1.9214 1.8949 1.8714 1.8503 1.8313 1.8141 1.6571 1.7841 50 0.975 2.2627 2.2162 2.1758 2.1404 2.109 2.081 2.0558 2.033 1.8267 1.9933 50 0.980 2.351 2.3007 2.257 2.2187 2.1847 2.1544 2.1272 2.1026 1.8805 2.0598 50 0.990 2.625 2.5625 2.5083 2.4609 2.419 2.3816 2.3481 2.3178 2.0463 2.2652 50 0.995 2.8997 2.8247 2.7599 2.7032 2.6531 2.6086 2.5686 2.5326 2.2112 2.4702 50 0.999 3.5476 3.4426 3.3521 3.2731 3.2035 3.1418 3.0865 3.0367 2.5964 2.9506 60 0.900 1.6805 1.6574 1.6372 1.6193 1.6034 1.589 1.576 1.5642 1.4541 1.5435 60 0.950 1.9522 1.9174 1.887 1.8602 1.8364 1.8151 1.7959 1.7784 1.6183 1.748 60 0.975 2.2159 2.1692 2.1286 2.0929 2.0613 2.033 2.0076 1.9846 1.7752 1.9445 60 0.980 2.2997 2.2492 2.2053 2.1668 2.1326 2.1021 2.0747 2.0499 1.8247 2.0067 60 0.990 2.5587 2.4961 2.4419 2.3943 2.3523 2.3148 2.2811 2.2507 1.9764 2.1978 60 0.995 2.8166 2.7419 2.6771 2.6205 2.5705 2.5259 2.4859 2.4498 2.1263 2.3872 60 0.999 3.4193 3.3153 3.2255 3.1472 3.0781 3.0167 2.9618 2.9123 2.4724 2.8266 70 0.900 1.6645 1.6413 1.6209 1.6028 1.5866 1.5721 1.5589 1.547 1.4348 1.5259 70 0.950 1.9283 1.8932 1.8627 1.8357 1.8117 1.7902 1.7708 1.7531 1.5906 1.7223 70 0.975 2.1829 2.1361 2.0953 2.0595 2.0277 1.9992 1.9736 1.9504 1.7386 1.91 70 0.980 2.2636 2.213 2.169 2.1303 2.0959 2.0653 2.0377 2.0127 1.7851 1.9691 70 0.990 2.5122 2.4496 2.3953 2.3477 2.3055 2.2679 2.2341 2.2036 1.9271 2.1504 70 0.995 2.7587 2.684 2.6193 2.5627 2.5127 2.4681 2.4281 2.3919 2.0666 2.3291 70 0.999 3.3304 3.2271 3.1378 3.0599 2.9912 2.9301 2.8754 2.826 2.3861 2.7405 80 0.900 1.6526 1.6292 1.6086 1.5904 1.5741 1.5594 1.5461 1.534 1.4203 1.5128 80 0.950 1.9105 1.8753 1.8445 1.8174 1.7932 1.7716 1.752 1.7342 1.5699 1.7032 80 0.975 2.1584 2.1115 2.0706 2.0346 2.0026 1.9741 1.9483 1.925 1.7112 1.8843 80 0.980 2.2369 2.1861 2.1419 2.1031 2.0687 2.0379 2.0101 1.985 1.7555 1.9412 80 0.990 2.4777 2.4151 2.3608 2.3131 2.2709 2.2332 2.1993 2.1686 1.8904 2.1153 80 0.995 2.7159 2.6413 2.5767 2.5201 2.47 2.4254 2.3854 2.3492 2.0223 2.2862 80 0.999 3.2652 3.1624 3.0735 2.9959 2.9274 2.8665 2.812 2.7627 2.3226 2.6774 90 0.900 1.6434 1.6199 1.5992 1.5808 1.5644 1.5496 1.5362 1.524 1.4089 1.5025 90 0.950 1.8967 1.8613 1.8305 1.8032 1.7789 1.7571 1.7375 1.7196 1.5537 1.6883 90 0.975 2.1395 2.0925 2.0515 2.0154 1.9833 1.9546 1.9288 1.9053 1.6899 1.8644 90 0.980 2.2162 2.1654 2.1211 2.0822 2.0476 2.0167 1.9889 1.9637 1.7325 1.9197 90 0.990 2.4513 2.3886 2.3342 2.2865 2.2442 2.2064 2.1725 2.1417 1.8619 2.0882 90 0.995 2.683 2.6085 2.5439 2.4873 2.4373 2.3926 2.3525 2.3163 1.9881 2.2532 90 0.999 3.2154 3.1129 3.0244 2.947 2.8787 2.8179 2.7634 2.7143 2.2739 2.6291 100 0.900 1.636 1.6124 1.5916 1.5731 1.5566 1.5418 1.5283 1.516 1.3998 1.4943 100 0.950 1.8857 1.8503 1.8193 1.7919 1.7675 1.7456 1.7259 1.7079 1.5407 1.6764 100 0.975 2.1245 2.0773 2.0363 2.0001 1.9679 1.9391 1.9132 1.8897 1.6729 1.8486 100 0.980 2.1998 2.1489 2.1045 2.0655 2.0309 1.9999 1.972 1.9467 1.7142 1.9025 100 0.990 2.4302 2.3676 2.3132 2.2654 2.223 2.1852 2.1511 2.1203 1.8393 2.0666 100 0.995 2.657 2.5825 2.518 2.4614 2.4113 2.3666 2.3265 2.2902 1.961 2.227 100 0.999 3.176 3.0739 2.9855 2.9083 2.8402 2.7795 2.7251 2.6761 2.2353 2.5909 110 0.900 1.63 1.6063 1.5854 1.5669 1.5503 1.5353 1.5218 1.5094 1.3923 1.4877 110 0.950 1.8767 1.8412 1.8101 1.7827 1.7582 1.7363 1.7164 1.6984 1.5301 1.6667 110 0.975 2.1123 2.065 