F Table: F Distribution Critical Values
Six complete F tables, one for each significance level from 0.10 down to 0.001, with numerator degrees of freedom to infinity and denominator degrees of freedom to 500 and infinity.
At a glance
- Computes
- F critical values at six significance levels, any numerator and denominator df
- You supply
- Numerator degrees of freedom, denominator degrees of freedom, and a significance level
- Use when
- You want the printable grids, a left-tail value, or a value off them
- Not for
- One critical value for one alpha and one df pair Critical Value Calculator
This page is the grid, and for the F distribution that means six grids: one for each significance level 0.10, 0.05, 0.025, 0.01, 0.005 and 0.001. For one alpha and one pair of degrees of freedom, use the critical value calculator. Both pages use the same quantile function. Read the numerator first: F on 10 and 12 degrees of freedom is not F on 12 and 10.
Type numerator and denominator degrees of freedom to highlight a cell.
Probability density; F, df1 3, df2 20
Most-used F values
| Numerator df | df2 10 | df2 20 | df2 30 | df2 60 |
|---|---|---|---|---|
| 1 | 4.9646 | 4.3512 | 4.1709 | 4.0012 |
| 2 | 4.1028 | 3.4928 | 3.3158 | 3.1504 |
| 3 | 3.7083 | 3.0984 | 2.9223 | 2.7581 |
Numerator first, and why it matters
F(df1, df2) is not F(df2, df1). At alpha 0.05, F(10, 12) is 2.7534 while F(12, 10) is 2.9130. An observed statistic of 2.85 clears one threshold and not the other.
Significance level 0.1 (cumulative probability 0.9)
| df2 / df1 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 12 | 15 | 20 | 24 | 30 | 40 | 60 | 120 | ∞ |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 39.8635 | 49.5000 | 53.5932 | 55.8330 | 57.2401 | 58.2044 | 58.9060 | 59.4390 | 59.8576 | 60.1950 | 60.7052 | 61.2203 | 61.7403 | 62.0020 | 62.2650 | 62.5291 | 62.7943 | 63.0606 | 63.3281 |
| 2 | 8.5263 | 9.0000 | 9.1618 | 9.2434 | 9.2926 | 9.3255 | 9.3491 | 9.3668 | 9.3805 | 9.3916 | 9.4081 | 9.4247 | 9.4413 | 9.4496 | 9.4579 | 9.4662 | 9.4746 | 9.4829 | 9.4912 |
| 3 | 5.5383 | 5.4624 | 5.3908 | 5.3426 | 5.3092 | 5.2847 | 5.2662 | 5.2517 | 5.2400 | 5.2304 | 5.2156 | 5.2003 | 5.1845 | 5.1764 | 5.1681 | 5.1597 | 5.1512 | 5.1425 | 5.1337 |
| 4 | 4.5448 | 4.3246 | 4.1909 | 4.1072 | 4.0506 | 4.0097 | 3.9790 | 3.9549 | 3.9357 | 3.9199 | 3.8955 | 3.8704 | 3.8443 | 3.8310 | 3.8174 | 3.8036 | 3.7896 | 3.7753 | 3.7607 |
| 5 | 4.0604 | 3.7797 | 3.6195 | 3.5202 | 3.4530 | 3.4045 | 3.3679 | 3.3393 | 3.3163 | 3.2974 | 3.2682 | 3.2380 | 3.2067 | 3.1905 | 3.1741 | 3.1573 | 3.1402 | 3.1228 | 3.1050 |
| 6 | 3.7759 | 3.4633 | 3.2888 | 3.1808 | 3.1075 | 3.0546 | 3.0145 | 2.9830 | 2.9577 | 2.9369 | 2.9047 | 2.8712 | 2.8363 | 2.8183 | 2.8000 | 2.7812 | 2.7620 | 2.7423 | 2.7222 |
| 7 | 3.5894 | 3.2574 | 3.0741 | 2.9605 | 2.8833 | 2.8274 | 2.7849 | 2.7516 | 2.7247 | 2.7025 | 2.6681 | 2.6322 | 2.5947 | 2.5753 | 2.5555 | 2.5351 | 2.5142 | 2.4928 | 2.4708 |
| 8 | 3.4579 | 3.1131 | 2.9238 | 2.8064 | 2.7264 | 2.6683 | 2.6241 | 2.5893 | 2.5612 | 2.5380 | 2.5020 | 2.4642 | 2.4246 | 2.4041 | 2.3830 | 2.3614 | 2.3391 | 2.3162 | 2.2926 |
| 9 | 3.3603 | 3.0065 | 2.8129 | 2.6927 | 2.6106 | 2.5509 | 2.5053 | 2.4694 | 2.4403 | 2.4163 | 2.3789 | 2.3396 | 2.2983 | 2.2768 | 2.2547 | 2.2320 | 2.2085 | 2.1843 | 2.1592 |
| 10 | 3.2850 | 2.9245 | 2.7277 | 2.6053 | 2.5216 | 2.4606 | 2.4140 | 2.3772 | 2.3473 | 2.3226 | 2.2841 | 2.2435 | 2.2007 | 2.1784 | 2.1554 | 2.1317 | 2.1072 | 2.0818 | 2.0554 |
| 11 | 3.2252 | 2.8595 | 2.6602 | 2.5362 | 2.4512 | 2.3891 | 2.3416 | 2.3040 | 2.2735 | 2.2482 | 2.2087 | 2.1671 | 2.1230 | 2.1000 | 2.0762 | 2.0516 | 2.0261 | 1.9997 | 1.9721 |
| 12 | 3.1765 | 2.8068 | 2.6055 | 2.4801 | 2.3940 | 2.3310 | 2.2828 | 2.2446 | 2.2135 | 2.1878 | 2.1474 | 2.1049 | 2.0597 | 2.0360 | 2.0115 | 1.9861 | 1.9597 | 1.9323 | 1.9036 |
| 13 | 3.1362 | 2.7632 | 2.5603 | 2.4337 | 2.3467 | 2.2830 | 2.2341 | 2.1953 | 2.1638 | 2.1376 | 2.0966 | 2.0532 | 2.0070 | 1.9827 | 1.9576 | 1.9315 | 1.9043 | 1.8759 | 1.8462 |
| 14 | 3.1022 | 2.7265 | 2.5222 | 2.3947 | 2.3069 | 2.2426 | 2.1931 | 2.1539 | 2.1220 | 2.0954 | 2.0537 | 2.0095 | 1.9625 | 1.9377 | 1.9119 | 1.8852 | 1.8572 | 1.8280 | 1.7973 |
| 15 | 3.0732 | 2.6952 | 2.4898 | 2.3614 | 2.2730 | 2.2081 | 2.1582 | 2.1185 | 2.0862 | 2.0593 | 2.0171 | 1.9722 | 1.9243 | 1.8990 | 1.8728 | 1.8454 | 1.8168 | 1.7867 | 1.7551 |
| 16 | 3.0481 | 2.6682 | 2.4618 | 2.3327 | 2.2438 | 2.1783 | 2.1280 | 2.0880 | 2.0553 | 2.0281 | 1.9854 | 1.9399 | 1.8913 | 1.8656 | 1.8388 | 1.8108 | 1.7816 | 1.7507 | 1.7182 |
| 17 | 3.0262 | 2.6446 | 2.4374 | 2.3077 | 2.2183 | 2.1524 | 2.1017 | 2.0613 | 2.0284 | 2.0009 | 1.9577 | 1.9117 | 1.8624 | 1.8362 | 1.8090 | 1.7805 | 1.7506 | 1.7191 | 1.6856 |
| 18 | 3.0070 | 2.6239 | 2.4160 | 2.2858 | 2.1958 | 2.1296 | 2.0785 | 2.0379 | 2.0047 | 1.9770 | 1.9333 | 1.8868 | 1.8368 | 1.8103 | 1.7827 | 1.7537 | 1.7232 | 1.6910 | 1.6567 |
| 19 | 2.9899 | 2.6056 | 2.3970 | 2.2663 | 2.1760 | 2.1094 | 2.0580 | 2.0171 | 1.9836 | 1.9557 | 1.9117 | 1.8647 | 1.8142 | 1.7873 | 1.7592 | 1.7298 | 1.6988 | 1.6659 | 1.6308 |
| 20 | 2.9747 | 2.5893 | 2.3801 | 2.2489 | 2.1582 | 2.0913 | 2.0397 | 1.9985 | 1.9649 | 1.9367 | 1.8924 | 1.8449 | 1.7938 | 1.7667 | 1.7382 | 1.7083 | 1.6768 | 1.6433 | 1.6074 |
| 21 | 2.9610 | 2.5746 | 2.3649 | 2.2333 | 2.1423 | 2.0751 | 2.0233 | 1.9819 | 1.9480 | 1.9197 | 1.8750 | 1.8271 | 1.7756 | 1.7481 | 1.7193 | 1.6890 | 1.6569 | 1.6228 | 1.5862 |
| 22 | 2.9486 | 2.5613 | 2.3512 | 2.2193 | 2.1279 | 2.0605 | 2.0084 | 1.9668 | 1.9327 | 1.9043 | 1.8593 | 1.8111 | 1.7590 | 1.7312 | 1.7021 | 1.6714 | 1.6389 | 1.6041 | 1.5668 |
| 23 | 2.9374 | 2.5493 | 2.3387 | 2.2065 | 2.1149 | 2.0472 | 1.9949 | 1.9531 | 1.9189 | 1.8903 | 1.8450 | 1.7964 | 1.7439 | 1.7159 | 1.6864 | 1.6554 | 1.6224 | 1.5871 | 1.5490 |
| 24 | 2.9271 | 2.5383 | 2.3274 | 2.1949 | 2.1030 | 2.0351 | 1.9826 | 1.9407 | 1.9063 | 1.8775 | 1.8319 | 1.7831 | 1.7302 | 1.7019 | 1.6721 | 1.6407 | 1.6073 | 1.5715 | 1.5327 |
| 25 | 2.9177 | 2.5283 | 2.3170 | 2.1842 | 2.0922 | 2.0241 | 1.9714 | 1.9292 | 1.8947 | 1.8658 | 1.8200 | 1.7708 | 1.7175 | 1.6890 | 1.6589 | 1.6272 | 1.5934 | 1.5570 | 1.5176 |
