Statistical Tables | Snedecor’s F Distribution
F Statistics for the Given Two-Tailed Probabilities (p) and Degrees of Freedom (df)
| dfEFFECT = 1 |
|
|
|
dfEFFECT = 2 |
|
|
|
dfEFFECT = 3 |
|
|
|
dfEFFECT = 4 |
|
|
| dfERROR |
p = .05 |
p = .01 |
|
dfERROR |
p = .05 |
p = .01 |
|
dfERROR |
p = .05 |
p = .01 |
|
dfERROR |
p = .05 |
p = .01 |
| 2 |
18.513 |
98.503 |
|
2 |
19.000 |
99.000 |
|
2 |
19.164 |
99.166 |
|
2 |
19.247 |
99.249 |
| 3 |
10.128 |
34.116 |
|
3 |
9.552 |
30.817 |
|
3 |
9.277 |
29.457 |
|
3 |
9.117 |
28.710 |
| 4 |
7.709 |
21.198 |
|
4 |
6.944 |
18.000 |
|
4 |
6.591 |
16.694 |
|
4 |
6.388 |
15.977 |
| 5 |
6.608 |
16.258 |
|
5 |
5.786 |
13.274 |
|
5 |
5.409 |
12.060 |
|
5 |
5.192 |
11.392 |
| 6 |
5.987 |
13.745 |
|
6 |
5.143 |
10.925 |
|
6 |
4.757 |
9.780 |
|
6 |
4.534 |
9.148 |
| 7 |
5.591 |
12.246 |
|
7 |
4.737 |
9.547 |
|
7 |
4.347 |
8.451 |
|
7 |
4.120 |
7.847 |
| 8 |
5.318 |
11.259 |
|
8 |
4.459 |
8.649 |
|
8 |
4.066 |
7.591 |
|
8 |
3.838 |
7.006 |
| 9 |
5.117 |
10.561 |
|
9 |
4.256 |
8.022 |
|
9 |
3.863 |
6.992 |
|
9 |
3.633 |
6.422 |
| 10 |
4.965 |
10.044 |
|
10 |
4.103 |
7.559 |
|
10 |
3.708 |
6.552 |
|
10 |
3.478 |
5.994 |
| 11 |
4.844 |
9.646 |
|
11 |
3.982 |
7.206 |
|
11 |
3.587 |
6.217 |
|
11 |
3.357 |
5.668 |
| 12 |
4.747 |
9.330 |
|
12 |
3.885 |
6.927 |
|
12 |
3.490 |
5.953 |
|
12 |
3.259 |
5.412 |
| 13 |
4.667 |
9.074 |
|
13 |
3.806 |
6.701 |
|
13 |
3.411 |
5.739 |
|
13 |
3.179 |
5.205 |
| 14 |
4.600 |
8.862 |
|
14 |
3.739 |
6.515 |
|
14 |
3.344 |
5.564 |
|
14 |
3.112 |
5.035 |
| 15 |
4.543 |
8.683 |
|
15 |
3.682 |
6.359 |
|
15 |
3.287 |
5.417 |
|
15 |
3.056 |
4.893 |
| 16 |
4.494 |
8.531 |
|
16 |
3.634 |
6.226 |
|
16 |
3.239 |
5.292 |
|
16 |
3.007 |
4.773 |
| 17 |
4.451 |
8.400 |
|
17 |
3.592 |
6.112 |
|
17 |
3.197 |
5.185 |
|
17 |
2.965 |
4.669 |
| 18 |
4.414 |
8.285 |
|
18 |
3.555 |
6.013 |
|
18 |
3.160 |
5.092 |
|
18 |
2.928 |
4.579 |
| 19 |
4.381 |
8.185 |
|
19 |
3.522 |
5.926 |
|
19 |
3.127 |
5.010 |
|
19 |
2.895 |
4.500 |
| 20 |
4.351 |
8.096 |
|
20 |
3.493 |
5.849 |
|
20 |
3.098 |
4.938 |
|
20 |
2.866 |
4.431 |
| 21 |
4.325 |
8.017 |
|
21 |
3.467 |
5.780 |
|
21 |
3.072 |
4.874 |
|
21 |
2.840 |