2.0239 1.9876 1.9554 1.9265 1.9005 1.8769 1.6591 1.8356 110 0.980 2.1864 2.1354 2.091 2.052 2.0173 1.9862 1.9582 1.9328 1.6992 1.8885 110 0.990 2.4132 2.3505 2.296 2.2482 2.2058 2.1679 2.1338 2.1029 1.8209 2.0491 110 0.995 2.6358 2.5614 2.4969 2.4403 2.3902 2.3455 2.3053 2.269 1.9389 2.2057 110 0.999 3.1442 3.0423 2.9541 2.8771 2.809 2.7485 2.6941 2.6451 2.2041 2.56 120 0.900 1.625 1.6012 1.5803 1.5617 1.545 1.53 1.5164 1.5039 1.3861 1.4821 120 0.950 1.8693 1.8337 1.8026 1.775 1.7505 1.7285 1.7085 1.6904 1.5213 1.6587 120 0.975 2.1021 2.0548 2.0136 1.9773 1.945 1.9161 1.89 1.8663 1.6475 1.8249 Upper Percentiles of the F-distribution 12 For each N, D, P, the entry is the 100Pth Percentile for the F-distribution with N and D degrees of Freedom D P N11 N12 N13 N14 N15 N16 N17 N18 N19 N20 120 0.980 2.1753 2.1243 2.0799 2.0407 2.0059 1.9748 1.9468 1.9213 1.6868 1.8769 120 0.990 2.399 2.3363 2.2818 2.2339 2.1915 2.1536 2.1194 2.0885 1.8055 2.0346 120 0.995 2.6183 2.5439 2.4794 2.4228 2.3727 2.328 2.2878 2.2514 1.9205 2.1881 120 0.999 3.1179 3.0162 2.9282 2.8512 2.7833 2.7228 2.6685 2.6195 2.1782 2.5344 1000000 0.900 1.5705 1.5458 1.524 1.5046 1.4871 1.4714 1.457 1.4439 1.316 1.4206 1000000 0.950 1.7887 1.7522 1.7202 1.6918 1.6664 1.6435 1.6228 1.6039 1.4229 1.5705 1000000 0.975 1.9927 1.9447 1.9028 1.8657 1.8326 1.8028 1.776 1.7515 1.5201 1.7085 1000000 0.980 2.0562 2.0045 1.9594 1.9195 1.884 1.8521 1.8233 1.797 1.5498 1.751 1000000 0.990 2.2477 2.1848 2.1299 2.0815 2.0385 2 1.9652 1.9336 1.6384 1.8783 1000000 0.995 2.4325 2.3583 2.2938 2.2371 2.1868 2.1417 2.1011 2.0643 1.7222 1.9999 1000000 0.999 2.8422 2.7425 2.656 2.5803 2.5132 2.4533 2.3995 2.3507 1.9034 2.2658 Upper Percentiles of the F-distribution 13 For each N, D, P, the entry is the 100Pth Percentile for the F-distribution with N and D degrees of Freedom D P N25 N30 N35 N40 N50 N60 N80 N100 N120 N1000000 1 0.900 62.055 62.265 62.416 62.529 62.688 62.794 62.927 63.007 63.061 63.328 1 0.950 249.26 250.1 250.69 251.14 251.77 252.2 252.72 253.04 253.25 254.31 1 0.975 998.08 1001.4 1003.8 1005.6 1008.1 1009.8 1011.9 1013.2 1014 1018.3 1 0.980 1559.7 1564.9 1568.6 1571.4 1575.4 1578 1581.3 1583.3 1584.6 1591.2 1 0.990 6239.8 6260.6 6275.6 6286.8 6302.5 6313 6326.2 6334.1 6339.4 6365.9 1 0.995 24960 25044 25103 25148 25211 25253 25306 25337 25359 25464 1 0.999 624017 626099 627591 628712 630285 631337 632653 633444 633972 636619 2 0.900 9.4513 9.4579 9.4627 9.4662 9.4712 9.4746 9.4787 9.4812 9.4829 9.4912 2 0.950 19.456 19.462 19.467 19.471 19.476 19.479 19.483 19.486 19.487 19.496 2 0.975 39.458 39.465 39.469 39.473 39.478 39.481 39.485 39.488 39.49 39.498 2 0.980 49.458 49.465 49.47 49.473 49.478 49.482 49.486 49.488 49.49 49.498 2 0.990 99.459 99.466 99.471 99.474 99.479 99.482 99.487 99.489 99.491 99.499 2 0.995 199.46 199.47 199.47 199.47 199.48 199.48 199.49 199.49 199.49 199.5 2 0.999 999.46 999.47 999.47 999.47 999.48 999.48 999.49 999.49 999.49 999.5 3 0.900 5.1747 5.1681 5.1633 5.1597 5.1546 5.1512 5.1469 5.1443 5.1425 5.1337 3 0.950 8.6341 8.6166 8.6039 8.5944 8.581 8.572 8.5607 8.5539 8.5494 8.5265 3 0.975 14.115 14.081 14.055 14.037 14.01 13.992 13.97 13.956 13.947 13.902 3 0.980 16.49 16.448 16.417 16.394 16.362 16.34 16.313 16.297 16.286 16.231 3 0.990 26.579 26.505 26.451 26.411 26.354 26.316 26.269 26.24 26.221 26.125 3 0.995 42.591 42.466 42.376 