| 26 | 2.9091 | 2.5191 | 2.3075 | 2.1745 | 2.0822 | 2.0139 | 1.9610 | 1.9188 | 1.8841 | 1.8550 | 1.8090 | 1.7596 | 1.7059 | 1.6771 | 1.6468 | 1.6147 | 1.5805 | 1.5437 | 1.5036 |
| 27 | 2.9012 | 2.5106 | 2.2987 | 2.1655 | 2.0730 | 2.0045 | 1.9515 | 1.9091 | 1.8743 | 1.8451 | 1.7989 | 1.7492 | 1.6951 | 1.6662 | 1.6356 | 1.6032 | 1.5686 | 1.5313 | 1.4906 |
| 28 | 2.8938 | 2.5028 | 2.2906 | 2.1571 | 2.0645 | 1.9959 | 1.9427 | 1.9001 | 1.8652 | 1.8359 | 1.7895 | 1.7395 | 1.6852 | 1.6560 | 1.6252 | 1.5925 | 1.5575 | 1.5198 | 1.4784 |
| 29 | 2.8870 | 2.4955 | 2.2831 | 2.1494 | 2.0566 | 1.9878 | 1.9345 | 1.8918 | 1.8568 | 1.8274 | 1.7808 | 1.7306 | 1.6759 | 1.6465 | 1.6155 | 1.5825 | 1.5472 | 1.5090 | 1.4670 |
| 30 | 2.8807 | 2.4887 | 2.2761 | 2.1422 | 2.0492 | 1.9803 | 1.9269 | 1.8841 | 1.8490 | 1.8195 | 1.7727 | 1.7223 | 1.6673 | 1.6377 | 1.6065 | 1.5732 | 1.5376 | 1.4989 | 1.4564 |
| 40 | 2.8354 | 2.4404 | 2.2261 | 2.0909 | 1.9968 | 1.9269 | 1.8725 | 1.8289 | 1.7929 | 1.7627 | 1.7146 | 1.6624 | 1.6052 | 1.5741 | 1.5411 | 1.5056 | 1.4672 | 1.4248 | 1.3769 |
| 50 | 2.8087 | 2.4120 | 2.1967 | 2.0608 | 1.9660 | 1.8954 | 1.8405 | 1.7963 | 1.7598 | 1.7291 | 1.6802 | 1.6269 | 1.5681 | 1.5361 | 1.5018 | 1.4648 | 1.4242 | 1.3789 | 1.3267 |
| 60 | 2.7911 | 2.3933 | 2.1774 | 2.0410 | 1.9457 | 1.8747 | 1.8194 | 1.7748 | 1.7380 | 1.7070 | 1.6574 | 1.6034 | 1.5435 | 1.5107 | 1.4755 | 1.4373 | 1.3952 | 1.3476 | 1.2915 |
| 80 | 2.7693 | 2.3701 | 2.1535 | 2.0165 | 1.9206 | 1.8491 | 1.7933 | 1.7483 | 1.7110 | 1.6796 | 1.6292 | 1.5741 | 1.5128 | 1.4790 | 1.4426 | 1.4027 | 1.3583 | 1.3071 | 1.2446 |
| 100 | 2.7564 | 2.3564 | 2.1394 | 2.0019 | 1.9057 | 1.8339 | 1.7778 | 1.7324 | 1.6949 | 1.6632 | 1.6124 | 1.5566 | 1.4943 | 1.4600 | 1.4227 | 1.3817 | 1.3356 | 1.2819 | 1.2142 |
| 120 | 2.7478 | 2.3473 | 2.1300 | 1.9923 | 1.8959 | 1.8238 | 1.7675 | 1.7220 | 1.6842 | 1.6524 | 1.6012 | 1.5450 | 1.4821 | 1.4472 | 1.4094 | 1.3676 | 1.3203 | 1.2646 | 1.1926 |
| 200 | 2.7308 | 2.3293 | 2.1114 | 1.9732 | 1.8763 | 1.8038 | 1.7470 | 1.7011 | 1.6630 | 1.6308 | 1.5789 | 1.5218 | 1.4575 | 1.4217 | 1.3826 | 1.3390 | 1.2891 | 1.2285 | 1.1439 |
| 500 | 2.7156 | 2.3132 | 2.0948 | 1.9561 | 1.8588 | 1.7859 | 1.7288 | 1.6825 | 1.6441 | 1.6115 | 1.5590 | 1.5010 | 1.4354 | 1.3986 | 1.3582 | 1.3129 | 1.2600 | 1.1936 | 1.0871 |
| ∞ | 2.7055 | 2.3026 | 2.0838 | 1.9449 | 1.8473 | 1.7741 | 1.7167 | 1.6702 | 1.6315 | 1.5987 | 1.5458 | 1.4871 | 1.4206 | 1.3832 | 1.3419 | 1.2951 | 1.2400 | 1.1686 | 1.0000 |
Significance level 0.05 (cumulative probability 0.95)
| df2 / df1 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 12 | 15 | 20 | 24 | 30 | 40 | 60 | 120 | ∞ |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 161.448 | 199.500 | 215.707 | 224.583 | 230.162 | 233.986 | 236.768 | 238.883 | 240.543 | 241.882 | 243.906 | 245.950 | 248.013 | 249.052 | 250.095 | 251.143 | 252.196 | 253.253 | 254.314 |
| 2 | 18.5128 | 19.0000 | 19.1643 | 19.2468 | 19.2964 | 19.3295 | 19.3532 | 19.3710 | 19.3848 | 19.3959 | 19.4125 | 19.4291 | 19.4458 | 19.4541 | 19.4624 | 19.4707 | 19.4791 | 19.4874 | 19.4957 |
| 3 | 10.1280 | 9.5521 | 9.2766 | 9.1172 | 9.0135 | 8.9406 | 8.8867 | 8.8452 | 8.8123 | 8.7855 | 8.7446 | 8.7029 | 8.6602 | 8.6385 | 8.6166 | 8.5944 | 8.5720 | 8.5494 | 8.5264 |
| 4 | 7.7086 | 6.9443 | 6.5914 | 6.3882 | 6.2561 | 6.1631 | 6.0942 | 6.0410 | 5.9988 | 5.9644 | 5.9117 | 5.8578 | 5.8025 | 5.7744 | 5.7459 | 5.7170 | 5.6877 | 5.6581 | 5.6281 |
| 5 | 6.6079 | 5.7861 | 5.4095 | 5.1922 | 5.0503 | 4.9503 | 4.8759 | 4.8183 | 4.7725 | 4.7351 | 4.6777 | 4.6188 | 4.5581 | 4.5272 | 4.4957 | 4.4638 | 4.4314 | 4.3985 | 4.3650 |
| 6 | 5.9874 | 5.1433 | 4.7571 | 4.5337 | 4.3874 | 4.2839 | 4.2067 | 4.1468 | 4.0990 | 4.0600 | 3.9999 | 3.9381 | 3.8742 | 3.8415 | 3.8082 | 3.7743 | 3.7398 | 3.7047 | 3.6689 |
| 7 | 5.5914 | 4.7374 | 4.3468 | 4.1203 | 3.9715 | 3.8660 | 3.7870 | 3.7257 | 3.6767 | 3.6365 | 3.5747 | 3.5107 | 3.4445 | 3.4105 | 3.3758 | 3.3404 | 3.3043 | 3.2674 | 3.2298 |
| 8 | 5.3177 | 4.4590 | 4.0662 | 3.8379 | 3.6875 | 3.5806 | 3.5005 | 3.4381 | 3.3881 | 3.3472 | 3.2839 | 3.2184 | 3.1503 | 3.1152 | 3.0794 | 3.0428 | 3.0053 | 2.9669 | 2.9276 |
| 9 | 5.1174 | 4.2565 | 3.8625 | 3.6331 | 3.4817 | 3.3738 | 3.2927 | 3.2296 | 3.1789 | 3.1373 | 3.0729 | 3.0061 | 2.9365 | 2.9005 | 2.8637 | 2.8259 | 2.7872 | 2.7475 | 2.7067 |
| 10 | 4.9646 | 4.1028 | 3.7083 | 3.4780 | 3.3258 | 3.2172 | 3.1355 | 3.0717 | 3.0204 | 2.9782 | 2.9130 | 2.8450 | 2.7740 | 2.7372 | 2.6996 | 2.6609 | 2.6211 | 2.5801 | 2.5379 |
| 11 | 4.8443 | 3.9823 | 3.5874 | 3.3567 | 3.2039 | 3.0946 | 3.0123 | 2.9480 | 2.8962 | 2.8536 | 2.7876 | 2.7186 | 2.6464 | 2.6090 | 2.5705 | 2.5309 | 2.4901 | 2.4480 | 2.4045 |
| 12 | 4.7472 | 3.8853 | 3.4903 | 3.2592 | 3.1059 | 2.9961 | 2.9134 | 2.8486 | 2.7964 | 2.7534 | 2.6866 | 2.6169 | 2.5436 | 2.5055 | 2.4663 | 2.4259 | 2.3842 | 2.3410 | 2.2962 |
| 13 | 4.6672 | 3.8056 | 3.4105 | 3.1791 | 3.0254 | 2.9153 | 2.8321 | 2.7669 | 2.7144 | 2.6710 | 2.6037 | 2.5331 | 2.4589 | 2.4202 | 2.3803 | 2.3392 | 2.2966 | 2.2524 | 2.2064 |
| 14 | 4.6001 | 3.7389 | 3.3439 | 3.1122 | 2.9582 | 2.8477 | 2.7642 | 2.6987 | 2.6458 | 2.6022 | 2.5342 | 2.4630 | 2.3879 | 2.3487 | 2.3082 | 2.2664 | 2.2229 | 2.1778 | 2.1307 |
| 15 | 4.5431 | 3.6823 | 3.2874 | 3.0556 | 2.9013 | 2.7905 | 2.7066 | 2.6408 | 2.5876 | 2.5437 | 2.4753 | 2.4034 | 2.3275 | 2.2878 | 2.2468 | 2.2043 | 2.1601 | 2.1141 | 2.0658 |
| 16 | 4.4940 | 3.6337 | 3.2389 | 3.0069 | 2.8524 | 2.7413 | 2.6572 | 2.5911 | 2.5377 | 2.4935 | 2.4247 | 2.3522 | 2.2756 | 2.2354 | 2.1938 | 2.1507 | 2.1058 | 2.0589 | 2.0096 |
| 17 | 4.4513 | 3.5915 | 3.1968 | 2.9647 | 2.8100 | 2.6987 | 2.6143 | 2.5480 | 2.4943 | 2.4499 | 2.3807 | 2.3077 | 2.2304 | 2.1898 | 2.1477 | 2.1040 | 2.0584 | 2.0107 | 1.9604 |
| 18 | 4.4139 | 3.5546 | 3.1599 | 2.9277 | 2.7729 | 2.6613 | 2.5767 | 2.5102 | 2.4563 | 2.4117 | 2.3421 | 2.2686 | 2.1906 | 2.1497 | 2.1071 | 2.0629 | 2.0166 | 1.9681 | 1.9168 |
| 19 | 4.3807 | 3.5219 | 3.1274 | 2.8951 | 2.7401 | 2.6283 | 2.5435 | 2.4768 | 2.4227 | 2.3779 | 2.3080 | 2.2341 | 2.1555 | 2.1141 | 2.0712 | 2.0264 | 1.9795 | 1.9302 | 1.8780 |