4.369 |
| 22 |
4.301 |
7.945 |
|
22 |
3.443 |
5.719 |
|
22 |
3.049 |
4.817 |
|
22 |
2.817 |
4.313 |
| 23 |
4.279 |
7.881 |
|
23 |
3.422 |
5.664 |
|
23 |
3.028 |
4.765 |
|
23 |
2.796 |
4.264 |
| 24 |
4.260 |
7.823 |
|
24 |
3.403 |
5.614 |
|
24 |
3.009 |
4.718 |
|
24 |
2.776 |
4.218 |
| 25 |
4.242 |
7.770 |
|
25 |
3.385 |
5.568 |
|
25 |
2.991 |
4.675 |
|
25 |
2.759 |
4.177 |
| 26 |
4.225 |
7.721 |
|
26 |
3.369 |
5.526 |
|
26 |
2.975 |
4.637 |
|
26 |
2.743 |
4.140 |
| 27 |
4.210 |
7.677 |
|
27 |
3.354 |
5.488 |
|
27 |
2.960 |
4.601 |
|
27 |
2.728 |
4.106 |
| 28 |
4.196 |
7.636 |
|
28 |
3.340 |
5.453 |
|
28 |
2.947 |
4.568 |
|
28 |
2.714 |
4.074 |
| 29 |
4.183 |
7.598 |
|
29 |
3.328 |
5.420 |
|
29 |
2.934 |
4.538 |
|
29 |
2.701 |
4.045 |
| 30 |
4.171 |
7.562 |
|
30 |
3.316 |
5.390 |
|
30 |
2.922 |
4.510 |
|
30 |
2.690 |
4.018 |
| 35 |
4.121 |
7.419 |
|
35 |
3.267 |
5.268 |
|
35 |
2.874 |
4.396 |
|
35 |
2.641 |
3.908 |
| 40 |
4.085 |
7.314 |
|
40 |
3.232 |
5.179 |
|
40 |
2.839 |
4.313 |
|
40 |
2.606 |
3.828 |
| 45 |
4.057 |
7.234 |
|
45 |
3.204 |
5.110 |
|
45 |
2.812 |
4.249 |
|
45 |
2.579 |
3.767 |
| 50 |
4.034 |
7.171 |
|
50 |
3.183 |
5.057 |
|
50 |
2.790 |
4.199 |
|
50 |
2.557 |
3.720 |
| 55 |
4.016 |
7.119 |
|
55 |
3.165 |
5.013 |
|
55 |
2.773 |
4.159 |
|
55 |
2.540 |
3.681 |
| 60 |
4.001 |
7.077 |
|
60 |
3.150 |
4.977 |
|
60 |
2.758 |
4.126 |
|
60 |
2.525 |
3.649 |
| 70 |
3.978 |
7.011 |
|
70 |
3.128 |
4.922 |
|
70 |
2.736 |
4.074 |
|
70 |
2.503 |
3.600 |
| 80 |
3.960 |
6.963 |
|
80 |
3.111 |
4.881 |
|
80 |
2.719 |
4.036 |
|
80 |
2.486 |
3.563 |
| 90 |
3.947 |
6.925 |
|
90 |
3.098 |
4.849 |
|
90 |
2.706 |
4.007 |
|
90 |
2.473 |
3.535 |
| 100 |
3.936 |
6.895 |
|
100 |
3.087 |
4.824 |
|
100 |
2.696 |
3.984 |
|
100 |
2.463 |
3.513 |
| 120 |
3.920 |
6.851 |
|
120 |
3.072 |
4.787 |
|
120 |
2.680 |
3.949 |
|
120 |
2.447 |
3.480 |
| 240 |
3.880 |
6.742 |
|
240 |
3.033 |
4.695 |
|
240 |
2.642 |
3.864 |
|
240 |
2.409 |
3.398 |
| ∞ |
3.842 |
6.635 |
|
∞ |
2.996 |
4.605 |
|
∞ |
2.605 |
3.782 |
|
∞ |
2.372 |
3.319 |
F Statistics for the Given Two-Tailed Probabilities (p) and dfEFFECT = 1
| dfERROR |
.90 |
.80 |
.70 |
.60 |
.50 |
.40 |