42.308 42.213 42.149 42.07 42.022 41.989 41.828 3 0.999 125.84 125.45 125.17 124.96 124.66 124.47 124.22 124.07 123.97 123.47 4 0.900 3.8283 3.8174 3.8096 3.8036 3.7952 3.7896 3.7825 3.7782 3.7753 3.7607 4 0.950 5.7687 5.7459 5.7294 5.717 5.6995 5.6877 5.673 5.6641 5.6581 5.6281 4 0.975 8.501 8.4613 8.4327 8.4111 8.3808 8.3604 8.3349 8.3195 8.3092 8.2573 4 0.980 9.6005 9.554 9.5205 9.4953 9.4598 9.436 9.4061 9.388 9.376 9.3154 4 0.990 13.911 13.838 13.785 13.745 13.69 13.652 13.605 13.577 13.558 13.463 4 0.995 20.002 19.892 19.812 19.752 19.667 19.611 19.54 19.497 19.468 19.325 4 0.999 45.699 45.429 45.235 45.089 44.883 44.746 44.573 44.469 44.4 44.051 5 0.900 3.1873 3.1741 3.1645 3.1573 3.1471 3.1402 3.1316 3.1263 3.1228 3.105 5 0.950 4.5209 4.4957 4.4775 4.4638 4.4444 4.4314 4.415 4.4051 4.3985 4.365 5 0.975 6.2679 6.2269 6.1973 6.175 6.1436 6.1225 6.096 6.08 6.0693 6.0153 5 0.980 6.9397 6.8926 6.8587 6.8331 6.797 6.7728 6.7424 6.7241 6.7118 6.6499 5 0.990 9.4491 9.3793 9.3291 9.2912 9.2378 9.202 9.157 9.1299 9.1118 9.0204 5 0.995 12.755 12.656 12.584 12.53 12.454 12.402 12.338 12.3 12.274 12.144 5 0.999 25.08 24.869 24.717 24.602 24.441 24.333 24.197 24.115 24.06 23.785 6 0.900 2.8147 2.8 2.7893 2.7812 2.7697 2.762 2.7522 2.7463 2.7423 2.7222 6 0.950 3.8348 3.8082 3.7889 3.7743 3.7537 3.7398 3.7223 3.7117 3.7047 3.6689 6 0.975 5.1069 5.0652 5.0352 5.0125 4.9804 4.9589 4.9318 4.9154 4.9044 4.8491 6 0.980 5.5811 5.5338 5.4998 5.474 5.4377 5.4133 5.3826 5.3641 5.3517 5.2891 6 0.990 7.296 7.2285 7.1799 7.1432 7.0915 7.0567 7.013 6.9867 6.969 6.88 6 0.995 9.4511 9.3582 9.2913 9.2408 9.1697 9.1219 9.0619 9.0257 9.0015 8.8793 6 0.999 16.853 16.672 16.542 16.445 16.307 16.214 16.098 16.028 15.981 15.745 7 0.900 2.5714 2.5555 2.5439 2.5351 2.5226 2.5142 2.5036 2.4971 2.4928 2.4708 7 0.950 3.4036 3.3758 3.3557 3.3404 3.3189 3.3043 3.286 3.2749 3.2674 3.2298 7 0.975 4.4045 4.3624 4.3319 4.3089 4.2763 4.2544 4.2268 4.2101 4.1989 4.1423 7 0.980 4.7693 4.7219 4.6877 4.6618 4.6252 4.6006 4.5696 4.5509 4.5383 4.4749 7 0.990 6.058 5.992 5.9444 5.9084 5.8577 5.8236 5.7806 5.7547 5.7373 5.6495 7 0.995 7.623 7.5345 7.4707 7.4224 7.3544 7.3088 7.2513 7.2165 7.1933 7.076 7 0.999 12.692 12.53 12.414 12.326 12.202 12.119 12.014 11.951 11.909 11.696 8 0.900 2.3999 2.383 2.3707 2.3614 2.3481 2.3391 2.3277 2.3208 2.3162 2.2926 8 0.950 3.1081 3.0794 3.0586 3.0428 3.0204 3.0053 2.9862 2.9747 2.9669 2.9276 Upper Percentiles of the F-distribution 14 For each N, D, P, the entry is the 100Pth Percentile for the F-distribution with N and D degrees of Freedom D P N25 N30 N35 N40 N50 N60 N80 N100 N120 N1000000 8 0.975 3.9367 3.894 3.8632 3.8398 3.8067 3.7844 3.7563 3.7393 3.7279 3.6702 8 0.980 4.2334 4.1857 4.1513 4.1252 4.0883 4.0634 4.0321 4.0131 4.0004 3.9361 8 0.990 5.2631 5.1981 5.1512 5.1156 5.0654 5.0316 4.989 4.9633 4.9461 4.8588 8 0.995 6.4817 6.3961 6.3343 6.2875 6.2215 6.1772 6.1213 6.0875 6.0649 5.9506 8 0.999 10.258 10.109 10.001 9.9194 9.8044 9.7272 9.63 9.5714 9.5321 9.3338 9 0.900 2.2725 2.2547 2.2418 2.232 2.218 2.2085 2.1965 2.1892 2.1843 2.1592 9 0.950 2.8932 2.8637 2.8422 2.8259 2.8028 2.7872 2.7675 2.7556 2.7475 2.7067 9 0.975 3.6035 3.5604 3.5292 3.5055 3.4719 3.4493 3.4207 3.4034 3.3918 3.3329 9 0.980 3.8544 3.8065 3.7718 3.7455 3.7082 3.6831 3.6514 3.6322 3.6193 3.554 9 0.990 4.713 4.6486 4.602 4.5666 4.5167 4.4831 