A.5: Table of critical values of F-distribution
- Page ID
- 45299
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| \(\alpha\)(1) | 0.25 | 0.100 | 0.05 | 0.025 | 0.01 | 0.005 | 0.0025 | 0.001 |
|---|---|---|---|---|---|---|---|---|
| \(\alpha\)(2) | 0.5 | 0.200 | 0.1 | 0.05 | 0.02 | 0.01 | 0.005 | 0.002 |
| Df=1,Df=1 | 5.828427 | 39.863 | 161.447639 | 647.789011 | 4052.180695 | 16210.72272 | 64844.89087 | 405284.0679 |
| 2 | 2.571 | 8.526 | 18.512821 | 38.506329 | 98.502513 | 198.501253 | 398.50063 | 998.50025 |
| 3 | 2.024 | 5.538 | 10.127964 | 17.443443 | 34.116222 | 55.551957 | 89.58433 | 167.02922 |
| 4 | 1.807 | 4.545 | 7.708647 | 12.217863 | 21.19769 | 31.332772 | 45.67398 | 74.13729 |
| 5 | 1.692 | 4.060 | 6.607891 | 10.006982 | 16.258177 | 22.784781 | 31.40667 | 47.18078 |
| 6 | 1.621 | 3.776 | 5.987378 | 8.813101 | 13.745023 | 18.634996 | 24.80731 | 35.50749 |
| 7 | 1.573 | 3.589 | 5.591448 | 8.072669 | 12.246383 | 16.235558 | 21.1107 | 29.24519 |
| 8 | 1.538 | 3.458 | 5.317655 | 7.570882 | 11.258624 | 14.688199 | 18.77965 | 25.41476 |
| 9 | 1.512 | 3.360 | 5.117355 | 7.209283 | 10.561431 | 13.613609 | 17.18757 | 22.85713 |
| 10 | 1.491 | 3.285 | 4.964603 | 6.936728 | 10.044289 | 12.82647 | 16.03626 | 21.0396 |
| 11 | 1.475 | 3.225 | 4.844336 | 6.72413 | 9.646034 | 12.226311 | 15.16738 | 19.68679 |
| 12 | 1.461 | 3.177 | 4.747225 | 6.553769 | 9.330212 | 11.75423 | 14.48958 | 18.64332 |
| 13 | 1.450 | 3.136 | 4.667193 | 6.414254 | 9.073806 | 11.37354 | 13.94676 | 17.81542 |
| 14 | 1.440 | 3.102213 | 4.60011 | 6.297939 | 8.861593 | 11.060253 | 13.50264 | 17.14336 |
| 15 | 1.432 | 3.073186 | 4.543077 | 6.199501 | 8.683117 | 10.798049 | 13.13278 | 16.58742 |
| 20 | 1.404 | 2.974653 | 4.351244 | 5.871494 | 8.095958 | 9.943935 | 11.94005 | 14.81878 |
| 30 | 1.376 | 2.880695 | 4.170877 | 5.567535 | 7.562476 | 9.179677 | 10.8893 | 13.29301 |
Numerator Df = 2
| \(\alpha\)(1) | 0.25 | 0.100 | 0.05 | 0.025 | 0.01 | 0.005 | 0.0025 | 0.001 |
|---|---|---|---|---|---|---|---|---|
| \(\alpha\)(2) | 0.5 | 0.200 | 0.1 | 0.05 | 0.02 | 0.01 | 0.005 | 0.002 |
| Df=2,Df=1 | 7.500 | 49.500 | 199.500 | 799.500 | 4999.500 | 19999.500 | 79999.500 | 499999.500 |
| 2 | 3.000 | 9.000 | 19.000 | 39.000 | 99.000 | 199.000 | 399.000 | 999.000 |
| 3 | 2.280 | 5.462 | 9.552 | 16.044 | 30.817 | 49.799 | 79.933 | 148.500 |
| 4 | 2.000 | 4.325 | 6.944 | 10.649 | 18.000 | 26.284 | 38.000 | 61.246 |
| 5 | 1.853 | 3.780 | 5.786 | 8.434 | 13.274 | 18.314 | 24.964 | 37.122 |
| 6 | 1.762 | 3.463 | 5.143 | 7.260 | 10.925 | 14.544 | 19.104 | 27.000 |
| 7 | 1.701 | 3.257 | 4.737 | 6.542 | 9.547 | 12.404 | 15.887 | 21.689 |