.30 |
.20 |
.10 |
.05 |
.04 |
.03 |
.02 |
.01 |
.001 |
| 2 |
.020 |
.083 |
.198 |
.381 |
.667 |
1.13 |
1.922 |
3.556 |
8.526 |
18.51 |
23.51 |
31.84 |
48.51 |
98.50 |
998.50 |
| 3 |
.019 |
.077 |
.180 |
.342 |
.585 |
.957 |
1.562 |
2.682 |
5.538 |
10.13 |
12.12 |
15.18 |
20.62 |
34.12 |
167.03 |
| 4 |
.018 |
.073 |
.172 |
.323 |
.549 |
.885 |
1.415 |
2.351 |
4.545 |
7.709 |
8.991 |
10.87 |
14.04 |
21.20 |
74.137 |
| 5 |
.017 |
.071 |
.167 |
.313 |
.528 |
.846 |
1.336 |
2.178 |
4.060 |
6.608 |
7.598 |
9.017 |
11.32 |
16.26 |
47.181 |
| 6 |
.017 |
.070 |
.163 |
.306 |
.515 |
.820 |
1.286 |
2.073 |
3.776 |
5.987 |
6.824 |
8.003 |
9.876 |
13.75 |
35.507 |
| 7 |
.017 |
.069 |
.161 |
.302 |
.506 |
.803 |
1.253 |
2.002 |
3.589 |
5.591 |
6.334 |
7.369 |
8.988 |
12.25 |
29.245 |
| 8 |
.017 |
.069 |
.160 |
.298 |
.499 |
.790 |
1.228 |
1.951 |
3.458 |
5.318 |
5.998 |
6.937 |
8.389 |
11.26 |
25.415 |
| 9 |
.017 |
.068 |
.158 |
.295 |
.494 |
.780 |
1.209 |
1.913 |
3.360 |
5.117 |
5.753 |
6.624 |
7.961 |
10.56 |
22.857 |
| 10 |
.017 |
.068 |
.157 |
.293 |
.490 |
.773 |
1.195 |
1.883 |
3.285 |
4.965 |
5.566 |
6.388 |
7.638 |
10.04 |
21.040 |
| 11 |
.017 |
.067 |
.156 |
.292 |
.486 |
.767 |
1.183 |
1.859 |
3.225 |
4.844 |
5.420 |
6.203 |
7.388 |
9.646 |
19.687 |
| 12 |
.016 |
.067 |
.156 |
.290 |
.484 |
.761 |
1.173 |
1.839 |
3.177 |
4.747 |
5.303 |
6.055 |
7.188 |
9.330 |
18.643 |
| 13 |
.016 |
.067 |
.155 |
.289 |
.481 |
.757 |
1.165 |
1.823 |
3.136 |
4.667 |
5.206 |
5.933 |
7.024 |
9.074 |
17.815 |
| 14 |
.016 |
.067 |
.155 |
.288 |
.479 |
.754 |
1.158 |
1.809 |
3.102 |
4.600 |
5.125 |
5.832 |
6.888 |
8.862 |
17.143 |
| 15 |
.016 |
.067 |
.154 |
.287 |
.478 |
.750 |
1.152 |
1.797 |
3.073 |
4.543 |
5.056 |
5.746 |
6.773 |
8.683 |
16.587 |
| 16 |
.016 |
.066 |
.154 |
.286 |
.476 |
.748 |
1.147 |
1.787 |
3.048 |
4.494 |
4.997 |
5.672 |
6.674 |
8.531 |
16.120 |
| 17 |
.016 |
.066 |
.154 |
.286 |
.475 |
.745 |
1.143 |
1.778 |
3.026 |
4.451 |
4.945 |
5.608 |
6.589 |
8.400 |
15.722 |
| 18 |
.016 |
.066 |
.153 |
.285 |
.474 |
.743 |
1.139 |
1.770 |
3.007 |
4.414 |
4.900 |
5.552 |
6.515 |
8.285 |
15.379 |
| 19 |
.016 |
.066 |
.153 |
.284 |
.473 |
.741 |
