Critical F-values

Find the appropriate critical value at the intersection of \(df_1\) and \(df_2\) at \(\alpha\) = 0.05 or \(\alpha\) = 0.01.

\(\alpha\) = 0.05
df 1 = 1 2 3 4 5 6 7 8 9 10 12 15 20 24 30 40 60 120 Inf
df 2
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 18.513 19.000 19.164 19.247 19.296 19.329 19.353 19.371 19.385 19.396 19.413 19.429 19.446 19.454 19.462 19.471 19.479 19.487 19.496
3 10.128 9.552 9.277 9.117 9.014 8.941 8.887 8.845 8.812 8.786 8.745 8.703 8.660 8.639 8.617 8.594 8.572 8.549 8.526
4 7.709 6.944 6.591 6.388 6.256 6.163 6.094 6.041 5.999 5.964 5.912 5.858 5.803 5.774 5.746 5.717 5.688 5.658 5.628
5 6.608 5.786 5.410 5.192 5.050 4.950 4.876 4.818 4.772 4.735 4.678 4.619 4.558 4.527 4.496 4.464 4.431 4.399 4.365
6 5.987 5.143 4.757 4.534 4.387 4.284 4.207 4.147 4.099 4.060 4.000 3.938 3.874 3.841 3.808 3.774 3.740 3.705 3.669
7 5.591 4.737 4.347 4.120 3.971 3.866 3.787 3.726 3.677 3.636 3.575 3.511 3.445 3.410 3.376 3.340 3.304 3.267 3.230
8 5.318 4.459 4.066 3.838 3.688 3.581 3.501 3.438 3.388 3.347 3.284 3.218 3.150 3.115 3.079 3.043 3.005 2.967 2.928
9 5.117 4.256 3.862 3.633 3.482 3.374 3.293 3.230 3.179 3.137 3.073 3.006 2.937 2.901 2.864 2.826 2.787 2.748 2.707
10 4.965 4.103 3.708 3.478 3.326 3.217 3.135 3.072 3.020 2.978 2.913 2.845 2.774 2.737 2.700 2.661 2.621 2.580 2.538
11 4.844 3.982 3.587 3.357 3.204 3.095 3.012 2.948 2.896 2.854 2.788 2.719 2.646 2.609 2.571 2.531 2.490 2.448 2.405
12 4.747 3.885 3.490 3.259 3.106 2.996 2.913 2.849 2.796 2.753 2.687 2.617 2.544 2.506 2.466 2.426 2.384 2.341 2.296
13 4.667 3.806 3.410 3.179 3.025 2.915 2.832 2.767 2.714 2.671 2.604 2.533 2.459 2.420 2.380 2.339 2.297 2.252 2.206
14 4.600 3.739 3.344 3.112 2.958 2.848 2.764 2.699 2.646 2.602 2.534 2.463 2.388 2.349 2.308 2.266 2.223 2.178 2.131
15 4.543 3.682 3.287 3.056 2.901 2.791 2.707 2.641 2.588 2.544 2.475 2.403 2.328 2.288 2.247 2.204 2.160 2.114 2.066
16 4.494 3.634 3.239 3.007 2.852 2.741 2.657 2.591 2.538 2.494 2.425 2.352 2.276 2.235 2.194 2.151 2.106 2.059 2.010
17 4.451 3.591 3.197 2.965 2.810 2.699 2.614 2.548 2.494 2.450 2.381 2.308 2.230 2.190 2.148 2.104 2.058 2.011 1.960
18 4.414 3.555 3.160 2.928 2.773 2.661 2.577 2.510 2.456 2.412 2.342 2.269 2.191 2.150 2.107 2.063 2.017 1.968 1.917
19 4.381 3.522 3.127 2.895 2.740 2.628 2.543 2.477 2.423 2.378 2.308 2.234 2.155 2.114 2.071 2.026 1.980 1.930 1.878
20 4.351 3.493 3.098 2.866 2.711 2.599 2.514 2.447 2.393 2.348 2.278 2.203 2.124 2.083 2.039 1.994 1.946 1.896 1.843
21 4.325 3.467 3.072 2.840 2.685 2.573 2.488 2.421 2.366 2.321 2.250 2.176 2.096 2.054 2.010 1.964 1.917 1.866 1.812
22 4.301 3.443 3.049 2.817 2.661 2.549 2.464 2.397 2.342 2.297 2.226 2.151 2.071 2.028 1.984 1.938 1.889 1.838 1.783