| 20 | 4.3512 | 3.4928 | 3.0984 | 2.8661 | 2.7109 | 2.5990 | 2.5140 | 2.4471 | 2.3928 | 2.3479 | 2.2776 | 2.2033 | 2.1242 | 2.0825 | 2.0391 | 1.9938 | 1.9464 | 1.8963 | 1.8432 |
| 21 | 4.3248 | 3.4668 | 3.0725 | 2.8401 | 2.6848 | 2.5727 | 2.4876 | 2.4205 | 2.3660 | 2.3210 | 2.2504 | 2.1757 | 2.0960 | 2.0540 | 2.0102 | 1.9645 | 1.9165 | 1.8657 | 1.8117 |
| 22 | 4.3009 | 3.4434 | 3.0491 | 2.8167 | 2.6613 | 2.5491 | 2.4638 | 2.3965 | 2.3419 | 2.2967 | 2.2258 | 2.1508 | 2.0707 | 2.0283 | 1.9842 | 1.9380 | 1.8894 | 1.8380 | 1.7831 |
| 23 | 4.2793 | 3.4221 | 3.0280 | 2.7955 | 2.6400 | 2.5277 | 2.4422 | 2.3748 | 2.3201 | 2.2747 | 2.2036 | 2.1282 | 2.0476 | 2.0050 | 1.9605 | 1.9139 | 1.8648 | 1.8128 | 1.7570 |
| 24 | 4.2597 | 3.4028 | 3.0088 | 2.7763 | 2.6207 | 2.5082 | 2.4226 | 2.3551 | 2.3002 | 2.2547 | 2.1834 | 2.1077 | 2.0267 | 1.9838 | 1.9390 | 1.8920 | 1.8424 | 1.7896 | 1.7330 |
| 25 | 4.2417 | 3.3852 | 2.9912 | 2.7587 | 2.6030 | 2.4904 | 2.4047 | 2.3371 | 2.2821 | 2.2365 | 2.1649 | 2.0889 | 2.0075 | 1.9643 | 1.9192 | 1.8718 | 1.8217 | 1.7684 | 1.7110 |
| 26 | 4.2252 | 3.3690 | 2.9752 | 2.7426 | 2.5868 | 2.4741 | 2.3883 | 2.3205 | 2.2655 | 2.2197 | 2.1479 | 2.0716 | 1.9898 | 1.9464 | 1.9010 | 1.8533 | 1.8027 | 1.7488 | 1.6906 |
| 27 | 4.2100 | 3.3541 | 2.9604 | 2.7278 | 2.5719 | 2.4591 | 2.3732 | 2.3053 | 2.2501 | 2.2043 | 2.1323 | 2.0558 | 1.9736 | 1.9299 | 1.8842 | 1.8361 | 1.7851 | 1.7306 | 1.6717 |
| 28 | 4.1960 | 3.3404 | 2.9467 | 2.7141 | 2.5581 | 2.4453 | 2.3593 | 2.2913 | 2.2360 | 2.1900 | 2.1179 | 2.0411 | 1.9586 | 1.9147 | 1.8687 | 1.8203 | 1.7689 | 1.7138 | 1.6541 |
| 29 | 4.1830 | 3.3277 | 2.9340 | 2.7014 | 2.5454 | 2.4324 | 2.3463 | 2.2783 | 2.2229 | 2.1768 | 2.1045 | 2.0275 | 1.9446 | 1.9005 | 1.8543 | 1.8055 | 1.7537 | 1.6981 | 1.6376 |
| 30 | 4.1709 | 3.3158 | 2.9223 | 2.6896 | 2.5336 | 2.4205 | 2.3343 | 2.2662 | 2.2107 | 2.1646 | 2.0921 | 2.0148 | 1.9317 | 1.8874 | 1.8409 | 1.7918 | 1.7396 | 1.6835 | 1.6223 |
| 40 | 4.0847 | 3.2317 | 2.8387 | 2.6060 | 2.4495 | 2.3359 | 2.2490 | 2.1802 | 2.1240 | 2.0772 | 2.0035 | 1.9245 | 1.8389 | 1.7929 | 1.7444 | 1.6928 | 1.6373 | 1.5766 | 1.5089 |
| 50 | 4.0343 | 3.1826 | 2.7900 | 2.5572 | 2.4004 | 2.2864 | 2.1992 | 2.1299 | 2.0734 | 2.0261 | 1.9515 | 1.8714 | 1.7841 | 1.7371 | 1.6872 | 1.6337 | 1.5757 | 1.5115 | 1.4383 |
| 60 | 4.0012 | 3.1504 | 2.7581 | 2.5252 | 2.3683 | 2.2541 | 2.1665 | 2.0970 | 2.0401 | 1.9926 | 1.9174 | 1.8364 | 1.7480 | 1.7001 | 1.6491 | 1.5943 | 1.5343 | 1.4673 | 1.3893 |
| 80 | 3.9604 | 3.1108 | 2.7188 | 2.4859 | 2.3287 | 2.2142 | 2.1263 | 2.0564 | 1.9991 | 1.9512 | 1.8753 | 1.7932 | 1.7032 | 1.6542 | 1.6017 | 1.5449 | 1.4821 | 1.4107 | 1.3247 |
| 100 | 3.9361 | 3.0873 | 2.6955 | 2.4626 | 2.3053 | 2.1906 | 2.1025 | 2.0323 | 1.9748 | 1.9267 | 1.8503 | 1.7675 | 1.6764 | 1.6267 | 1.5733 | 1.5151 | 1.4504 | 1.3757 | 1.2832 |
| 120 | 3.9201 | 3.0718 | 2.6802 | 2.4472 | 2.2899 | 2.1750 | 2.0868 | 2.0164 | 1.9588 | 1.9105 | 1.8337 | 1.7505 | 1.6587 | 1.6084 | 1.5543 | 1.4952 | 1.4290 | 1.3519 | 1.2539 |
| 200 | 3.8884 | 3.0411 | 2.6498 | 2.4168 | 2.2592 | 2.1441 | 2.0556 | 1.9849 | 1.9269 | 1.8783 | 1.8008 | 1.7166 | 1.6233 | 1.5720 | 1.5164 | 1.4551 | 1.3856 | 1.3024 | 1.1885 |
| 500 | 3.8601 | 3.0138 | 2.6227 | 2.3898 | 2.2320 | 2.1167 | 2.0279 | 1.9569 | 1.8986 | 1.8496 | 1.7715 | 1.6864 | 1.5916 | 1.5392 | 1.4821 | 1.4186 | 1.3455 | 1.2551 | 1.1132 |
| ∞ | 3.8415 | 2.9957 | 2.6049 | 2.3719 | 2.2141 | 2.0986 | 2.0096 | 1.9384 | 1.8799 | 1.8307 | 1.7522 | 1.6664 | 1.5705 | 1.5173 | 1.4591 | 1.3940 | 1.3180 | 1.2214 | 1.0000 |
Significance level 0.025 (cumulative probability 0.975)
| df2 / df1 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 12 | 15 | 20 | 24 | 30 | 40 | 60 | 120 | ∞ |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 647.789 | 799.500 | 864.163 | 899.583 | 921.848 | 937.111 | 948.217 | 956.656 | 963.285 | 968.627 | 976.708 | 984.867 | 993.103 | 997.249 | 1001.41 | 1005.60 | 1009.80 | 1014.02 | 1018.26 |
| 2 | 38.5063 | 39.0000 | 39.1655 | 39.2484 | 39.2982 | 39.3315 | 39.3552 | 39.3730 | 39.3869 | 39.3980 | 39.4146 | 39.4313 | 39.4479 | 39.4562 | 39.4646 | 39.4729 | 39.4812 | 39.4896 | 39.4979 |
| 3 | 17.4434 | 16.0441 | 15.4392 | 15.1010 | 14.8848 | 14.7347 | 14.6244 | 14.5399 | 14.4731 | 14.4189 | 14.3366 | 14.2527 | 14.1674 | 14.1241 | 14.0805 | 14.0365 | 13.9921 | 13.9473 | 13.9021 |
| 4 | 12.2179 | 10.6491 | 9.9792 | 9.6045 | 9.3645 | 9.1973 | 9.0741 | 8.9796 | 8.9047 | 8.8439 | 8.7512 | 8.6565 | 8.5599 | 8.5109 | 8.4613 | 8.4111 | 8.3604 | 8.3092 | 8.2573 |
| 5 | 10.0070 | 8.4336 | 7.7636 | 7.3879 | 7.1464 | 6.9777 | 6.8531 | 6.7572 | 6.6811 | 6.6192 | 6.5245 | 6.4277 | 6.3286 | 6.2780 | 6.2269 | 6.1750 | 6.1225 | 6.0693 | 6.0153 |
| 6 | 8.8131 | 7.2599 | 6.5988 | 6.2272 | 5.9876 | 5.8198 | 5.6955 | 5.5996 | 5.5234 | 5.4613 | 5.3662 | 5.2687 | 5.1684 | 5.1172 | 5.0652 | 5.0125 | 4.9589 | 4.9044 | 4.8491 |
| 7 | 8.0727 | 6.5415 | 5.8898 | 5.5226 | 5.2852 | 5.1186 | 4.9949 | 4.8993 | 4.8232 | 4.7611 | 4.6658 | 4.5678 | 4.4667 | 4.4150 | 4.3624 | 4.3089 | 4.2544 | 4.1989 | 4.1423 |
| 8 | 7.5709 | 6.0595 | 5.4160 | 5.0526 | 4.8173 | 4.6517 | 4.5286 | 4.4333 | 4.3572 | 4.2951 | 4.1997 | 4.1012 | 3.9995 | 3.9472 | 3.8940 | 3.8398 | 3.7844 | 3.7279 | 3.6702 |
| 9 | 7.2093 | 5.7147 | 5.0781 | 4.7181 | 4.4844 | 4.3197 | 4.1970 | 4.1020 | 4.0260 | 3.9639 | 3.8682 | 3.7694 | 3.6669 | 3.6142 | 3.5604 | 3.5055 | 3.4493 | 3.3918 | 3.3329 |
| 10 | 6.9367 | 5.4564 | 4.8256 | 4.4683 | 4.2361 | 4.0721 | 3.9498 | 3.8549 | 3.7790 | 3.7168 | 3.6209 | 3.5217 | 3.4185 | 3.3654 | 3.3110 | 3.2554 | 3.1984 | 3.1399 | 3.0798 |
| 11 | 6.7241 | 5.2559 | 4.6300 | 4.2751 | 4.0440 | 3.8807 | 3.7586 | 3.6638 | 3.5879 | 3.5257 | 3.4296 | 3.3299 | 3.2261 | 3.1725 | 3.1176 | 3.0613 | 3.0035 | 2.9441 | 2.8828 |
| 12 | 6.5538 | 5.0959 | 4.4742 | 4.1212 | 3.8911 | 3.7283 | 3.6065 | 3.5118 | 3.4358 | 3.3736 | 3.2773 | 3.1772 | 3.0728 | 3.0187 | 2.9633 | 2.9063 | 2.8478 | 2.7874 | 2.7249 |
| 13 | 6.4143 | 4.9653 | 4.3472 | 3.9959 | 3.7667 | 3.6043 | 3.4827 | 3.3880 | 3.3120 | 3.2497 | 3.1532 | 3.0527 | 2.9477 | 2.8932 | 2.8372 | 2.7797 | 2.7204 | 2.6590 | 2.5955 |