1.135 |
1.763 |
2.990 |
4.381 |
4.861 |
5.502 |
6.449 |
8.185 |
15.081 |
| 20 |
.016 |
.066 |
.153 |
.284 |
.472 |
.740 |
1.132 |
1.757 |
2.975 |
4.351 |
4.825 |
5.458 |
6.391 |
8.096 |
14.819 |
| 21 |
.016 |
.066 |
.153 |
.284 |
.471 |
.738 |
1.129 |
1.751 |
2.961 |
4.325 |
4.794 |
5.419 |
6.339 |
8.017 |
14.587 |
| 22 |
.016 |
.066 |
.152 |
.283 |
.470 |
.737 |
1.127 |
1.746 |
2.949 |
4.301 |
4.765 |
5.383 |
6.292 |
7.945 |
14.380 |
| 23 |
.016 |
.066 |
.152 |
.283 |
.470 |
.735 |
1.124 |
1.741 |
2.937 |
4.279 |
4.739 |
5.351 |
6.249 |
7.881 |
14.195 |
| 24 |
.016 |
.066 |
.152 |
.282 |
.469 |
.734 |
1.122 |
1.737 |
2.927 |
4.260 |
4.716 |
5.322 |
6.211 |
7.823 |
14.028 |
| 25 |
.016 |
.066 |
.152 |
.282 |
.468 |
.733 |
1.120 |
1.733 |
2.918 |
4.242 |
4.694 |
5.295 |
6.176 |
7.770 |
13.877 |
| 26 |
.016 |
.066 |
.152 |
.282 |
.468 |
.732 |
1.118 |
1.729 |
2.909 |
4.225 |
4.674 |
5.271 |
6.144 |
7.721 |
13.739 |
| 27 |
.016 |
.065 |
.152 |
.282 |
.467 |
.731 |
1.117 |
1.726 |
2.901 |
4.210 |
4.656 |
5.248 |
6.114 |
7.677 |
13.613 |
| 28 |
.016 |
.065 |
.152 |
.281 |
.467 |
.730 |
1.115 |
1.723 |
2.894 |
4.196 |
4.639 |
5.228 |
6.087 |
7.636 |
13.498 |
| 29 |
.016 |
.065 |
.151 |
.281 |
.467 |
.730 |
1.114 |
1.720 |
2.887 |
4.183 |
4.624 |
5.208 |
6.062 |
7.598 |
13.391 |
| 30 |
.016 |
.065 |
.151 |
.281 |
.466 |
.729 |
1.112 |
1.717 |
2.881 |
4.171 |
4.609 |
5.190 |
6.038 |
7.562 |
13.293 |
| 35 |
.016 |
.065 |
.151 |
.280 |
.465 |
.726 |
1.107 |
1.706 |
2.855 |
4.121 |
4.550 |
5.117 |
5.942 |
7.419 |
12.896 |
| 40 |
.016 |
.065 |
.151 |
.279 |
.463 |
.724 |
1.103 |
1.698 |
2.835 |
4.085 |
4.507 |
5.064 |
5.872 |
7.314 |
12.609 |
| 45 |
.016 |
.065 |
.150 |
.279 |
.462 |
.722 |
1.099 |
1.692 |
2.820 |
4.057 |
4.473 |
5.022 |
5.818 |
7.234 |
12.392 |
| 50 |
.016 |
.065 |
.150 |
.279 |
.462 |
.721 |
1.097 |
1.687 |
2.809 |
4.034 |
4.447 |
4.990 |
5.776 |
7.171 |
12.222 |
| 55 |
.016 |
.065 |
.150 |
.278 |
.461 |
.719 |
1.095 |
1.683 |
2.799 |
4.016 |
4.425 |
4.963 |
5.741 |
7.119 |
12.085 |
| 60 |
.016 |
.065 |
.150 |
.278 |
.460 |
.719 |
1.093 |
1.679 |
2.791 |
4.001 |
4.407 |
4.941 |
5.713 |
7.077 |
11.973 |
| 70 |
.016 |
.065 |