4.4407 4.415 4.3978 4.3106 9 0.995 5.7084 5.6248 5.5643 5.5186 5.4539 5.4104 5.3555 5.3223 5.3001 5.1875 9 0.999 8.6888 8.5476 8.4456 8.3685 8.2597 8.1865 8.0944 8.0387 8.0014 7.8129 10 0.900 2.1739 2.1554 2.142 2.1317 2.1171 2.1072 2.0946 2.0869 2.0818 2.0554 10 0.950 2.7298 2.6996 2.6776 2.6609 2.6371 2.6211 2.6008 2.5884 2.5801 2.5379 10 0.975 3.3546 3.311 3.2794 3.2554 3.2214 3.1984 3.1694 3.1517 3.1399 3.0798 10 0.980 3.5728 3.5245 3.4895 3.463 3.4254 3.4 3.3679 3.3484 3.3354 3.269 10 0.990 4.3111 4.2469 4.2005 4.1653 4.1155 4.0819 4.0394 4.0137 3.9965 3.909 10 0.995 5.1528 5.0706 5.011 4.9659 4.9022 4.8592 4.805 4.7721 4.7501 4.6385 10 0.999 7.6041 7.4688 7.3711 7.2971 7.1927 7.1224 7.0338 6.9802 6.9443 6.7625 11 0.900 2.0953 2.0762 2.0623 2.0516 2.0364 2.0261 2.013 2.005 1.9997 1.9721 11 0.950 2.6014 2.5705 2.548 2.5309 2.5066 2.4901 2.4692 2.4566 2.448 2.4045 11 0.975 3.1616 3.1176 3.0856 3.0613 3.0268 3.0035 2.974 2.9561 2.9441 2.8828 11 0.980 3.3555 3.3069 3.2716 3.2448 3.2068 3.1811 3.1486 3.1289 3.1156 3.0482 11 0.990 4.0051 3.9411 3.8948 3.8596 3.8097 3.7761 3.7335 3.7077 3.6904 3.6025 11 0.995 4.7356 4.6543 4.5955 4.5508 4.4876 4.445 4.3912 4.3585 4.3367 4.2255 11 0.999 6.8147 6.6839 6.5894 6.5178 6.4165 6.3483 6.2623 6.2102 6.1753 5.9983 12 0.900 2.0312 2.0115 1.9971 1.9861 1.9704 1.9597 1.9461 1.9379 1.9323 1.9036 12 0.950 2.4977 2.4663 2.4433 2.4259 2.401 2.3842 2.3628 2.3498 2.341 2.2962 12 0.975 3.0077 2.9633 2.9309 2.9063 2.8714 2.8478 2.8178 2.7996 2.7874 2.7249 12 0.980 3.1828 3.1338 3.0982 3.0712 3.0328 3.0068 2.9739 2.9539 2.9405 2.872 12 0.990 3.7647 3.7008 3.6544 3.6192 3.5692 3.5355 3.4928 3.4668 3.4494 3.3608 12 0.995 4.4115 4.3309 4.2725 4.2282 4.1653 4.1229 4.0693 4.0368 4.0149 3.9039 12 0.999 6.2172 6.0898 5.9976 5.9278 5.829 5.7623 5.6782 5.6272 5.5931 5.4196 13 0.900 1.9778 1.9576 1.9428 1.9315 1.9153 1.9043 1.8903 1.8817 1.8759 1.8462 13 0.950 2.4123 2.3803 2.357 2.3392 2.3138 2.2966 2.2747 2.2614 2.2524 2.2064 13 0.975 2.8821 2.8372 2.8046 2.7797 2.7443 2.7204 2.69 2.6715 2.659 2.5955 13 0.980 3.0422 2.9929 2.9571 2.9298 2.891 2.8647 2.8314 2.8112 2.7975 2.728 13 0.990 3.571 3.507 3.4606 3.4253 3.3752 3.3413 3.2984 3.2723 3.2548 3.1654 13 0.995 4.1528 4.0727 4.0146 3.9704 3.9078 3.8655 3.812 3.7795 3.7577 3.6465 13 0.999 5.7505 5.6258 5.5355 5.467 5.37 5.3046 5.2219 5.1718 5.1381 4.9671 14 0.900 1.9326 1.9119 1.8968 1.8852 1.8686 1.8572 1.8428 1.834 1.828 1.7973 14 0.950 2.3407 2.3082 2.2845 2.2664 2.2405 2.2229 2.2006 2.187 2.1778 2.1307 14 0.975 2.7777 2.7324 2.6994 2.6742 2.6384 2.6142 2.5833 2.5646 2.5519 2.4872 14 0.980 2.9257 2.876 2.8399 2.8123 2.7732 2.7466 2.7129 2.6924 2.6786 2.608 14 0.990 3.4116 3.3476 3.301 3.2656 3.2153 3.1813 3.1381 3.1118 3.0942 3.004 14 0.995 3.9417 3.8619 3.804 3.76 3.6975 3.6552 3.6017 3.5692 3.5473 3.4359 14 0.999 5.3767 5.2542 5.1653 5.0979 5.0023 4.9378 4.8562 4.8067 4.7735 4.6043 15 0.900 1.8939 1.8728 1.8573 1.8454 1.8284 1.8168 1.8019 1.7929 1.7867 1.7551 15 0.950 2.2797 2.2468 2.2227 2.2043 2.178 2.1601 2.1373 2.1234 2.1141 2.0659 15 0.975 2.6894 2.6437 2.6104 2.585 2.5488 2.5242 2.493 2.4739 2.4611 2.3954 15 0.980 2.8274 2.7775 2.741 2.7132 2.6737 2.6469 2.6128 2.592 2.578 2.5063 Upper Percentiles of the F-distribution 15 For each N, D, P, the entry is the 100Pth Percentile for the F-distribution with N and D degrees of Freedom D P