| 14 | 6.2979 | 4.8567 | 4.2417 | 3.8919 | 3.6634 | 3.5014 | 3.3799 | 3.2853 | 3.2093 | 3.1469 | 3.0502 | 2.9493 | 2.8437 | 2.7888 | 2.7324 | 2.6742 | 2.6142 | 2.5519 | 2.4872 |
| 15 | 6.1995 | 4.7650 | 4.1528 | 3.8043 | 3.5764 | 3.4147 | 3.2934 | 3.1987 | 3.1227 | 3.0602 | 2.9633 | 2.8621 | 2.7559 | 2.7006 | 2.6437 | 2.5850 | 2.5242 | 2.4611 | 2.3953 |
| 16 | 6.1151 | 4.6867 | 4.0768 | 3.7294 | 3.5021 | 3.3406 | 3.2194 | 3.1248 | 3.0488 | 2.9862 | 2.8890 | 2.7875 | 2.6808 | 2.6252 | 2.5678 | 2.5085 | 2.4471 | 2.3831 | 2.3163 |
| 17 | 6.0420 | 4.6189 | 4.0112 | 3.6648 | 3.4379 | 3.2767 | 3.1556 | 3.0610 | 2.9849 | 2.9222 | 2.8249 | 2.7230 | 2.6158 | 2.5598 | 2.5020 | 2.4422 | 2.3801 | 2.3153 | 2.2474 |
| 18 | 5.9781 | 4.5597 | 3.9539 | 3.6083 | 3.3820 | 3.2209 | 3.0999 | 3.0053 | 2.9291 | 2.8664 | 2.7689 | 2.6667 | 2.5590 | 2.5027 | 2.4445 | 2.3842 | 2.3214 | 2.2558 | 2.1869 |
| 19 | 5.9216 | 4.5075 | 3.9034 | 3.5587 | 3.3327 | 3.1718 | 3.0509 | 2.9563 | 2.8801 | 2.8172 | 2.7196 | 2.6171 | 2.5089 | 2.4523 | 2.3937 | 2.3329 | 2.2696 | 2.2032 | 2.1333 |
| 20 | 5.8715 | 4.4613 | 3.8587 | 3.5147 | 3.2891 | 3.1283 | 3.0074 | 2.9128 | 2.8365 | 2.7737 | 2.6758 | 2.5731 | 2.4645 | 2.4076 | 2.3486 | 2.2873 | 2.2234 | 2.1562 | 2.0853 |
| 21 | 5.8266 | 4.4199 | 3.8188 | 3.4754 | 3.2501 | 3.0895 | 2.9686 | 2.8740 | 2.7977 | 2.7348 | 2.6368 | 2.5338 | 2.4247 | 2.3675 | 2.3082 | 2.2465 | 2.1819 | 2.1141 | 2.0422 |
| 22 | 5.7863 | 4.3828 | 3.7829 | 3.4401 | 3.2151 | 3.0546 | 2.9338 | 2.8392 | 2.7628 | 2.6998 | 2.6017 | 2.4984 | 2.3890 | 2.3315 | 2.2718 | 2.2097 | 2.1446 | 2.0760 | 2.0032 |
| 23 | 5.7498 | 4.3492 | 3.7505 | 3.4083 | 3.1835 | 3.0232 | 2.9023 | 2.8077 | 2.7313 | 2.6682 | 2.5699 | 2.4665 | 2.3567 | 2.2989 | 2.2389 | 2.1763 | 2.1107 | 2.0415 | 1.9677 |
| 24 | 5.7166 | 4.3187 | 3.7211 | 3.3794 | 3.1548 | 2.9946 | 2.8738 | 2.7791 | 2.7027 | 2.6396 | 2.5411 | 2.4374 | 2.3273 | 2.2693 | 2.2090 | 2.1460 | 2.0799 | 2.0099 | 1.9353 |
| 25 | 5.6864 | 4.2909 | 3.6943 | 3.3530 | 3.1287 | 2.9685 | 2.8478 | 2.7531 | 2.6766 | 2.6135 | 2.5149 | 2.4110 | 2.3005 | 2.2422 | 2.1816 | 2.1183 | 2.0516 | 1.9811 | 1.9055 |
| 26 | 5.6586 | 4.2655 | 3.6697 | 3.3289 | 3.1048 | 2.9447 | 2.8240 | 2.7293 | 2.6528 | 2.5896 | 2.4908 | 2.3867 | 2.2759 | 2.2174 | 2.1565 | 2.0928 | 2.0257 | 1.9545 | 1.8781 |
| 27 | 5.6331 | 4.2421 | 3.6472 | 3.3067 | 3.0828 | 2.9228 | 2.8021 | 2.7074 | 2.6309 | 2.5676 | 2.4688 | 2.3644 | 2.2533 | 2.1946 | 2.1334 | 2.0693 | 2.0018 | 1.9299 | 1.8527 |
| 28 | 5.6096 | 4.2205 | 3.6264 | 3.2863 | 3.0626 | 2.9027 | 2.7820 | 2.6872 | 2.6106 | 2.5473 | 2.4484 | 2.3438 | 2.2324 | 2.1735 | 2.1121 | 2.0477 | 1.9797 | 1.9072 | 1.8291 |
| 29 | 5.5878 | 4.2006 | 3.6072 | 3.2674 | 3.0438 | 2.8840 | 2.7633 | 2.6686 | 2.5919 | 2.5286 | 2.4295 | 2.3248 | 2.2131 | 2.1540 | 2.0923 | 2.0276 | 1.9591 | 1.8861 | 1.8072 |
| 30 | 5.5675 | 4.1821 | 3.5894 | 3.2499 | 3.0265 | 2.8667 | 2.7460 | 2.6513 | 2.5746 | 2.5112 | 2.4120 | 2.3072 | 2.1952 | 2.1359 | 2.0739 | 2.0089 | 1.9400 | 1.8664 | 1.7867 |
| 40 | 5.4239 | 4.0510 | 3.4633 | 3.1261 | 2.9037 | 2.7444 | 2.6238 | 2.5289 | 2.4519 | 2.3882 | 2.2882 | 2.1819 | 2.0677 | 2.0069 | 1.9429 | 1.8752 | 1.8028 | 1.7242 | 1.6371 |
| 50 | 5.3403 | 3.9749 | 3.3902 | 3.0544 | 2.8327 | 2.6736 | 2.5530 | 2.4579 | 2.3808 | 2.3168 | 2.2162 | 2.1090 | 1.9933 | 1.9313 | 1.8659 | 1.7963 | 1.7211 | 1.6386 | 1.5452 |
| 60 | 5.2856 | 3.9253 | 3.3425 | 3.0077 | 2.7863 | 2.6274 | 2.5068 | 2.4117 | 2.3344 | 2.2702 | 2.1692 | 2.0613 | 1.9445 | 1.8817 | 1.8152 | 1.7440 | 1.6668 | 1.5810 | 1.4821 |
| 80 | 5.2184 | 3.8643 | 3.2841 | 2.9504 | 2.7295 | 2.5708 | 2.4502 | 2.3549 | 2.2775 | 2.2130 | 2.1115 | 2.0026 | 1.8843 | 1.8204 | 1.7523 | 1.6790 | 1.5987 | 1.5079 | 1.3997 |
| 100 | 5.1786 | 3.8284 | 3.2496 | 2.9166 | 2.6961 | 2.5374 | 2.4168 | 2.3215 | 2.2439 | 2.1793 | 2.0773 | 1.9679 | 1.8486 | 1.7839 | 1.7148 | 1.6401 | 1.5575 | 1.4631 | 1.3473 |
| 120 | 5.1523 | 3.8046 | 3.2269 | 2.8943 | 2.6740 | 2.5154 | 2.3948 | 2.2994 | 2.2217 | 2.1570 | 2.0548 | 1.9450 | 1.8249 | 1.7597 | 1.6899 | 1.6141 | 1.5299 | 1.4327 | 1.3104 |
| 200 | 5.1004 | 3.7578 | 3.1820 | 2.8503 | 2.6304 | 2.4720 | 2.3513 | 2.2558 | 2.1780 | 2.1130 | 2.0103 | 1.8996 | 1.7780 | 1.7117 | 1.6403 | 1.5621 | 1.4742 | 1.3700 | 1.2290 |
| 500 | 5.0543 | 3.7162 | 3.1423 | 2.8114 | 2.5919 | 2.4335 | 2.3129 | 2.2172 | 2.1392 | 2.0740 | 1.9708 | 1.8592 | 1.7362 | 1.6687 | 1.5957 | 1.5151 | 1.4231 | 1.3105 | 1.1365 |
| ∞ | 5.0239 | 3.6889 | 3.1161 | 2.7858 | 2.5665 | 2.4082 | 2.2875 | 2.1918 | 2.1136 | 2.0483 | 1.9447 | 1.8326 | 1.7085 | 1.6402 | 1.5660 | 1.4835 | 1.3883 | 1.2684 | 1.0000 |
Significance level 0.01 (cumulative probability 0.99)
| df2 / df1 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 12 | 15 | 20 | 24 | 30 | 40 | 60 | 120 | ∞ |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 4052.18 | 4999.50 | 5403.35 | 5624.58 | 5763.65 | 5858.99 | 5928.36 | 5981.07 | 6022.47 | 6055.85 | 6106.32 | 6157.28 | 6208.73 | 6234.63 | 6260.65 | 6286.78 | 6313.03 | 6339.39 | 6365.86 |
| 2 | 98.5025 | 99.0000 | 99.1662 | 99.2494 | 99.2993 | 99.3326 | 99.3564 | 99.3742 | 99.3881 | 99.3992 | 99.4159 | 99.4325 | 99.4492 | 99.4575 | 99.4658 | 99.4742 | 99.4825 | 99.4908 | 99.4992 |
| 3 | 34.1162 | 30.8165 | 29.4567 | 28.7099 | 28.2371 | 27.9107 | 27.6717 | 27.4892 | 27.3452 | 27.2287 | 27.0518 | 26.8722 | 26.6898 | 26.5975 | 26.5045 | 26.4108 | 26.3164 | 26.2211 | 26.1252 |
| 4 | 21.1977 | 18.0000 | 16.6944 | 15.9770 | 15.5219 | 15.2069 | 14.9758 | 14.7989 | 14.6591 | 14.5459 | 14.3736 | 14.1982 | 14.0196 | 13.9291 | 13.8377 | 13.7454 | 13.6522 | 13.5581 | 13.4631 |
| 5 | 16.2582 | 13.2739 | 12.0600 | 11.3919 | 10.9670 | 10.6723 | 10.4555 | 10.2893 | 10.1578 | 10.0510 | 9.8883 | 9.7222 | 9.5526 | 9.4665 | 9.3793 | 9.2912 | 9.2020 | 9.1118 | 9.0204 |
| 6 | 13.7450 | 10.9248 | 9.7795 | 9.1483 | 8.7459 | 8.4661 | 8.2600 | 8.1017 | 7.9761 | 7.8741 | 7.7183 | 7.5590 | 7.3958 | 7.3127 | 7.2285 | 7.1432 | 7.0567 | 6.9690 | 6.8800 |