.150 |
.278 |
.460 |
.717 |
1.090 |
1.674 |
2.779 |
3.978 |
4.380 |
4.907 |
5.668 |
7.011 |
11.799 |
| 80 |
.016 |
.065 |
.150 |
.277 |
.459 |
.716 |
1.088 |
1.670 |
2.769 |
3.960 |
4.359 |
4.882 |
5.635 |
6.963 |
11.671 |
| 90 |
.016 |
.065 |
.149 |
.277 |
.459 |
.715 |
1.087 |
1.667 |
2.762 |
3.947 |
4.343 |
4.862 |
5.610 |
6.925 |
11.573 |
| 100 |
.016 |
.065 |
.149 |
.277 |
.458 |
.714 |
1.085 |
1.664 |
2.756 |
3.936 |
4.330 |
4.847 |
5.590 |
6.895 |
11.495 |
| 120 |
.016 |
.064 |
.149 |
.276 |
.458 |
.713 |
1.084 |
1.661 |
2.748 |
3.920 |
4.311 |
4.823 |
5.559 |
6.851 |
11.380 |
| 240 |
.016 |
.064 |
.149 |
.276 |
.456 |
.711 |
1.079 |
1.651 |
2.727 |
3.880 |
4.264 |
4.766 |
5.485 |
6.742 |
11.099 |
| ∞ |
.016 |
.064 |
.148 |
.275 |
.455 |
.708 |
1.074 |
1.642 |
2.706 |
3.842 |
4.218 |
4.709 |
5.412 |
6.635 |
10.828 |
F Statistics for the Given Two-Tailed Probabilities (p) and dfEFFECT = 2
| dfERROR |
.90 |
.80 |
.70 |
.60 |
.50 |
.40 |
.30 |
.20 |
.10 |
.05 |
.04 |
.03 |
.02 |
.01 |
.001 |
| 2 |
.111 |
.250 |
.429 |
.667 |
1.00 |
1.50 |
2.333 |
4.000 |
9.000 |
19.00 |
24.00 |
32.33 |
49.00 |
99.00 |
999.00 |
| 3 |
.109 |
.241 |
.403 |
.609 |
.881 |
1.26 |
1.847 |
2.886 |
5.462 |
9.552 |
11.32 |
14.04 |
18.86 |
30.82 |
148.50 |
| 4 |
.108 |
.236 |
.390 |
.582 |
.828 |
1.16 |
1.651 |
2.472 |
4.325 |
6.944 |
8.000 |
9.547 |
12.14 |
18.00 |
61.246 |
| 5 |
.108 |
.233 |
.383 |
.567 |
.799 |
1.11 |
1.547 |
2.259 |
3.780 |
5.786 |
6.560 |
7.665 |
9.454 |
13.27 |
37.122 |
| 6 |
.107 |
.232 |
.379 |
.557 |
.780 |
1.07 |
1.481 |
2.130 |
3.463 |
5.143 |
5.772 |
6.655 |
8.052 |
10.92 |
27.000 |
| 7 |
.107 |
.230 |
.375 |
.550 |
.767 |
1.05 |
1.437 |
2.043 |
3.257 |
4.737 |
5.280 |
6.032 |
7.203 |
9.547 |
21.689 |
| 8 |
.107 |
.229 |
.373 |
.545 |
.757 |
1.03 |
1.405 |
1.981 |
3.113 |
4.459 |
4.944 |
5.611 |
6.637 |
8.649 |
18.494 |
| 9 |
.107 |
.229 |
.371 |
.541 |
.749 |
1.02 |
1.380 |
1.935 |
3.006 |
4.256 |
4.702 |
5.309 |
6.234 |
8.022 |
16.387 |
| 10 |
.106 |
.228 |
.370 |
.538 |
.743 |
1.01 |
1.361 |
1.899 |
2.924 |
4.103 |
4.518 |
5.082 |
5.934 |
7.559 |
14.905 |
| 11 |
.106 |
.228 |
.368 |
.535 |
.739 |
.997 |
1.346 |
1.870 |