| 8 | 1.657 | 3.113 | 4.459 | 6.059 | 8.649 | 11.042 | 13.889 | 18.494 |
| 9 | 1.624 | 3.006 | 4.256 | 5.715 | 8.022 | 10.107 | 12.539 | 16.387 |
| 10 | 1.598 | 2.924 | 4.103 | 5.456 | 7.559 | 9.427 | 11.572 | 14.905 |
| 11 | 1.577 | 2.860 | 3.982 | 5.256 | 7.206 | 8.912 | 10.848 | 13.812 |
| 12 | 1.560 | 2.807 | 3.885 | 5.096 | 6.927 | 8.510 | 10.287 | 12.974 |
| 13 | 1.545 | 2.763 | 3.806 | 4.965 | 6.701 | 8.186 | 9.839 | 12.313 |
| 14 | 1.533 | 2.726 | 3.739 | 4.857 | 6.515 | 7.922 | 9.475 | 11.779 |
| 15 | 1.523 | 2.695 | 3.682 | 4.765 | 6.359 | 7.701 | 9.173 | 11.339 |
| 20 | 1.487 | 2.589 | 3.493 | 4.461 | 5.849 | 6.986 | 8.206 | 9.953 |
| 30 | 1.452 | 2.489 | 3.316 | 4.182 | 5.390 | 6.355 | 7.365 | 8.773 |
Numerator Df = 3
| \(\alpha\)(1) | 0.25 | 0.100 | 0.05 | 0.025 | 0.01 | 0.005 | 0.0025 | 0.001 |
|---|---|---|---|---|---|---|---|---|
| \(\alpha\)(2) | 0.5 | 0.200 | 0.1 | 0.05 | 0.02 | 0.01 | 0.005 | 0.002 |
| Df=3,Df=1 | 8.200 | 53.593 | 215.707 | 864.163 | 5403.352 | 21614.741 | 86460.299 | 540379.200 |
| 2 | 3.153 | 9.162 | 19.164 | 39.165 | 99.166 | 199.166 | 399.167 | 999.167 |
| 3 | 2.356 | 5.391 | 9.277 | 15.439 | 29.457 | 47.467 | 76.056 | 141.109 |
| 4 | 2.047 | 4.191 | 6.591 | 9.979 | 16.694 | 24.259 | 34.956 | 56.177 |
| 5 | 1.884 | 3.619 | 5.409 | 7.764 | 12.060 | 16.530 | 22.426 | 33.202 |
| 6 | 1.784 | 3.289 | 4.757 | 6.599 | 9.780 | 12.917 | 16.867 | 23.703 |
| 7 | 1.717 | 3.074 | 4.347 | 5.890 | 8.451 | 10.882 | 13.843 | 18.772 |
| 8 | 1.668 | 2.924 | 4.066 | 5.416 | 7.591 | 9.596 | 11.979 | 15.829 |
| 9 | 1.632 | 2.813 | 3.863 | 5.078 | 6.992 | 8.717 | 10.726 | 13.902 |
| 10 | 1.603 | 2.728 | 3.708 | 4.826 | 6.552 | 8.081 | 9.833 | 12.553 |
| 11 | 1.580 | 2.660 | 3.587 | 4.630 | 6.217 | 7.600 | 9.167 | 11.561 |
| 12 | 1.561 | 2.606 | 3.490 | 4.474 | 5.953 | 7.226 | 8.652 | 10.804 |
| 13 | 1.545 | 2.560 | 3.411 | 4.347 | 5.739 | 6.926 | 8.242 | 10.209 |
| 14 | 1.532 | 2.522 | 3.344 | 4.242 | 5.564 | 6.680 | 7.910 | 9.729 |
| 15 | 1.520 | 2.490 | 3.287 | 4.153 | 5.417 | 6.476 | 7.634 | 9.335 |
| 20 | 1.481 | 2.380 | 3.098 | 3.859 | 4.938 | 5.818 | 6.757 | 8.098 |
| 30 | 1.443 | 2.276 | 2.922 | 3.589 | 4.510 | 5.239 | 5.999 | 7.054 |
Numerator Df = 4
| \(\alpha\)(1) | 0.25 | 0.100 | 0.05 | 0.025 | 0.01 | 0.005 | 0.0025 | 0.001 |
|---|---|---|---|---|---|---|---|---|
| \(\alpha\)(2) | 0.5 | 0.200 | 0.1 | 0.05 | 0.02 | 0.01 | 0.005 | 0.002 |
| Df=4,Df=1 | 8.581 | 55.833 | 224.583 | 899.583 | 5624.583 | 22499.583 | 89999.583 | 562499.600 |
| 2 | 3.232 | 9.243 | 19.247 | 39.248 | 99.249 | 199.250 | 399.250 | 999.250 |
| 3 | 2.390 | 5.343 | 9.117 | 15.101 | 28.710 | 46.195 | 73.948 | 137.100 |