| 7 | 12.2464 | 9.5466 | 8.4513 | 7.8466 | 7.4604 | 7.1914 | 6.9928 | 6.8400 | 6.7188 | 6.6201 | 6.4691 | 6.3143 | 6.1554 | 6.0743 | 5.9920 | 5.9084 | 5.8236 | 5.7373 | 5.6495 |
| 8 | 11.2586 | 8.6491 | 7.5910 | 7.0061 | 6.6318 | 6.3707 | 6.1776 | 6.0289 | 5.9106 | 5.8143 | 5.6667 | 5.5151 | 5.3591 | 5.2793 | 5.1981 | 5.1156 | 5.0316 | 4.9461 | 4.8588 |
| 9 | 10.5614 | 8.0215 | 6.9919 | 6.4221 | 6.0569 | 5.8018 | 5.6129 | 5.4671 | 5.3511 | 5.2565 | 5.1114 | 4.9621 | 4.8080 | 4.7290 | 4.6486 | 4.5666 | 4.4831 | 4.3978 | 4.3105 |
| 10 | 10.0443 | 7.5594 | 6.5523 | 5.9943 | 5.6363 | 5.3858 | 5.2001 | 5.0567 | 4.9424 | 4.8491 | 4.7059 | 4.5581 | 4.4054 | 4.3269 | 4.2469 | 4.1653 | 4.0819 | 3.9965 | 3.9090 |
| 11 | 9.6460 | 7.2057 | 6.2167 | 5.6683 | 5.3160 | 5.0692 | 4.8861 | 4.7445 | 4.6315 | 4.5393 | 4.3974 | 4.2509 | 4.0990 | 4.0209 | 3.9411 | 3.8596 | 3.7761 | 3.6904 | 3.6024 |
| 12 | 9.3302 | 6.9266 | 5.9525 | 5.4120 | 5.0643 | 4.8206 | 4.6395 | 4.4994 | 4.3875 | 4.2961 | 4.1553 | 4.0096 | 3.8584 | 3.7805 | 3.7008 | 3.6192 | 3.5355 | 3.4494 | 3.3608 |
| 13 | 9.0738 | 6.7010 | 5.7394 | 5.2053 | 4.8616 | 4.6204 | 4.4410 | 4.3021 | 4.1911 | 4.1003 | 3.9603 | 3.8154 | 3.6646 | 3.5868 | 3.5070 | 3.4253 | 3.3413 | 3.2548 | 3.1654 |
| 14 | 8.8616 | 6.5149 | 5.5639 | 5.0354 | 4.6950 | 4.4558 | 4.2779 | 4.1399 | 4.0297 | 3.9394 | 3.8001 | 3.6557 | 3.5052 | 3.4274 | 3.3476 | 3.2656 | 3.1813 | 3.0942 | 3.0040 |
| 15 | 8.6831 | 6.3589 | 5.4170 | 4.8932 | 4.5556 | 4.3183 | 4.1415 | 4.0045 | 3.8948 | 3.8049 | 3.6662 | 3.5222 | 3.3719 | 3.2940 | 3.2141 | 3.1319 | 3.0471 | 2.9595 | 2.8684 |
| 16 | 8.5310 | 6.2262 | 5.2922 | 4.7726 | 4.4374 | 4.2016 | 4.0259 | 3.8896 | 3.7804 | 3.6909 | 3.5527 | 3.4089 | 3.2587 | 3.1808 | 3.1007 | 3.0182 | 2.9330 | 2.8447 | 2.7528 |
| 17 | 8.3997 | 6.1121 | 5.1850 | 4.6690 | 4.3359 | 4.1015 | 3.9267 | 3.7910 | 3.6822 | 3.5931 | 3.4552 | 3.3117 | 3.1615 | 3.0835 | 3.0032 | 2.9205 | 2.8348 | 2.7459 | 2.6530 |
| 18 | 8.2854 | 6.0129 | 5.0919 | 4.5790 | 4.2479 | 4.0146 | 3.8406 | 3.7054 | 3.5971 | 3.5082 | 3.3706 | 3.2273 | 3.0771 | 2.9990 | 2.9185 | 2.8354 | 2.7493 | 2.6597 | 2.5660 |
| 19 | 8.1849 | 5.9259 | 5.0103 | 4.5003 | 4.1708 | 3.9386 | 3.7653 | 3.6305 | 3.5225 | 3.4338 | 3.2965 | 3.1533 | 3.0031 | 2.9249 | 2.8442 | 2.7608 | 2.6742 | 2.5839 | 2.4893 |
| 20 | 8.0960 | 5.8489 | 4.9382 | 4.4307 | 4.1027 | 3.8714 | 3.6987 | 3.5644 | 3.4567 | 3.3682 | 3.2311 | 3.0880 | 2.9377 | 2.8594 | 2.7785 | 2.6947 | 2.6077 | 2.5168 | 2.4212 |
| 21 | 8.0166 | 5.7804 | 4.8740 | 4.3688 | 4.0421 | 3.8117 | 3.6396 | 3.5056 | 3.3981 | 3.3098 | 3.1730 | 3.0300 | 2.8796 | 2.8010 | 2.7200 | 2.6359 | 2.5484 | 2.4568 | 2.3603 |
| 22 | 7.9454 | 5.7190 | 4.8166 | 4.3134 | 3.9880 | 3.7583 | 3.5867 | 3.4530 | 3.3458 | 3.2576 | 3.1209 | 2.9779 | 2.8274 | 2.7488 | 2.6675 | 2.5831 | 2.4951 | 2.4029 | 2.3055 |
| 23 | 7.8811 | 5.6637 | 4.7649 | 4.2636 | 3.9392 | 3.7102 | 3.5390 | 3.4057 | 3.2986 | 3.2106 | 3.0740 | 2.9311 | 2.7805 | 2.7017 | 2.6202 | 2.5355 | 2.4471 | 2.3542 | 2.2558 |
| 24 | 7.8229 | 5.6136 | 4.7181 | 4.2184 | 3.8951 | 3.6667 | 3.4959 | 3.3629 | 3.2560 | 3.1681 | 3.0316 | 2.8887 | 2.7380 | 2.6591 | 2.5773 | 2.4923 | 2.4035 | 2.3100 | 2.2107 |
| 25 | 7.7698 | 5.5680 | 4.6755 | 4.1774 | 3.8550 | 3.6272 | 3.4568 | 3.3239 | 3.2172 | 3.1294 | 2.9931 | 2.8502 | 2.6993 | 2.6203 | 2.5383 | 2.4530 | 2.3637 | 2.2696 | 2.1694 |
| 26 | 7.7213 | 5.5263 | 4.6366 | 4.1400 | 3.8183 | 3.5911 | 3.4210 | 3.2884 | 3.1818 | 3.0941 | 2.9578 | 2.8150 | 2.6640 | 2.5848 | 2.5026 | 2.4170 | 2.3273 | 2.2325 | 2.1315 |
| 27 | 7.6767 | 5.4881 | 4.6009 | 4.1056 | 3.7848 | 3.5580 | 3.3882 | 3.2558 | 3.1494 | 3.0618 | 2.9256 | 2.7827 | 2.6316 | 2.5522 | 2.4699 | 2.3840 | 2.2938 | 2.1985 | 2.0965 |
| 28 | 7.6356 | 5.4529 | 4.5681 | 4.0740 | 3.7539 | 3.5276 | 3.3581 | 3.2259 | 3.1195 | 3.0320 | 2.8959 | 2.7530 | 2.6017 | 2.5223 | 2.4397 | 2.3535 | 2.2629 | 2.1670 | 2.0642 |
| 29 | 7.5977 | 5.4204 | 4.5378 | 4.0449 | 3.7254 | 3.4995 | 3.3303 | 3.1982 | 3.0920 | 3.0045 | 2.8685 | 2.7256 | 2.5742 | 2.4946 | 2.4118 | 2.3253 | 2.2344 | 2.1379 | 2.0342 |
| 30 | 7.5625 | 5.3903 | 4.5097 | 4.0179 | 3.6990 | 3.4735 | 3.3045 | 3.1726 | 3.0665 | 2.9791 | 2.8431 | 2.7002 | 2.5487 | 2.4689 | 2.3860 | 2.2992 | 2.2079 | 2.1108 | 2.0062 |
| 40 | 7.3141 | 5.1785 | 4.3126 | 3.8283 | 3.5138 | 3.2910 | 3.1238 | 2.9930 | 2.8876 | 2.8005 | 2.6648 | 2.5216 | 2.3689 | 2.2880 | 2.2034 | 2.1142 | 2.0194 | 1.9172 | 1.8047 |
| 50 | 7.1706 | 5.0566 | 4.1993 | 3.7195 | 3.4077 | 3.1864 | 3.0202 | 2.8900 | 2.7850 | 2.6981 | 2.5625 | 2.4190 | 2.2652 | 2.1835 | 2.0976 | 2.0066 | 1.9090 | 1.8026 | 1.6831 |
| 60 | 7.0771 | 4.9774 | 4.1259 | 3.6490 | 3.3389 | 3.1187 | 2.9530 | 2.8233 | 2.7185 | 2.6318 | 2.4961 | 2.3523 | 2.1978 | 2.1154 | 2.0285 | 1.9360 | 1.8363 | 1.7263 | 1.6006 |
| 80 | 6.9627 | 4.8807 | 4.0363 | 3.5631 | 3.2550 | 3.0361 | 2.8713 | 2.7420 | 2.6374 | 2.5508 | 2.4151 | 2.2709 | 2.1153 | 2.0318 | 1.9435 | 1.8489 | 1.7459 | 1.6305 | 1.4942 |
| 100 | 6.8953 | 4.8239 | 3.9837 | 3.5127 | 3.2059 | 2.9877 | 2.8233 | 2.6943 | 2.5898 | 2.5033 | 2.3676 | 2.2230 | 2.0666 | 1.9826 | 1.8933 | 1.7972 | 1.6918 | 1.5723 | 1.4272 |
| 120 | 6.8509 | 4.7865 | 3.9491 | 3.4795 | 3.1735 | 2.9559 | 2.7918 | 2.6629 | 2.5586 | 2.4721 | 2.3363 | 2.1915 | 2.0346 | 1.9500 | 1.8600 | 1.7628 | 1.6557 | 1.5330 | 1.3805 |
| 200 | 6.7633 | 4.7129 | 3.8810 | 3.4143 | 3.1100 | 2.8933 | 2.7298 | 2.6012 | 2.4971 | 2.4106 | 2.2747 | 2.1294 | 1.9713 | 1.8857 | 1.7941 | 1.6945 | 1.5833 | 1.4527 | 1.2785 |
| 500 | 6.6858 | 4.6478 | 3.8210 | 3.3569 | 3.0540 | 2.8381 | 2.6751 | 2.5469 | 2.4429 | 2.3565 | 2.2204 | 2.0746 | 1.9152 | 1.8285 | 1.7353 | 1.6332 | 1.5174 | 1.3774 | 1.1644 |
| ∞ | 6.6349 | 4.6052 | 3.7816 | 3.3192 | 3.0173 | 2.8020 | 2.6393 | 2.5113 | 2.4073 | 2.3209 | 2.1847 | 2.0385 | 1.8783 | 1.7908 | 1.6964 | 1.5923 | 1.4730 | 1.3246 | 1.0000 |
Significance level 0.005 (cumulative probability 0.995)
No second published table covers this significance level. Its 740 continuous cells are checked against the reciprocal identity and direct survival residual; the remaining doubly-infinite point-mass cell is exactly 1.