2.860 |
3.982 |
4.375 |
4.905 |
5.701 |
7.206 |
13.812 |
| 12 |
.106 |
.227 |
.367 |
.533 |
.735 |
.990 |
1.333 |
1.846 |
2.807 |
3.885 |
4.260 |
4.764 |
5.516 |
6.927 |
12.974 |
| 13 |
.106 |
.227 |
.367 |
.531 |
.731 |
.984 |
1.323 |
1.826 |
2.763 |
3.806 |
4.165 |
4.648 |
5.366 |
6.701 |
12.313 |
| 14 |
.106 |
.227 |
.366 |
.530 |
.729 |
.979 |
1.314 |
1.809 |
2.726 |
3.739 |
4.087 |
4.552 |
5.241 |
6.515 |
11.779 |
| 15 |
.106 |
.226 |
.365 |
.529 |
.726 |
.975 |
1.306 |
1.795 |
2.695 |
3.682 |
4.020 |
4.470 |
5.135 |
6.359 |
11.339 |
| 16 |
.106 |
.226 |
.365 |
.527 |
.724 |
.971 |
1.299 |
1.783 |
2.668 |
3.634 |
3.963 |
4.401 |
5.046 |
6.226 |
10.971 |
| 17 |
.106 |
.226 |
.364 |
.526 |
.722 |
.968 |
1.293 |
1.772 |
2.645 |
3.592 |
3.913 |
4.340 |
4.968 |
6.112 |
10.658 |
| 18 |
.106 |
.226 |
.364 |
.526 |
.721 |
.965 |
1.288 |
1.762 |
2.624 |
3.555 |
3.870 |
4.288 |
4.900 |
6.013 |
10.390 |
| 19 |
.106 |
.226 |
.363 |
.525 |
.719 |
.962 |
1.284 |
1.754 |
2.606 |
3.522 |
3.831 |
4.241 |
4.840 |
5.926 |
10.157 |
| 20 |
.106 |
.226 |
.363 |
.524 |
.718 |
.960 |
1.279 |
1.746 |
2.589 |
3.493 |
3.797 |
4.200 |
4.788 |
5.849 |
9.953 |
| 21 |
.106 |
.226 |
.363 |
.523 |
.717 |
.957 |
1.276 |
1.739 |
2.575 |
3.467 |
3.767 |
4.163 |
4.740 |
5.780 |
9.772 |
| 22 |
.106 |
.225 |
.363 |
.523 |
.715 |
.956 |
1.272 |
1.733 |
2.561 |
3.443 |
3.739 |
4.130 |
4.698 |
5.719 |
9.612 |
| 23 |
.106 |
.225 |
.362 |
.522 |
.714 |
.954 |
1.269 |
1.728 |
2.549 |
3.422 |
3.715 |
4.100 |
4.660 |
5.664 |
9.469 |
| 24 |
.106 |
.225 |
.362 |
.522 |
.714 |
.952 |
1.266 |
1.722 |
2.538 |
3.403 |
3.692 |
4.073 |
4.625 |
5.614 |
9.339 |
| 25 |
.106 |
.225 |
.362 |
.521 |
.713 |
.951 |
1.264 |
1.718 |
2.528 |
3.385 |
3.671 |
4.048 |
4.593 |
5.568 |
9.223 |
| 26 |
.106 |
.225 |
.362 |
.521 |
.712 |
.949 |
1.261 |
1.713 |
2.519 |
3.369 |
3.652 |
4.025 |
4.564 |
5.526 |
9.116 |
| 27 |
.106 |
.225 |
.361 |
.521 |
.711 |
.948 |
1.259 |
1.709 |
2.511 |
3.354 |
3.635 |
4.004 |
4.538 |
5.488 |
9.019 |
| 28 |
.106 |
.225 |
.361 |
.520 |
.711 |
.947 |
1.257 |
1.706 |
2.503 |
3.340 |
3.619 |
3.985 |
4.513 |
5.453 |
8.931 |
| 29 |
.106 |
.225 |
.361 |
.520 |
.710 |