23 4.279 3.422 3.028 2.796 2.640 2.528 2.442 2.375 2.320 2.275 2.204 2.128 2.048 2.005 1.960 1.914 1.865 1.813 1.757
24 4.260 3.403 3.009 2.776 2.621 2.508 2.423 2.355 2.300 2.255 2.183 2.108 2.027 1.984 1.939 1.892 1.842 1.790 1.733
25 4.242 3.385 2.991 2.759 2.603 2.490 2.405 2.337 2.282 2.236 2.165 2.089 2.007 1.964 1.919 1.872 1.822 1.768 1.711
26 4.225 3.369 2.975 2.743 2.587 2.474 2.388 2.321 2.265 2.220 2.148 2.072 1.990 1.946 1.901 1.853 1.803 1.749 1.691
27 4.210 3.354 2.960 2.728 2.572 2.459 2.373 2.305 2.250 2.204 2.132 2.056 1.974 1.930 1.884 1.836 1.785 1.731 1.672
28 4.196 3.340 2.947 2.714 2.558 2.445 2.359 2.291 2.236 2.190 2.118 2.041 1.959 1.915 1.869 1.820 1.769 1.714 1.654
29 4.183 3.328 2.934 2.701 2.545 2.432 2.346 2.278 2.223 2.177 2.104 2.027 1.945 1.901 1.854 1.806 1.754 1.698 1.638
30 4.171 3.316 2.922 2.690 2.534 2.421 2.334 2.266 2.211 2.165 2.092 2.015 1.932 1.887 1.841 1.792 1.740 1.683 1.622
40 4.085 3.232 2.839 2.606 2.450 2.336 2.249 2.180 2.124 2.077 2.003 1.925 1.839 1.793 1.744 1.693 1.637 1.577 1.509
60 4.001 3.150 2.758 2.525 2.368 2.254 2.167 2.097 2.040 1.993 1.917 1.836 1.748 1.700 1.649 1.594 1.534 1.467 1.389
120 3.920 3.072 2.680 2.447 2.290 2.175 2.087 2.016 1.959 1.911 1.834 1.750 1.659 1.608 1.554 1.495 1.429 1.352 1.254
Inf 3.841 2.996 2.605 2.372 2.214 2.099 2.010 1.938 1.880 1.831 1.752 1.666 1.571 1.517 1.459 1.394 1.318 1.221 1.000
\(\alpha\) = 0.01
df1 = 1 2 3 4 5 6 7 8 9 10 12 15 20 24 30 40 60 120 Inf
df2
1 		4052.181 4999.500 5403.352 5624.583 5763.650 5858.986 5928.356 5981.070 6022.473 6055.847 6106.321 6157.285 6208.730 6234.631 6260.649 6286.782 6313.030 6339.391 6365.864
2 98.502 99.000 99.166 99.249 99.299 99.333 99.356 99.374 99.388 99.399 99.416 99.433 99.449 99.457 99.466 99.474 99.483 99.491 99.499
3 34.116 30.817 29.457 28.710 28.237 27.911 27.672 27.489 27.345 27.229 27.052 26.872 26.690 26.598 26.505 26.411 26.316 26.221 26.125
4 21.198 18.000 16.694 15.977 15.522 15.207 14.976 14.799 14.659 14.546 14.374 14.198 14.020 13.929 13.838 13.745 13.652 13.558 13.463
5 16.258 13.274 12.060 11.392 10.967 10.672 10.456 10.289 10.158 10.051 9.888 9.722 9.553 9.466 9.379 9.291 9.202 9.112 9.020
6 13.745 10.925 9.780 9.148 8.746 8.466 8.260 8.102 7.976 7.874 7.718 7.559 7.396 7.313 7.229 7.143 7.057 6.969 6.880
7 12.246 9.547 8.451 7.847 7.460 7.191 6.993 6.840 6.719 6.620 6.469 6.314 6.155 6.074 5.992 5.908 5.824 5.737 5.649
8 11.259 8.649 7.591 7.006 6.632 6.371 6.178 6.029 5.911 5.814 5.667 5.515 5.359 5.279 5.198 5.116 5.032 4.946 4.859
9 10.561 8.021 6.992 6.422 6.057 5.802 5.613 5.467 5.351 5.256 5.111 4.962 4.808 4.729 4.649 4.567 4.483 4.398 4.311
10 10.044 7.559 6.552 5.994 5.636 5.386 5.200 5.057 4.942 4.849 4.706 4.558 4.405 4.327 4.247 4.165 4.082 3.997 3.909