| df2 / df1 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 12 | 15 | 20 | 24 | 30 | 40 | 60 | 120 | ∞ |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 16210.7 | 19999.5 | 21614.7 | 22499.6 | 23055.8 | 23437.1 | 23714.6 | 23925.4 | 24091.0 | 24224.5 | 24426.4 | 24630.2 | 24836.0 | 24939.6 | 25043.6 | 25148.2 | 25253.1 | 25358.6 | 25464.5 |
| 2 | 198.501 | 199.000 | 199.166 | 199.250 | 199.300 | 199.333 | 199.357 | 199.375 | 199.388 | 199.400 | 199.416 | 199.433 | 199.450 | 199.458 | 199.466 | 199.475 | 199.483 | 199.491 | 199.500 |
| 3 | 55.5520 | 49.7993 | 47.4672 | 46.1946 | 45.3916 | 44.8385 | 44.4341 | 44.1256 | 43.8824 | 43.6858 | 43.3874 | 43.0847 | 42.7775 | 42.6222 | 42.4658 | 42.3082 | 42.1494 | 41.9895 | 41.8283 |
| 4 | 31.3328 | 26.2843 | 24.2591 | 23.1545 | 22.4564 | 21.9746 | 21.6217 | 21.3520 | 21.1391 | 20.9667 | 20.7047 | 20.4383 | 20.1673 | 20.0300 | 19.8915 | 19.7518 | 19.6107 | 19.4684 | 19.3247 |
| 5 | 22.7848 | 18.3138 | 16.5298 | 15.5561 | 14.9396 | 14.5133 | 14.2004 | 13.9610 | 13.7716 | 13.6182 | 13.3845 | 13.1463 | 12.9035 | 12.7802 | 12.6556 | 12.5297 | 12.4024 | 12.2737 | 12.1435 |
| 6 | 18.6350 | 14.5441 | 12.9166 | 12.0275 | 11.4637 | 11.0730 | 10.7859 | 10.5658 | 10.3915 | 10.2500 | 10.0343 | 9.8140 | 9.5888 | 9.4742 | 9.3582 | 9.2408 | 9.1219 | 9.0015 | 8.8793 |
| 7 | 16.2356 | 12.4040 | 10.8824 | 10.0505 | 9.5221 | 9.1553 | 8.8854 | 8.6781 | 8.5138 | 8.3803 | 8.1764 | 7.9678 | 7.7540 | 7.6450 | 7.5345 | 7.4224 | 7.3088 | 7.1933 | 7.0760 |
| 8 | 14.6882 | 11.0424 | 9.5965 | 8.8051 | 8.3018 | 7.9520 | 7.6941 | 7.4959 | 7.3386 | 7.2106 | 7.0149 | 6.8143 | 6.6082 | 6.5029 | 6.3961 | 6.2875 | 6.1772 | 6.0649 | 5.9506 |
| 9 | 13.6136 | 10.1067 | 8.7171 | 7.9559 | 7.4712 | 7.1339 | 6.8849 | 6.6933 | 6.5411 | 6.4172 | 6.2274 | 6.0325 | 5.8318 | 5.7292 | 5.6248 | 5.5186 | 5.4104 | 5.3001 | 5.1875 |
| 10 | 12.8265 | 9.4270 | 8.0807 | 7.3428 | 6.8724 | 6.5446 | 6.3025 | 6.1159 | 5.9676 | 5.8467 | 5.6613 | 5.4707 | 5.2740 | 5.1732 | 5.0706 | 4.9659 | 4.8592 | 4.7501 | 4.6385 |
| 11 | 12.2263 | 8.9122 | 7.6004 | 6.8809 | 6.4217 | 6.1016 | 5.8648 | 5.6821 | 5.5368 | 5.4183 | 5.2363 | 5.0489 | 4.8552 | 4.7557 | 4.6543 | 4.5508 | 4.4450 | 4.3367 | 4.2255 |
| 12 | 11.7542 | 8.5096 | 7.2258 | 6.5211 | 6.0711 | 5.7570 | 5.5245 | 5.3451 | 5.2021 | 5.0855 | 4.9062 | 4.7213 | 4.5299 | 4.4314 | 4.3309 | 4.2282 | 4.1229 | 4.0149 | 3.9039 |
| 13 | 11.3735 | 8.1865 | 6.9258 | 6.2335 | 5.7910 | 5.4819 | 5.2529 | 5.0761 | 4.9351 | 4.8199 | 4.6429 | 4.4600 | 4.2703 | 4.1726 | 4.0727 | 3.9704 | 3.8655 | 3.7577 | 3.6465 |
| 14 | 11.0603 | 7.9216 | 6.6804 | 5.9984 | 5.5623 | 5.2574 | 5.0313 | 4.8566 | 4.7173 | 4.6034 | 4.4281 | 4.2468 | 4.0585 | 3.9614 | 3.8619 | 3.7600 | 3.6552 | 3.5473 | 3.4359 |
| 15 | 10.7980 | 7.7008 | 6.4760 | 5.8029 | 5.3721 | 5.0708 | 4.8473 | 4.6744 | 4.5364 | 4.4235 | 4.2497 | 4.0698 | 3.8826 | 3.7859 | 3.6867 | 3.5850 | 3.4803 | 3.3722 | 3.2602 |
| 16 | 10.5755 | 7.5138 | 6.3034 | 5.6378 | 5.2117 | 4.9134 | 4.6920 | 4.5207 | 4.3838 | 4.2719 | 4.0994 | 3.9205 | 3.7342 | 3.6378 | 3.5389 | 3.4372 | 3.3324 | 3.2240 | 3.1115 |
| 17 | 10.3842 | 7.3536 | 6.1556 | 5.4967 | 5.0746 | 4.7789 | 4.5594 | 4.3894 | 4.2535 | 4.1424 | 3.9709 | 3.7929 | 3.6073 | 3.5112 | 3.4124 | 3.3108 | 3.2058 | 3.0971 | 2.9839 |
| 18 | 10.2181 | 7.2148 | 6.0278 | 5.3746 | 4.9560 | 4.6627 | 4.4448 | 4.2759 | 4.1410 | 4.0305 | 3.8599 | 3.6827 | 3.4977 | 3.4017 | 3.3030 | 3.2014 | 3.0962 | 2.9871 | 2.8732 |
| 19 | 10.0725 | 7.0935 | 5.9161 | 5.2681 | 4.8526 | 4.5614 | 4.3448 | 4.1770 | 4.0428 | 3.9329 | 3.7631 | 3.5866 | 3.4020 | 3.3062 | 3.2075 | 3.1058 | 3.0004 | 2.8908 | 2.7762 |
| 20 | 9.9439 | 6.9865 | 5.8177 | 5.1743 | 4.7616 | 4.4721 | 4.2569 | 4.0900 | 3.9564 | 3.8470 | 3.6779 | 3.5020 | 3.3178 | 3.2220 | 3.1234 | 3.0215 | 2.9159 | 2.8058 | 2.6904 |
| 21 | 9.8295 | 6.8914 | 5.7304 | 5.0911 | 4.6809 | 4.3931 | 4.1789 | 4.0128 | 3.8799 | 3.7709 | 3.6024 | 3.4270 | 3.2431 | 3.1474 | 3.0488 | 2.9467 | 2.8408 | 2.7302 | 2.6140 |
| 22 | 9.7271 | 6.8064 | 5.6524 | 5.0168 | 4.6088 | 4.3225 | 4.1094 | 3.9440 | 3.8116 | 3.7030 | 3.5350 | 3.3600 | 3.1764 | 3.0807 | 2.9821 | 2.8799 | 2.7736 | 2.6625 | 2.5455 |
| 23 | 9.6348 | 6.7300 | 5.5823 | 4.9500 | 4.5441 | 4.2591 | 4.0469 | 3.8822 | 3.7502 | 3.6420 | 3.4745 | 3.2999 | 3.1165 | 3.0208 | 2.9221 | 2.8197 | 2.7132 | 2.6015 | 2.4837 |
| 24 | 9.5513 | 6.6609 | 5.5190 | 4.8898 | 4.4857 | 4.2019 | 3.9905 | 3.8264 | 3.6949 | 3.5870 | 3.4199 | 3.2456 | 3.0624 | 2.9667 | 2.8679 | 2.7654 | 2.6585 | 2.5463 | 2.4276 |
| 25 | 9.4753 | 6.5982 | 5.4615 | 4.8351 | 4.4327 | 4.1500 | 3.9394 | 3.7758 | 3.6447 | 3.5370 | 3.3704 | 3.1963 | 3.0133 | 2.9176 | 2.8187 | 2.7160 | 2.6088 | 2.4961 | 2.3765 |
| 26 | 9.4059 | 6.5409 | 5.4091 | 4.7852 | 4.3844 | 4.1027 | 3.8928 | 3.7297 | 3.5989 | 3.4916 | 3.3252 | 3.1515 | 2.9685 | 2.8728 | 2.7738 | 2.6709 | 2.5633 | 2.4501 | 2.3297 |
| 27 | 9.3423 | 6.4885 | 5.3611 | 4.7396 | 4.3402 | 4.0594 | 3.8501 | 3.6875 | 3.5571 | 3.4499 | 3.2839 | 3.1104 | 2.9275 | 2.8318 | 2.7327 | 2.6296 | 2.5217 | 2.4079 | 2.2867 |
| 28 | 9.2838 | 6.4403 | 5.3170 | 4.6977 | 4.2996 | 4.0197 | 3.8110 | 3.6487 | 3.5186 | 3.4117 | 3.2460 | 3.0727 | 2.8899 | 2.7941 | 2.6949 | 2.5916 | 2.4834 | 2.3690 | 2.2470 |
| 29 | 9.2297 | 6.3958 | 5.2764 | 4.6591 | 4.2622 | 3.9831 | 3.7749 | 3.6131 | 3.4832 | 3.3765 | 3.2110 | 3.0379 | 2.8551 | 2.7594 | 2.6600 | 2.5565 | 2.4479 | 2.3331 | 2.2102 |