.946 |
1.255 |
1.702 |
2.495 |
3.328 |
3.604 |
3.967 |
4.491 |
5.420 |
8.849 |
| 30 |
.106 |
.225 |
.361 |
.520 |
.709 |
.945 |
1.254 |
1.699 |
2.489 |
3.316 |
3.590 |
3.950 |
4.470 |
5.390 |
8.773 |
| 35 |
.106 |
.225 |
.360 |
.518 |
.707 |
.941 |
1.246 |
1.686 |
2.461 |
3.267 |
3.534 |
3.883 |
4.384 |
5.268 |
8.470 |
| 40 |
.106 |
.224 |
.360 |
.517 |
.705 |
.938 |
1.241 |
1.676 |
2.440 |
3.232 |
3.492 |
3.833 |
4.321 |
5.179 |
8.251 |
| 45 |
.106 |
.224 |
.360 |
.517 |
.704 |
.935 |
1.237 |
1.668 |
2.425 |
3.204 |
3.461 |
3.795 |
4.273 |
5.110 |
8.086 |
| 50 |
.106 |
.224 |
.359 |
.516 |
.703 |
.933 |
1.233 |
1.662 |
2.412 |
3.183 |
3.435 |
3.764 |
4.235 |
5.057 |
7.956 |
| 55 |
.106 |
.224 |
.359 |
.516 |
.702 |
.932 |
1.231 |
1.657 |
2.402 |
3.165 |
3.415 |
3.740 |
4.204 |
5.013 |
7.853 |
| 60 |
.106 |
.224 |
.359 |
.515 |
.701 |
.930 |
1.228 |
1.653 |
2.393 |
3.150 |
3.398 |
3.720 |
4.179 |
4.977 |
7.768 |
| 70 |
.106 |
.224 |
.358 |
.515 |
.700 |
.928 |
1.225 |
1.647 |
2.380 |
3.128 |
3.372 |
3.688 |
4.139 |
4.922 |
7.637 |
| 80 |
.105 |
.224 |
.358 |
.514 |
.699 |
.927 |
1.222 |
1.642 |
2.370 |
3.111 |
3.352 |
3.665 |
4.110 |
4.881 |
7.540 |
| 90 |
.105 |
.224 |
.358 |
.514 |
.699 |
.926 |
1.220 |
1.639 |
2.363 |
3.098 |
3.337 |
3.647 |
4.087 |
4.849 |
7.466 |
| 100 |
.105 |
.224 |
.358 |
.513 |
.698 |
.925 |
1.219 |
1.636 |
2.356 |
3.087 |
3.325 |
3.632 |
4.069 |
4.824 |
7.408 |
| 120 |
.105 |
.224 |
.358 |
.513 |
.697 |
.923 |
1.216 |
1.631 |
2.347 |
3.072 |
3.307 |
3.611 |
4.042 |
4.787 |
7.321 |
| 240 |
.105 |
.223 |
.357 |
.512 |
.695 |
.920 |
1.210 |
1.620 |
2.325 |
3.033 |
3.262 |
3.558 |
3.976 |
4.695 |
7.110 |
| ∞ |
.105 |
.223 |
.357 |
.511 |
.693 |
.916 |
1.204 |
1.609 |
2.303 |
2.996 |
3.219 |
3.507 |
3.912 |
4.605 |
6.908 |
F Statistics for the Given Two-Tailed Probabilities (p) and dfEFFECT = 3
| dfERROR |
.90 |
.80 |
.70 |
.60 |
.50 |
.40 |
.30 |
.20 |
.10 |
.05 |
.04 |
.03 |
.02 |
.01 |
.001 |
| 2 |
.183 |
.346 |
.541 |
.792 |
1.13 |
1.64 |
2.484 |
4.156 |
9.162 |
19.16 |
24.16 |
32.50 |
49.17 |
99.17 |
999.17 |
| 3 |
.186 |
.341 |
.516 |
.728 |
1.00 |
1.37 |
1.940 |
2.936 |
5.391 |
9.277 |
10.96 |
13.53 |