| 4 | 2.064 | 4.107 | 6.388 | 9.605 | 15.977 | 23.155 | 33.303 | 53.436 |
| 5 | 1.893 | 3.520 | 5.192 | 7.388 | 11.392 | 15.556 | 21.048 | 31.085 |
| 6 | 1.787 | 3.181 | 4.534 | 6.227 | 9.148 | 12.028 | 15.652 | 21.924 |
| 7 | 1.716 | 2.961 | 4.120 | 5.523 | 7.847 | 10.050 | 12.733 | 17.198 |
| 8 | 1.664 | 2.806 | 3.838 | 5.053 | 7.006 | 8.805 | 10.941 | 14.392 |
| 9 | 1.625 | 2.693 | 3.633 | 4.718 | 6.422 | 7.956 | 9.741 | 12.560 |
| 10 | 1.595 | 2.605 | 3.478 | 4.468 | 5.994 | 7.343 | 8.888 | 11.283 |
| 11 | 1.570 | 2.536 | 3.357 | 4.275 | 5.668 | 6.881 | 8.252 | 10.346 |
| 12 | 1.550 | 2.480 | 3.259 | 4.121 | 5.412 | 6.521 | 7.762 | 9.633 |
| 13 | 1.534 | 2.434 | 3.179 | 3.996 | 5.205 | 6.233 | 7.373 | 9.073 |
| 14 | 1.519 | 2.395 | 3.112 | 3.892 | 5.035 | 5.998 | 7.057 | 8.622 |
| 15 | 1.507 | 2.361 | 3.056 | 3.804 | 4.893 | 5.803 | 6.796 | 8.253 |
| 20 | 1.465 | 2.249 | 2.866 | 3.515 | 4.431 | 5.174 | 5.967 | 7.096 |
| 30 | 1.424 | 2.142 | 2.690 | 3.250 | 4.018 | 4.623 | 5.253 | 6.125 |
Numerator Df = 5
| \(\alpha\)(1) | 0.25 | 0.100 | 0.05 | 0.025 | 0.01 | 0.005 | 0.0025 | 0.001 |
|---|---|---|---|---|---|---|---|---|
| \(\alpha\)(2) | 0.5 | 0.200 | 0.1 | 0.05 | 0.02 | 0.01 | 0.005 | 0.002 |
| Df=5,Df=1 | 8.820 | 57.240 | 230.162 | 921.848 | 5763.650 | 23055.798 | 92224.393 | 576404.600 |
| 2 | 3.280 | 9.293 | 19.296 | 39.298 | 99.299 | 199.300 | 399.300 | 999.300 |
| 3 | 2.409 | 5.309 | 9.013 | 14.885 | 28.237 | 45.392 | 72.621 | 134.580 |
| 4 | 2.072 | 4.051 | 6.256 | 9.364 | 15.522 | 22.456 | 32.261 | 51.712 |
| 5 | 1.895 | 3.453 | 5.050 | 7.146 | 10.967 | 14.940 | 20.178 | 29.752 |
| 6 | 1.785 | 3.108 | 4.387 | 5.988 | 8.746 | 11.464 | 14.884 | 20.803 |
| 7 | 1.711 | 2.883 | 3.972 | 5.285 | 7.460 | 9.522 | 12.031 | 16.206 |
| 8 | 1.658 | 2.726 | 3.687 | 4.817 | 6.632 | 8.302 | 10.283 | 13.485 |
| 9 | 1.617 | 2.611 | 3.482 | 4.484 | 6.057 | 7.471 | 9.116 | 11.714 |
| 10 | 1.585 | 2.522 | 3.326 | 4.236 | 5.636 | 6.872 | 8.288 | 10.481 |
| 11 | 1.560 | 2.451 | 3.204 | 4.044 | 5.316 | 6.422 | 7.671 | 9.578 |
| 12 | 1.539 | 2.394 | 3.106 | 3.891 | 5.064 | 6.071 | 7.196 | 8.892 |
| 13 | 1.521 | 2.347 | 3.025 | 3.767 | 4.862 | 5.791 | 6.820 | 8.354 |
| 14 | 1.507 | 2.307 | 2.958 | 3.663 | 4.695 | 5.562 | 6.515 | 7.922 |
| 15 | 1.494 | 2.273 | 2.901 | 3.576 | 4.556 | 5.372 | 6.263 | 7.567 |
| 20 | 1.450 | 2.158 | 2.711 | 3.289 | 4.103 | 4.762 | 5.463 | 6.461 |
| 30 | 1.407 | 2.049 | 2.534 | 3.026 | 3.699 | 4.228 | 4.776 | 5.534 |
R code used was
qf(c(alpha), df1=dfn, df2=dfd, lower.tail=FALSE)
Where dfn refers to numerator degrees of freedom and dfd refers to denominator degrees of freedom.