APPENDIX A Tables and Formulas 737 TABLE A-5 (continued) F Distribution (a = 0.025 in the right tail) Numerator degrees of freedom (df1) 10 12 15 20 24 30 40 60 120 ∞ Denominator degrees of freedom (df2) 1 968.63 976.71 984.87 993.10 997.25 1001.4 1005.6 1009.8 1014.0 1018.3 2 39.398 39.415 39.431 39.448 39.456 39.465 39.473 39.481 39.490 39.498 3 14.419 14.337 14.253 14.167 14.124 14.081 14.037 13.992 13.947 13.902 4 8.8439 8.7512 8.6565 8.5599 8.5109 8.4613 8.4111 8.3604 8.3092 8.2573 5 6.6192 6.5245 6.4277 6.3286 6.2780 6.2269 6.1750 6.1225 6.0693 6.0153 6 5.4613 5.3662 5.2687 5.1684 5.1172 5.0652 5.0125 4.9589 4.9044 4.8491 7 4.7611 4.6658 4.5678 4.4667 4.4150 4.3624 4.3089 4.2544 4.1989 4.1423 8 4.2951 4.1997 4.1012 3.9995 3.9472 3.8940 3.8398 3.7844 3.7279 3.6702 9 3.9639 3.8682 3.7694 3.6669 3.6142 3.5604 3.5055 3.4493 3.3918 3.3329 10 3.7168 3.6209 3.5217 3.4185 3.3654 3.3110 3.2554 3.1984 3.1399 3.0798 11 3.5257 3.4296 3.3299 3.2261 3.1725 3.1176 3.0613 3.0035 2.9441 2.8828 12 3.3736 3.2773 3.1772 3.0728 3.0187 2.9633 2.9063 2.8478 2.7874 2.7249 13 3.2497 3.1532 3.0527 2.9477 2.8932 2.8372 2.7797 2.7204 2.6590 2.5955 14 3.1469 3.0502 2.9493 2.8437 2.7888 2.7324 2.6742 2.6142 2.5519 2.4872 15 3.0602 2.9633 2.8621 2.7559 2.7006 2.6437 2.5850 2.5242 2.4611 2.3953 16 2.9862 2.8890 2.7875 2.6808 2.6252 2.5678 2.5085 2.4471 2.3831 2.3163 17 2.9222 2.8249 2.7230 2.6158 2.5598 2.5020 2.4422 2.3801 2.3153 2.2474 18 2.8664 2.7689 2.6667 2.5590 2.5027 2.4445 2.3842 2.3214 2.2558 2.1869 19 2.8172 2.7196 2.6171 2.5089 2.4523 2.3937 2.3329 2.2696 2.2032 2.1333 20 2.7737 2.6758 2.5731 2.4645 2.4076 2.3486 2.2873 2.2234 2.1562 2.0853 21 2.7348 2.6368 2.5338 2.4247 2.3675 2.3082 2.2465 2.1819 2.1141 2.0422 22 2.6998 2.6017 2.4984 2.3890 2.3315 2.2718 2.2097 2.1446 2.0760 2.0032 23 2.6682 2.5699 2.4665 2.3567 2.2989 2.2389 2.1763 2.1107 2.0415 1.9677 24 2.6396 2.5411 2.4374 2.3273 2.2693 2.2090 2.1460 2.0799 2.0099 1.9353 25 2.6135 2.5149 2.4110 2.3005 2.2422 2.1816 2.1183 2.0516 1.9811 1.9055 26 2.5896 2.4908 2.3867 2.2759 2.2174 2.1565 2.0928 2.0257 1.9545 1.8781 27 2.5676 2.4688 2.3644 2.2533 2.1946 2.1334 2.0693 2.0018 1.9299 1.8527 28 2.5473 2.4484 2.3438 2.2324 2.1735 2.1121 2.0477 1.9797 1.9072 1.8291 29 2.5286 2.4295 2.3248 2.2131 2.1540 2.0923 2.0276 1.9591 1.8861 1.8072 30 2.5112 2.4120 2.3072 2.1952 2.1359 2.0739 2.0089 1.9400 1.8664 1.7867 40 2.3882 2.2882 2.1819 2.0677 2.0069 1.9429 1.8752 1.8028 1.7242 1.6371 60 2.2702 2.1692 2.0613 1.9445 1.8817 1.8152 1.7440 1.6668 1.5810 1.4821 120 2.1570 2.0548 1.9450 1.8249 1.7597 1.6899 1.6141 1.5299 1.4327 1.3104 ∞ 2.0483 1.9447 1.8326 1.7085 1.6402 1.5660 1.4835 1.3883 1.2684 1.0000 Based on data from Maxine Merrington and Catherine M. Thompson, “Tables of Percentage Points of the Inverted Beta (F ) Distribution,” Biometrika 33 (1943): 80–84.
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