| 30 | 9.1797 | 6.3547 | 5.2388 | 4.6234 | 4.2276 | 3.9492 | 3.7416 | 3.5801 | 3.4505 | 3.3440 | 3.1787 | 3.0057 | 2.8230 | 2.7272 | 2.6278 | 2.5241 | 2.4151 | 2.2998 | 2.1760 |
| 40 | 8.8279 | 6.0664 | 4.9758 | 4.3738 | 3.9860 | 3.7129 | 3.5088 | 3.3498 | 3.2220 | 3.1167 | 2.9531 | 2.7811 | 2.5984 | 2.5020 | 2.4015 | 2.2958 | 2.1838 | 2.0636 | 1.9318 |
| 50 | 8.6258 | 5.9016 | 4.8259 | 4.2316 | 3.8486 | 3.5785 | 3.3765 | 3.2189 | 3.0920 | 2.9875 | 2.8247 | 2.6531 | 2.4702 | 2.3732 | 2.2717 | 2.1644 | 2.0499 | 1.9254 | 1.7863 |
| 60 | 8.4946 | 5.7950 | 4.7290 | 4.1399 | 3.7599 | 3.4918 | 3.2911 | 3.1344 | 3.0083 | 2.9042 | 2.7419 | 2.5705 | 2.3872 | 2.2898 | 2.1874 | 2.0789 | 1.9622 | 1.8341 | 1.6885 |
| 80 | 8.3346 | 5.6652 | 4.6113 | 4.0285 | 3.6524 | 3.3867 | 3.1876 | 3.0320 | 2.9066 | 2.8031 | 2.6413 | 2.4700 | 2.2862 | 2.1881 | 2.0845 | 1.9739 | 1.8540 | 1.7203 | 1.5634 |
| 100 | 8.2406 | 5.5892 | 4.5424 | 3.9634 | 3.5895 | 3.3252 | 3.1271 | 2.9722 | 2.8472 | 2.7440 | 2.5825 | 2.4113 | 2.2270 | 2.1283 | 2.0239 | 1.9119 | 1.7896 | 1.6516 | 1.4853 |
| 120 | 8.1788 | 5.5393 | 4.4972 | 3.9207 | 3.5482 | 3.2849 | 3.0874 | 2.9330 | 2.8083 | 2.7052 | 2.5439 | 2.3727 | 2.1881 | 2.0890 | 1.9840 | 1.8709 | 1.7469 | 1.6055 | 1.4311 |
| 200 | 8.0572 | 5.4412 | 4.4084 | 3.8368 | 3.4674 | 3.2059 | 3.0097 | 2.8560 | 2.7319 | 2.6292 | 2.4683 | 2.2970 | 2.1116 | 2.0116 | 1.9051 | 1.7897 | 1.6614 | 1.5118 | 1.3137 |
| 500 | 7.9498 | 5.3549 | 4.3304 | 3.7632 | 3.3963 | 3.1366 | 2.9414 | 2.7885 | 2.6649 | 2.5625 | 2.4018 | 2.2304 | 2.0441 | 1.9432 | 1.8352 | 1.7172 | 1.5843 | 1.4245 | 1.1840 |
| ∞ | 7.8794 | 5.2983 | 4.2794 | 3.7151 | 3.3499 | 3.0913 | 2.8968 | 2.7444 | 2.6210 | 2.5188 | 2.3583 | 2.1868 | 1.9998 | 1.8983 | 1.7891 | 1.6691 | 1.5325 | 1.3637 | 1.0000 |
Significance level 0.001 (cumulative probability 0.999)
| df2 / df1 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 12 | 15 | 20 | 24 | 30 | 40 | 60 | 120 | ∞ |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 405284 | 500000 | 540379 | 562500 | 576405 | 585937 | 592873 | 598144 | 602284 | 605621 | 610668 | 615764 | 620908 | 623497 | 626099 | 628712 | 631337 | 633972 | 636619 |
| 2 | 998.500 | 999.000 | 999.167 | 999.250 | 999.300 | 999.333 | 999.357 | 999.375 | 999.389 | 999.400 | 999.417 | 999.433 | 999.450 | 999.458 | 999.467 | 999.475 | 999.483 | 999.492 | 999.500 |
| 3 | 167.029 | 148.500 | 141.108 | 137.100 | 134.580 | 132.847 | 131.583 | 130.619 | 129.860 | 129.247 | 128.316 | 127.374 | 126.418 | 125.935 | 125.449 | 124.959 | 124.466 | 123.969 | 123.469 |
| 4 | 74.1373 | 61.2456 | 56.1772 | 53.4358 | 51.7116 | 50.5250 | 49.6579 | 48.9962 | 48.4745 | 48.0526 | 47.4118 | 46.7612 | 46.1003 | 45.7658 | 45.4286 | 45.0886 | 44.7457 | 44.3998 | 44.0509 |
| 5 | 47.1808 | 37.1223 | 33.2025 | 31.0850 | 29.7524 | 28.8344 | 28.1626 | 27.6495 | 27.2445 | 26.9166 | 26.4180 | 25.9108 | 25.3946 | 25.1329 | 24.8688 | 24.6020 | 24.3326 | 24.0605 | 23.7854 |
| 6 | 35.5075 | 27.0000 | 23.7033 | 21.9235 | 20.8027 | 20.0297 | 19.4634 | 19.0303 | 18.6882 | 18.4109 | 17.9888 | 17.5587 | 17.1201 | 16.8974 | 16.6722 | 16.4445 | 16.2143 | 15.9812 | 15.7453 |
| 7 | 29.2452 | 21.6890 | 18.7723 | 17.1980 | 16.2058 | 15.5208 | 15.0186 | 14.6340 | 14.3299 | 14.0833 | 13.7073 | 13.3237 | 12.9316 | 12.7322 | 12.5304 | 12.3260 | 12.1189 | 11.9090 | 11.6960 |
| 8 | 25.4148 | 18.4937 | 15.8295 | 14.3916 | 13.4847 | 12.8580 | 12.3980 | 12.0455 | 11.7665 | 11.5401 | 11.1945 | 10.8413 | 10.4797 | 10.2954 | 10.1087 | 9.9194 | 9.7272 | 9.5321 | 9.3337 |
| 9 | 22.8571 | 16.3871 | 13.9018 | 12.5603 | 11.7137 | 11.1281 | 10.6979 | 10.3680 | 10.1066 | 9.8943 | 9.5700 | 9.2381 | 8.8976 | 8.7239 | 8.5476 | 8.3685 | 8.1865 | 8.0014 | 7.8128 |
| 10 | 21.0396 | 14.9054 | 12.5527 | 11.2828 | 10.4807 | 9.9256 | 9.5175 | 9.2041 | 8.9558 | 8.7539 | 8.4452 | 8.1288 | 7.8037 | 7.6376 | 7.4688 | 7.2971 | 7.1224 | 6.9443 | 6.7625 |
| 11 | 19.6868 | 13.8116 | 11.5611 | 10.3461 | 9.5784 | 9.0466 | 8.6553 | 8.3548 | 8.1163 | 7.9224 | 7.6256 | 7.3210 | 7.0076 | 6.8471 | 6.6839 | 6.5178 | 6.3483 | 6.1753 | 5.9983 |
| 12 | 18.6433 | 12.9737 | 10.8042 | 9.6327 | 8.8921 | 8.3788 | 8.0009 | 7.7104 | 7.4797 | 7.2920 | 7.0046 | 6.7092 | 6.4048 | 6.2488 | 6.0898 | 5.9278 | 5.7623 | 5.5931 | 5.4195 |
| 13 | 17.8154 | 12.3127 | 10.2089 | 9.0727 | 8.3541 | 7.8557 | 7.4886 | 7.2061 | 6.9818 | 6.7992 | 6.5192 | 6.2312 | 5.9340 | 5.7814 | 5.6258 | 5.4670 | 5.3046 | 5.1381 | 4.9671 |
| 14 | 17.1434 | 11.7789 | 9.7294 | 8.6223 | 7.9218 | 7.4358 | 7.0775 | 6.8017 | 6.5826 | 6.4041 | 6.1302 | 5.8483 | 5.5568 | 5.4070 | 5.2542 | 5.0979 | 4.9378 | 4.7735 | 4.6042 |
| 15 | 16.5874 | 11.3391 | 9.3353 | 8.2527 | 7.5674 | 7.0917 | 6.7408 | 6.4707 | 6.2559 | 6.0808 | 5.8121 | 5.5351 | 5.2484 | 5.1009 | 4.9502 | 4.7959 | 4.6377 | 4.4750 | 4.3070 |
| 16 | 16.1202 | 10.9710 | 9.0059 | 7.9442 | 7.2719 | 6.8049 | 6.4604 | 6.1950 | 5.9839 | 5.8117 | 5.5473 | 5.2745 | 4.9918 | 4.8462 | 4.6972 | 4.5446 | 4.3878 | 4.2263 | 4.0592 |
| 17 | 15.7222 | 10.6584 | 8.7269 | 7.6831 | 7.0219 | 6.5625 | 6.2234 | 5.9620 | 5.7541 | 5.5844 | 5.3237 | 5.0544 | 4.7751 | 4.6311 | 4.4836 | 4.3323 | 4.1767 | 4.0160 | 3.8496 |
| 18 | 15.3793 | 10.3899 | 8.4875 | 7.4593 | 6.8078 | 6.3550 | 6.0206 | 5.7628 | 5.5575 | 5.3900 | 5.1324 | 4.8663 | 4.5899 | 4.4471 | 4.3009 | 4.1507 | 3.9960 | 3.8360 | 3.6698 |
| 19 | 15.0808 | 10.1568 | 8.2799 | 7.2655 | 6.6225 | 6.1754 | 5.8452 | 5.5904 | 5.3876 | 5.2219 | 4.9672 | 4.7037 | 4.4297 | 4.2881 | 4.1429 | 3.9936 | 3.8396 | 3.6801 | 3.5141 |