N25 N30 N35 N40 N50 N60 N80 N100 N120 N1000000 15 0.990 3.2782 3.2141 3.1674 3.1319 3.0814 3.0471 3.0037 2.9772 2.9595 2.8684 15 0.995 3.7662 3.6867 3.6289 3.585 3.5225 3.4803 3.4267 3.3941 3.3722 3.2602 15 0.999 5.071 4.9502 4.8625 4.7959 4.7015 4.6377 4.5569 4.5079 4.475 4.307 16 0.900 1.8603 1.8388 1.823 1.8108 1.7934 1.7816 1.7664 1.757 1.7507 1.7182 16 0.950 2.2272 2.1938 2.1694 2.1507 2.124 2.1058 2.0826 2.0685 2.0589 2.0096 16 0.975 2.6138 2.5678 2.5342 2.5085 2.4719 2.4471 2.4154 2.3961 2.3831 2.3163 16 0.980 2.7435 2.6932 2.6565 2.6285 2.5886 2.5614 2.527 2.5059 2.4918 2.419 16 0.990 3.165 3.1007 3.0539 3.0182 2.9675 2.933 2.8893 2.8627 2.8447 2.7528 16 0.995 3.6182 3.5389 3.4811 3.4372 3.3747 3.3324 3.2787 3.246 3.224 3.1115 16 0.999 4.8167 4.6972 4.6105 4.5446 4.4511 4.3878 4.3077 4.259 4.2263 4.0593 17 0.900 1.8309 1.809 1.7929 1.7805 1.7628 1.7506 1.7351 1.7255 1.7191 1.6856 17 0.950 2.1815 2.1477 2.1229 2.104 2.0769 2.0584 2.0348 2.0204 2.0107 1.9604 17 0.975 2.5484 2.502 2.4681 2.4422 2.4053 2.3801 2.3481 2.3285 2.3153 2.2474 17 0.980 2.671 2.6203 2.5834 2.5551 2.5148 2.4875 2.4526 2.4313 2.417 2.3432 17 0.990 3.0676 3.0032 2.9563 2.9205 2.8694 2.8348 2.7908 2.7639 2.7459 2.653 17 0.995 3.4916 3.4124 3.3547 3.3108 3.2482 3.2058 3.152 3.1192 3.0971 2.9839 17 0.999 4.6019 4.4836 4.3976 4.3323 4.2395 4.1767 4.097 4.0486 4.016 3.8496 18 0.900 1.8049 1.7827 1.7663 1.7537 1.7356 1.7232 1.7073 1.6976 1.691 1.6567 18 0.950 2.1413 2.1071 2.0821 2.0629 2.0354 2.0166 1.9927 1.978 1.9681 1.9168 18 0.975 2.4912 2.4445 2.4103 2.3842 2.3468 2.3214 2.289 2.2692 2.2558 2.1869 18 0.980 2.6076 2.5567 2.5195 2.491 2.4504 2.4227 2.3875 2.366 2.3515 2.2767 18 0.990 2.9831 2.9185 2.8714 2.8354 2.7841 2.7493 2.705 2.6779 2.6597 2.566 18 0.995 3.3822 3.303 3.2453 3.2014 3.1387 3.0962 3.0422 3.0093 2.9871 2.8732 18 0.999 4.4182 4.3009 4.2156 4.1507 4.0584 3.996 3.9167 3.8685 3.836 3.6699 19 0.900 1.7818 1.7592 1.7426 1.7298 1.7114 1.6988 1.6826 1.6726 1.6659 1.6308 19 0.950 2.1057 2.0712 2.0458 2.0264 1.9986 1.9795 1.9552 1.9403 1.9302 1.878 19 0.975 2.4408 2.3937 2.3593 2.3329 2.2952 2.2696 2.2368 2.2167 2.2032 2.1333 19 0.980 2.5519 2.5006 2.4632 2.4345 2.3935 2.3656 2.33 2.3083 2.2936 2.2178 19 0.990 2.9089 2.8442 2.7969 2.7608 2.7093 2.6742 2.6296 2.6023 2.5839 2.4893 19 0.995 3.2867 3.2075 3.1498 3.1058 3.043 3.0004 2.9462 2.9131 2.8908 2.7762 19 0.999 4.2594 4.1429 4.0581 3.9936 3.9018 3.8396 3.7606 3.7125 3.6801 3.5141 20 0.900 1.7611 1.7382 1.7213 1.7083 1.6896 1.6768 1.6603 1.6501 1.6433 1.6074 20 0.950 2.0739 2.0391 2.0135 1.9938 1.9656 1.9464 1.9217 1.9066 1.8963 1.8432 20 0.975 2.3959 2.3486 2.3139 2.2873 2.2493 2.2234 2.1902 2.1699 2.1562 2.0853 20 0.980 2.5024 2.4509 2.4131 2.3843 2.343 2.3148 2.2789 2.2569 2.2421 2.1653 20 0.990 2.8434 2.7785 2.731 2.6947 2.643 2.6077 2.5628 2.5353 2.5168 2.4212 20 0.995 3.2025 3.1234 3.0656 3.0215 2.9586 2.9159 2.8614 2.8282 2.8058 2.6904 20 0.999 4.1208 4.005 3.9207 3.8564 3.765 3.703 3.6242 3.5762 3.5438 3.3778 21 0.900 1.7424 1.7193 1.7021 1.689 1.67 1.6569 1.6401 1.6298 1.6228 1.5862 21 0.950 2.0454 2.0102 1.9844 1.9645 1.936 1.9165 1.8915 1.8761 1.8657 1.8117 21 0.975 2.3558 2.3082 2.2733 2.2465 2.2081 2.1819 2.1485 2.128 2.1141 2.0422 21 0.980 2.4581 2.4064 2.3684 2.3393 2.2977 2.2693 2.2331 2.2109 2.1958 2.1181 21 0.990 2.785 2.72 2.6723 2.6359 2.5838 2.5484 2.5032 