11 9.646 7.206 6.217 5.668 5.316 5.069 4.886 4.745 4.631 4.539 4.397 4.251 4.099 4.021 3.941 3.860 3.776 3.690 3.602
12 9.330 6.927 5.952 5.412 5.064 4.821 4.639 4.499 4.388 4.296 4.155 4.010 3.858 3.780 3.701 3.619 3.535 3.449 3.361
13 9.074 6.701 5.739 5.205 4.862 4.620 4.441 4.302 4.191 4.100 3.960 3.815 3.665 3.587 3.507 3.425 3.341 3.255 3.165
14 8.862 6.515 5.564 5.035 4.695 4.456 4.278 4.140 4.030 3.939 3.800 3.656 3.505 3.427 3.348 3.266 3.181 3.094 3.004
15 8.683 6.359 5.417 4.893 4.556 4.318 4.141 4.005 3.895 3.805 3.666 3.522 3.372 3.294 3.214 3.132 3.047 2.959 2.868
16 8.531 6.226 5.292 4.773 4.437 4.202 4.026 3.890 3.780 3.691 3.553 3.409 3.259 3.181 3.101 3.018 2.933 2.845 2.753
17 8.400 6.112 5.185 4.669 4.336 4.101 3.927 3.791 3.682 3.593 3.455 3.312 3.162 3.083 3.003 2.921 2.835 2.746 2.653
18 8.285 6.013 5.092 4.579 4.248 4.015 3.841 3.705 3.597 3.508 3.371 3.227 3.077 2.999 2.918 2.835 2.749 2.660 2.566
19 8.185 5.926 5.010 4.500 4.171 3.939 3.765 3.631 3.522 3.434 3.296 3.153 3.003 2.925 2.844 2.761 2.674 2.584 2.489
20 8.096 5.849 4.938 4.431 4.103 3.871 3.699 3.564 3.457 3.368 3.231 3.088 2.938 2.859 2.779 2.695 2.608 2.517 2.421
21 8.017 5.780 4.874 4.369 4.042 3.812 3.640 3.506 3.398 3.310 3.173 3.030 2.880 2.801 2.720 2.636 2.548 2.457 2.360
22 7.945 5.719 4.817 4.313 3.988 3.758 3.587 3.453 3.346 3.258 3.121 2.978 2.827 2.749 2.667 2.583 2.495 2.403 2.305
23 7.881 5.664 4.765 4.264 3.939 3.710 3.539 3.406 3.299 3.211 3.074 2.931 2.780 2.702 2.620 2.535 2.447 2.354 2.256
24 7.823 5.614 4.718 4.218 3.895 3.667 3.496 3.363 3.256 3.168 3.032 2.889 2.738 2.659 2.577 2.492 2.404 2.310 2.211
25 7.770 5.568 4.676 4.177 3.855 3.627 3.457 3.324 3.217 3.129 2.993 2.850 2.699 2.620 2.538 2.453 2.364 2.270 2.169
26 7.721 5.526 4.637 4.140 3.818 3.591 3.421 3.288 3.182 3.094 2.958 2.815 2.664 2.585 2.503 2.417 2.327 2.232 2.131
27 7.677 5.488 4.601 4.106 3.785 3.558 3.388 3.256 3.149 3.062 2.926 2.783 2.632 2.552 2.470 2.384 2.294 2.199 2.096
28 7.636 5.453 4.568 4.074 3.754 3.528 3.358 3.226 3.119 3.032 2.896 2.753 2.602 2.522 2.440 2.353 2.263 2.167 2.064
29 7.598 5.420 4.538 4.045 3.725 3.499 3.330 3.198 3.092 3.005 2.869 2.726 2.574 2.495 2.412 2.325 2.234 2.138 2.034
30 7.562 5.390 4.510 4.018 3.699 3.474 3.304 3.173 3.066 2.979 2.843 2.700 2.549 2.469 2.386 2.299 2.208 2.111 2.006
40 7.314 5.178 4.313 3.828 3.514 3.291 3.124 2.993 2.888 2.800 2.665 2.522 2.369 2.288 2.203 2.114 2.019 1.917 1.805
60 7.077 4.977 4.126 3.649 3.339 3.119 2.953 2.823 2.719 2.632 2.496 2.352 2.198 2.115 2.029 1.936 1.836 1.726 1.601
120 6.851 4.787 3.949 3.479 3.174 2.956 2.792 2.663 2.559 2.472 2.336 2.192 2.035 1.950 1.860 1.763 1.656 1.533 1.381
Inf 6.635 4.605 3.782 3.319 3.017 2.802 2.639 2.511 2.407 2.321 2.185 2.038 1.878 1.791 1.696 1.592 1.473 1.325 1.000