| 20 | 14.8188 | 9.9526 | 8.0984 | 7.0960 | 6.4606 | 6.0186 | 5.6920 | 5.4400 | 5.2392 | 5.0752 | 4.8229 | 4.5618 | 4.2900 | 4.1493 | 4.0050 | 3.8564 | 3.7030 | 3.5438 | 3.3778 |
| 21 | 14.5869 | 9.7723 | 7.9383 | 6.9467 | 6.3179 | 5.8805 | 5.5571 | 5.3076 | 5.1087 | 4.9462 | 4.6960 | 4.4369 | 4.1670 | 4.0272 | 3.8836 | 3.7357 | 3.5827 | 3.4237 | 3.2575 |
| 22 | 14.3803 | 9.6120 | 7.7960 | 6.8142 | 6.1914 | 5.7580 | 5.4376 | 5.1901 | 4.9929 | 4.8317 | 4.5835 | 4.3262 | 4.0579 | 3.9189 | 3.7759 | 3.6285 | 3.4759 | 3.3170 | 3.1505 |
| 23 | 14.1950 | 9.4685 | 7.6688 | 6.6957 | 6.0783 | 5.6486 | 5.3308 | 5.0853 | 4.8896 | 4.7296 | 4.4831 | 4.2274 | 3.9606 | 3.8222 | 3.6798 | 3.5328 | 3.3804 | 3.2216 | 3.0548 |
| 24 | 14.0280 | 9.3394 | 7.5545 | 6.5892 | 5.9768 | 5.5504 | 5.2349 | 4.9912 | 4.7968 | 4.6379 | 4.3929 | 4.1387 | 3.8732 | 3.7354 | 3.5935 | 3.4468 | 3.2946 | 3.1357 | 2.9685 |
| 25 | 13.8767 | 9.2225 | 7.4511 | 6.4931 | 5.8851 | 5.4617 | 5.1484 | 4.9063 | 4.7131 | 4.5551 | 4.3116 | 4.0587 | 3.7944 | 3.6570 | 3.5155 | 3.3692 | 3.2171 | 3.0581 | 2.8904 |
| 26 | 13.7390 | 9.1163 | 7.3572 | 6.4057 | 5.8018 | 5.3812 | 5.0698 | 4.8292 | 4.6372 | 4.4801 | 4.2378 | 3.9861 | 3.7228 | 3.5859 | 3.4448 | 3.2987 | 3.1467 | 2.9875 | 2.8193 |
| 27 | 13.6131 | 9.0194 | 7.2715 | 6.3261 | 5.7259 | 5.3078 | 4.9983 | 4.7590 | 4.5680 | 4.4117 | 4.1706 | 3.9200 | 3.6576 | 3.5211 | 3.3803 | 3.2344 | 3.0825 | 2.9231 | 2.7543 |
| 28 | 13.4976 | 8.9305 | 7.1931 | 6.2532 | 5.6565 | 5.2407 | 4.9328 | 4.6947 | 4.5047 | 4.3491 | 4.1091 | 3.8595 | 3.5980 | 3.4618 | 3.3213 | 3.1755 | 3.0236 | 2.8640 | 2.6947 |
| 29 | 13.3912 | 8.8488 | 7.1210 | 6.1863 | 5.5927 | 5.1791 | 4.8727 | 4.6358 | 4.4466 | 4.2917 | 4.0526 | 3.8039 | 3.5432 | 3.4074 | 3.2671 | 3.1215 | 2.9695 | 2.8097 | 2.6397 |
| 30 | 13.2930 | 8.7734 | 7.0545 | 6.1245 | 5.5339 | 5.1223 | 4.8173 | 4.5814 | 4.3930 | 4.2388 | 4.0006 | 3.7527 | 3.4928 | 3.3572 | 3.2171 | 3.0716 | 2.9196 | 2.7595 | 2.5889 |
| 40 | 12.6094 | 8.2508 | 6.5945 | 5.6981 | 5.1283 | 4.7306 | 4.4355 | 4.2070 | 4.0243 | 3.8744 | 3.6425 | 3.4003 | 3.1450 | 3.0111 | 2.8721 | 2.7268 | 2.5737 | 2.4103 | 2.2326 |
| 50 | 12.2221 | 7.9564 | 6.3364 | 5.4593 | 4.9013 | 4.5117 | 4.2224 | 3.9980 | 3.8185 | 3.6711 | 3.4426 | 3.2035 | 2.9506 | 2.8175 | 2.6787 | 2.5329 | 2.3782 | 2.2113 | 2.0264 |
| 60 | 11.9730 | 7.7678 | 6.1712 | 5.3067 | 4.7565 | 4.3721 | 4.0864 | 3.8648 | 3.6873 | 3.5415 | 3.3153 | 3.0781 | 2.8266 | 2.6938 | 2.5549 | 2.4086 | 2.2523 | 2.0821 | 1.8905 |
| 80 | 11.6714 | 7.5401 | 5.9723 | 5.1231 | 4.5824 | 4.2043 | 3.9232 | 3.7049 | 3.5298 | 3.3859 | 3.1624 | 2.9274 | 2.6774 | 2.5448 | 2.4057 | 2.2582 | 2.0992 | 1.9235 | 1.7197 |
| 100 | 11.4954 | 7.4077 | 5.8568 | 5.0167 | 4.4815 | 4.1071 | 3.8286 | 3.6123 | 3.4387 | 3.2959 | 3.0739 | 2.8402 | 2.5909 | 2.4584 | 2.3189 | 2.1704 | 2.0094 | 1.8294 | 1.6150 |
| 120 | 11.3802 | 7.3211 | 5.7814 | 4.9472 | 4.4157 | 4.0437 | 3.7670 | 3.5519 | 3.3792 | 3.2372 | 3.0162 | 2.7833 | 2.5344 | 2.4019 | 2.2621 | 2.1128 | 1.9502 | 1.7667 | 1.5433 |
| 200 | 11.1545 | 7.1519 | 5.6341 | 4.8116 | 4.2874 | 3.9203 | 3.6469 | 3.4343 | 3.2635 | 3.1228 | 2.9038 | 2.6724 | 2.4243 | 2.2916 | 2.1510 | 1.9999 | 1.8333 | 1.6410 | 1.3904 |
| 500 | 10.9567 | 7.0041 | 5.5057 | 4.6935 | 4.1756 | 3.8128 | 3.5424 | 3.3320 | 3.1628 | 3.0234 | 2.8060 | 2.5759 | 2.3282 | 2.1952 | 2.0537 | 1.9004 | 1.7292 | 1.5259 | 1.2256 |
| ∞ | 10.8276 | 6.9078 | 5.4221 | 4.6167 | 4.1030 | 3.7430 | 3.4746 | 3.2656 | 3.0975 | 2.9588 | 2.7425 | 2.5132 | 2.2657 | 2.1324 | 1.9901 | 1.8350 | 1.6601 | 1.4468 | 1.0000 |
How to read this table
Pick the table for your significance level. Find numerator df across the top and denominator df down the left. Reject when the observed F statistic exceeds the cell.
Left-tail values, and the reciprocal identity
Printed F tables give upper-tail values. The lower value follows from the reciprocal distribution with the degrees of freedom swapped: the cumulative quantile Q(p; d1, d2) equals 1 divided by Q(1-p; d2, d1). The Both tails mode shows both values.
Degrees of freedom that are not on the grid
Interpolation in two dimensions is unnecessary here. Enter the exact numerator and denominator df and the value is computed for that pair. The printed artifact is bounded at nineteen numerator values and thirty-nine denominator values.
P(F <= x) = I_z(df1 / 2, df2 / 2)
How?
How this is calculated
Published upper-tail cells are solved through the reciprocal lower-tail identity so their small tail keeps its significant digits. Infinite degrees of freedom use exact chi-square limits rather than a large finite substitute.
The alpha 0.005 grid is verified by internal consistency: each of its 740 continuous cells satisfies the reciprocal identity and its direct survival residual; its remaining doubly-infinite point-mass cell is exactly 1. No second published table covers that complete level, so this page does not claim one.
The one cell where this page disagrees with a published table. At significance level 0.01 with one numerator and one denominator degree of freedom, NIST prints 4052.19 and this page prints 4052.18. The closed form tan squared at 0.495 pi gives 4052.180695476829122, which rounds to 4052.18.
Formula: P(F <= x) = I_z(df1 / 2, df2 / 2)
Sources
- Upper Critical Values of the F Distribution (e-Handbook 1.3.6.7.3). NIST/SEMATECH. Retrieved .
- F-distribution, definition and quantile relationships. Wikipedia. Retrieved .
- Numerical Recipes section 6.4, incomplete beta function. Press, Teukolsky, Vetterling and Flannery. Retrieved .