2.4755 2.4568 2.3603 21 0.995 3.1279 3.0488 2.9909 2.9467 2.8837 2.8408 2.7861 2.7527 2.7302 2.614 21 0.999 3.9988 3.8836 3.7996 3.7357 3.6445 3.5827 3.504 3.456 3.4237 3.2575 22 0.900 1.7255 1.7021 1.6847 1.6714 1.6521 1.6389 1.6218 1.6113 1.6041 1.5668 22 0.950 2.0196 1.9842 1.9581 1.938 1.9092 1.8894 1.8641 1.8486 1.838 1.7831 22 0.975 2.3198 2.2718 2.2366 2.2097 2.171 2.1446 2.1108 2.0901 2.076 2.0032 22 0.980 2.4184 2.3663 2.3282 2.2989 2.257 2.2284 2.1918 2.1693 2.1542 2.0755 22 0.990 2.7328 2.6675 2.6197 2.5831 2.5308 2.4951 2.4496 2.4217 2.4029 2.3055 22 0.995 3.0613 2.9821 2.9241 2.8799 2.8167 2.7736 2.7187 2.6852 2.6625 2.5455 Upper Percentiles of the F-distribution 16 For each N, D, P, the entry is the 100Pth Percentile for the F-distribution with N and D degrees of Freedom D P N25 N30 N35 N40 N50 N60 N80 N100 N120 N1000000 22 0.999 3.8906 3.7759 3.6923 3.6285 3.5376 3.4759 3.3973 3.3493 3.317 3.1505 23 0.900 1.7101 1.6864 1.6689 1.6554 1.6358 1.6224 1.6051 1.5944 1.5871 1.549 23 0.950 1.9963 1.9605 1.9342 1.9139 1.8848 1.8648 1.8392 1.8234 1.8128 1.757 23 0.975 2.2871 2.2389 2.2035 2.1763 2.1374 2.1107 2.0766 2.0557 2.0415 1.9677 23 0.980 2.3825 2.3302 2.2918 2.2623 2.2201 2.1913 2.1543 2.1317 2.1164 2.0367 23 0.990 2.6856 2.6202 2.5722 2.5355 2.4829 2.4471 2.4013 2.3732 2.3542 2.2559 23 0.995 3.0014 2.9221 2.8641 2.8197 2.7564 2.7132 2.6581 2.6243 2.6015 2.4837 23 0.999 3.794 3.6798 3.5964 3.5328 3.4421 3.3804 3.3019 3.2539 3.2216 3.0548 24 0.900 1.696 1.6721 1.6544 1.6407 1.6209 1.6073 1.5897 1.5788 1.5715 1.5327 24 0.950 1.975 1.939 1.9124 1.892 1.8625 1.8424 1.8164 1.8005 1.7896 1.7331 24 0.975 2.2574 2.209 2.1733 2.146 2.1067 2.0799 2.0454 2.0243 2.0099 1.9353 24 0.980 2.3498 2.2973 2.2587 2.229 2.1865 2.1575 2.1202 2.0974 2.0819 2.0014 24 0.990 2.643 2.5773 2.5292 2.4923 2.4395 2.4035 2.3573 2.3291 2.31 2.2107 24 0.995 2.9472 2.8679 2.8098 2.7654 2.7018 2.6585 2.6031 2.5692 2.5463 2.4276 24 0.999 3.7073 3.5935 3.5103 3.4468 3.3562 3.2946 3.2161 3.1681 3.1357 2.9685 25 0.900 1.6831 1.6589 1.641 1.6272 1.6072 1.5934 1.5755 1.5645 1.557 1.5176 25 0.950 1.9554 1.9192 1.8924 1.8718 1.8421 1.8217 1.7955 1.7794 1.7684 1.711 25 0.975 2.2303 2.1816 2.1458 2.1183 2.0787 2.0516 2.0169 1.9955 1.9811 1.9055 25 0.980 2.32 2.2673 2.2284 2.1986 2.1559 2.1266 2.0891 2.066 2.0504 1.9689 25 0.990 2.6041 2.5383 2.49 2.453 2.3999 2.3637 2.3173 2.2888 2.2696 2.1694 25 0.995 2.8981 2.8187 2.7605 2.716 2.6522 2.6088 2.5532 2.5191 2.4961 2.3765 25 0.999 3.6291 3.5155 3.4325 3.3692 3.2787 3.2171 3.1386 3.0905 3.0581 2.8904 30 0.900 1.6316 1.6065 1.5877 1.5732 1.5522 1.5376 1.5187 1.5069 1.4989 1.4564 30 0.950 1.8782 1.8409 1.8132 1.7918 1.7609 1.7396 1.7121 1.695 1.6835 1.6223 30 0.975 2.1237 2.0739 2.0372 2.0089 1.9681 1.94 1.9039 1.8816 1.8664 1.7867 30 0.980 2.2032 2.1493 2.1096 2.079 2.035 2.0048 1.9658 1.9418 1.9255 1.8398 30 0.990 2.4526 2.386 2.3369 2.2992 2.245 2.2079 2.1601 2.1307 2.1108 2.0062 30 0.995 2.7076 2.6278 2.5691 2.5241 2.4594 2.4151 2.3584 2.3234 2.2998 2.176 30 0.999 3.3296 3.2171 3.1347 3.0716 2.9813 2.9196 2.8407 2.7923 2.7595 2.5889 35 0.900 1.595 1.5691 1.5497 1.5346 1.5127 1.4975 1.4776 1.4653 1.4568 1.4115 35 0.950 1.8239 1.7856 1.7571 1.7351 1.7032 1.6811 1.6525 1.6347 1.6226 1.558 35 0.975 2.0493 1.9986 1.9611 1.9321 1.8902 1.8613 1.824 1.8009 1.7851 1.7016 35 0.980 2.1218 2.0671 2.0266 1.9954 1.9503 1.9192 1.879 1.8542 1.8372 1.7476 35 0.990 2.348 2.2806 2.2309 2.1926 2.1374 2.0994 2.0505 2.0202 1.9996 1.891 35 0.995 2.5772 2.4969 2.4377 2.3922 2.3266 2.2816 2.2237 2.188 2.1637 2.0359 35 0.999 3.1283 3.0163 2.9341 2.8711 2.7806 2.7187 2.6391 2.5902 2.557 2.3829 40 0.900 1.5677 1.5411 1.5211 1.5056 1.483 1.4672 1.4465 1.4336 1.4248 1.3769 40 0.950 1.7835 1.7444 1.7154 1.6928 1.66 1.6373 1.6077 1.5892 1.5766 1.5089 40 0.975 1.9943 1.9429 1.9047 1.8752 1.8324 1.8028 1.7644 1.7405 1.7242 1.6371 40 0.980 2.0618 2.0064 1.9653 1.9335 1.8874 1.8556 1.8144 1.7888 1.7713 1.678 40 0.990 2.2714 2.2034 2.1531 2.1142 2.0581 2.0194 1.9694 1.9383 1.9172 1.8047 40 0.995 2.4823 2.4015 2.3418 2.2958 2.2295 2.1838 2.1249 2.0884 2.0636 1.9318 40 0.999 2.9838 2.8721 2.7899 2.7268 2.636 2.5737 2.4934 2.4439 2.4103 2.2326 45 0.900 1.5464 1.5193 1.4989 1.483 1.4597 1.4434 1.4221 1.4087 1.3995 1.3493 45 0.950 1.7522 1.7126 1.683 1.6599 1.6264 1.6031 1.5726 1.5536 1.5406 1.47 45 0.975 1.9521 1.9 1.8613 1.8313 1.7876 1.7574 1.7181 1.6935 1.6767 1.5864 45 0.980 2.0158 1.9597 1.918 1.8858 1.8389 1.8064 1.7643 1.738 1.72 1.6234 45 0.990 2.2129 2.1443 2.0934 2.0542 1.9972 1.9579 1.9069 1.8751 1.8535 1.7374 45 0.995 2.4101 2.3288 2.2687 2.2224 2.1553 2.109 2.0491 2.0119 1.9865 1.851 45 0.999 2.875 2.7635 2.6812 2.618 2.5268 2.464 2.3831 2.333 2.2989 2.1176 50 0.900 1.5294 1.5018 1.481 1.4648 1.4409 1.4242 1.4023 1.3885 1.3789 1.3267 Upper Percentiles of the F-distribution 17 For each N, D, P, the entry is the 100Pth Percentile for the F-distribution with N and D degrees of Freedom D P N25 N30 N35 N40 N50 N60 N80 N100 N120 N1000000 50 0.950 1.7273 1.6872 1.6571 1.6337 1.5995 1.5757 1.5445 1.5249 1.5115 1.4383 50 0.975 1.9186 1.8659 1.8267 1.7963 1.752 1.7211 1.681 1.6558 1.6386 1.5453 50 0.980 1.9793 1.9227 1.8805 1.8478 1.8003 1.7672 1.7242 1.6973 1.6789 1.5791 50 0.990 2.1667 2.0976 2.0463 2.0066 1.949 1.909 1.8571 1.8248 1.8026 1.6831 50 0.995 2.3533 2.2717 2.2112 2.1644 2.0967 2.0499 1.9891 1.9512 1.9254 1.7863 50 0.999 2.7902 2.6787 2.5964 2.5329 2.4413 2.3782 2.2965 2.2458 2.2113 2.0265 60 0.900 1.5039 1.4755 1.4541 1.4373 1.4126 1.3952 1.3722 1.3576 1.3476 1.2915 60 0.950 1.6902 1.6491 1.6183 1.5943 1.559 1.5343 1.5019 1.4814 1.4673 1.3893 60 0.975 1.8687 1.8152 1.7752 1.744 1.6985 1.6668 1.6252 1.599 1.581 1.4822 60 0.980 1.9251 1.8676 1.8247 1.7913 1.7425 1.7085 1.664 1.6361 1.6168 1.5114 60 0.990 2.0984 2.0285 1.9764 1.936 1.8772 1.8363 1.7828 1.7493 1.7263 1.6007 60 0.995 2.2697 2.1874 2.1263 2.0789 2.01 1.9622 1.8998 1.8609 1.8341 1.6885 60 0.999 2.6665 2.5549 2.4724 2.4086 2.3162 2.2523 2.1693 2.1175 2.0821 1.8905 70 0.900 1.4857 1.4567 1.4348 1.4176 1.3922 1.3742 1.3503 1.3352 1.3246 1.2652 70 0.950 1.6638 1.622 1.5906 1.5661 1.53 1.5046 1.4711 1.4498 1.4351 1.3529 70 0.975 1.8334 1.7792 1.7386 1.7069 1.6604 1.6279 1.5851 1.5581 1.5394 1.4357 70 0.980 1.8869 1.8286 1.7851 1.7511 1.7014 1.6666 1.6209 1.592 1.5721 1.4616 70 0.990 2.0503 1.9797 1.9271 1.8861 1.8263 1.7846 1.7298 1.6954 1.6717 1.5405 70 0.995 2.2112 2.1283 2.0666 2.0186 1.9488 1.9002 1.8365 1.7966 1.7691 1.6176 70 0.999 2.5807 2.4689 2.3861 2.322 2.2289 2.1643 2.0801 2.0274 1.9912 1.7932 80 0.900 1.472 1.4426 1.4203 1.4027 1.3767 1.3583 1.3337 1.318 1.3071 1.2446 80 0.950 1.644 1.6017 1.5699 1.5449 1.5081 1.4821 1.4477 1.4259 1.4107 1.3247 80 0.975 1.8071 1.7523 1.7112 1.679 1.6318 1.5987 1.5549 1.5271 1.5079 1.3998 80 0.980 1.8583 1.7996 1.7555 1.7211 1.6705 1.6351 1.5884 1.5588 1.5383 1.4232 80 0.990 2.0146 1.9435 1.8904 1.8489 1.7883 1.7459 1.6901 1.6548 1.6305 1.4942 80 0.995 2.1678 2.0845 2.0223 1.9739 1.9033 1.854 1.7892 1.7484 1.7203 1.5634 80 0.999 2.5176 2.4057 2.3226 2.2582 2.1644 2.0992 2.0139 1.9604 1.9235 1.7197 90 0.900 1.4613 1.4315 1.4089 1.3911 1.3646 1.3457 1.3206 1.3044 1.2932 1.228 90 0.950 1.6286 1.5859 1.5537 1.5284 1.491 1.4645 1.4294 1.407 1.3914 1.302 90 0.975 1.7867 1.7315 1.6899 1.6574 1.6095 1.5758 1.5312 1.5028 1.4831 1.371 90 0.980 1.8363 1.777 1.7325 1.6977 1.6465 1.6106 1.5629 1.5327 1.5117 1.3925 90 0.990 1.9871 1.9155 1.8619 1.8201 1.7588 1.7158 1.6591 1.6231 1.5982 1.4574 90 0.995 2.1345 2.0507 1.9881 1.9394 1.8681 1.8182 1.7525 1.7109 1.6822 1.5204 90 0.999 2.4693 2.3572 2.2739 2.2092 2.1149 2.0491 1.9629 1.9086 1.8712 1.6619 100 0.900 1.4528 1.4227 1.3998 1.3817 1.3548 1.3356 1.31 1.2934 1.2819 1.2142 100 0.950 1.6163 1.5733 1.5407 1.5151 1.4772 1.4504 1.4146 1.3917 1.3757 1.2832 100 0.975 1.7705 1.7148 1.6729 1.6401 1.5917 1.5575 1.5122 1.4833 1.4631 1.3473 100 0.980 1.8187 1.7591 1.7142 1.6791 1.6273 1.5909 1.5425 1.5117 1.4902 1.3672 100 0.990 1.9652 1.8933 1.8393 1.7972 1.7353 1.6918 1.6342 1.5977 1.5723 1.4273 100 0.995 2.108 2.0239 1.961 1.9119 1.84 1.7896 1.7231 1.6809 1.6516 1.4853 100 0.999 2.4311 2.3189 2.2353 2.1704 2.0756 2.0094 1.9224 1.8674 1.8294 1.6151 110 0.900 1.4458 1.4154 1.3923 1.374 1.3468 1.3273 1.3012 1.2843 1.2725 1.2026 110 0.950 1.6063 1.563 1.5301 1.5043 1.466 1.4388 1.4024 1.3791 1.3628 1.2674 110 0.975 1.7572 1.7013 1.6591 1.6259 1.5771 1.5425 1.4965 1.4671 1.4466 1.3274 110 0.980 1.8043 1.7444 1.6992 1.6638 1.6116 1.5747 1.5257 1.4944 1.4725 1.346 110 0.990 1.9473 1.8751 1.8209 1.7784 1.716 1.6721 1.6139 1.5767 1.5509 1.402 110 0.995 2.0864 2.0021 1.9389 1.8895 1.8172 1.7663 1.699 1.6562 1.6265 1.456 110 0.999 2.4002 2.2878 2.2041 2.1389 2.0437 1.977 1.8893 1.8337 1.7952 1.5762 120 0.900 1.4399 1.4094 1.3861 1.3676 1.34 1.3203 1.2938 1.2767 1.2646 1.1926 120 0.950 1.598 1.5543 1.5213 1.4952 1.4565 1.429 1.3922 1.3685 1.3519 1.2539 120 0.975 1.7462 1.6899 1.6475 1.6141 1.5649 1.5299 1.4834 1.4536 1.4327 1.3105 Upper Percentiles of the F-distribution 18 For each N, D, P, the entry is the 100Pth Percentile for the F-distribution with N and D degrees of Freedom D P N25 N30 N35 N40 N50 N60 N80 N100 N120 N1000000 120 0.980 1.7924 1.7322 1.6868 1.6511 1.5985 1.5612 1.5117 1.4799 1.4577 1.3279 120 0.990 1.9325 1.86 1.8055 1.7628 1.7 1.6557 1.5968 1.5592 1.533 1.3805 120 0.995 2.0686 1.984 1.9205 1.8709 1.7981 1.7469 1.6789 1.6357 1.6055 1.4311 120 0.999 2.3746 2.2621 2.1782 2.1128 2.0172 1.9502 1.8618 1.8057 1.7667 1.5433 1000000 0.900 1.3753 1.3419 1.316 1.2951 1.2634 1.24 1.2072 1.185 1.1686 1.0026 1000000 0.950 1.5061 1.4591 1.4229 1.394 1.3501 1.318 1.2735 1.2434 1.2214 1.0033 1000000 0.975 1.6259 1.566 1.5201 1.4836 1.4284 1.3883 1.3329 1.2956 1.2685 1.0039 1000000 0.980 1.6627 1.5987 1.5498 1.5109 1.4523 1.4097 1.3509 1.3114 1.2827 1.0041 1000000 0.990 1.7726 1.6964 1.6384 1.5923 1.5231 1.473 1.4041 1.3581 1.3246 1.0047 1000000 0.995 1.8771 1.7891 1.7222 1.6692 1.5898 1.5326 1.454 1.4017 1.3638 1.0052 1000000 0.999 2.1048 1.9901 1.9034 1.8351 1.7332 1.6602 1.5605 1.4945 1.4469 1.0062