18.11 |
29.46 |
141.11 |
| 4 |
.187 |
.338 |
.504 |
.699 |
.941 |
1.26 |
1.721 |
2.485 |
4.191 |
6.591 |
7.557 |
8.972 |
11.34 |
16.69 |
56.177 |
| 5 |
.188 |
.337 |
.497 |
.682 |
.907 |
1.20 |
1.605 |
2.253 |
3.619 |
5.409 |
6.098 |
7.080 |
8.670 |
12.06 |
33.202 |
| 6 |
.189 |
.337 |
.493 |
.672 |
.886 |
1.16 |
1.532 |
2.113 |
3.289 |
4.757 |
5.305 |
6.073 |
7.287 |
9.780 |
23.703 |
| 7 |
.190 |
.336 |
.490 |
.664 |
.871 |
1.13 |
1.482 |
2.019 |
3.074 |
4.347 |
4.811 |
5.454 |
6.454 |
8.451 |
18.772 |
| 8 |
.190 |
.336 |
.488 |
.659 |
.860 |
1.11 |
1.446 |
1.951 |
2.924 |
4.066 |
4.476 |
5.039 |
5.901 |
7.591 |
15.829 |
| 9 |
.191 |
.336 |
.487 |
.655 |
.852 |
1.10 |
1.419 |
1.901 |
2.813 |
3.863 |
4.234 |
4.741 |
5.510 |
6.992 |
13.902 |
| 10 |
.191 |
.336 |
.485 |
.651 |
.845 |
1.08 |
1.398 |
1.861 |
2.728 |
3.708 |
4.052 |
4.517 |
5.218 |
6.552 |
12.553 |
| 11 |
.191 |
.336 |
.484 |
.649 |
.840 |
1.07 |
1.381 |
1.830 |
2.660 |
3.587 |
3.910 |
4.344 |
4.993 |
6.217 |
11.561 |
| 12 |
.192 |
.336 |
.483 |
.646 |
.835 |
1.07 |
1.366 |
1.804 |
2.606 |
3.490 |
3.795 |
4.205 |
4.814 |
5.953 |
10.804 |
| 13 |
.192 |
.335 |
.483 |
.645 |
.832 |
1.06 |
1.355 |
1.783 |
2.560 |
3.411 |
3.702 |
4.092 |
4.669 |
5.739 |
10.209 |
| 14 |
.192 |
.335 |
.482 |
.643 |
.828 |
1.05 |
1.345 |
1.765 |
2.522 |
3.344 |
3.624 |
3.998 |
4.549 |
5.564 |
9.729 |
| 15 |
.192 |
.335 |
.482 |
.642 |
.826 |
1.05 |
1.336 |
1.749 |
2.490 |
3.287 |
3.558 |
3.918 |
4.447 |
5.417 |
9.335 |
| 16 |
.192 |
.335 |
.481 |
.640 |
.823 |
1.04 |
1.328 |
1.736 |
2.462 |
3.239 |
3.502 |
3.850 |
4.361 |
5.292 |
9.006 |
| 17 |
.193 |
.335 |
.481 |
.639 |
.821 |
1.04 |
1.322 |
1.724 |
2.437 |
3.197 |
3.453 |
3.791 |
4.286 |
5.185 |
8.727 |
| 18 |
.193 |
.335 |
.480 |
.638 |
.819 |
1.04 |
1.316 |
1.713 |
2.416 |
3.160 |
3.410 |
3.740 |
4.221 |
5.092 |
8.487 |
| 19 |
.193 |
.335 |
.480 |
.638 |
.818 |
1.03 |
1.311 |
1.704 |
2.397 |
3.127 |
3.372 |
3.694 |
4.164 |
5.010 |
8.280 |
| 20 |
.193 |
.335 |
.480 |
.637 |
.816 |
1.03 |
1.306 |
1.696 |
2.380 |
3.098 |
3.338 |
3.654 |
4.113 |
4.938 |
8.098 |
| 21 |
.193 |
.335 |
.479 |
.636 |
.815 |
1.03 |
1.302 |
1.688 |
2.365 |
3.072 |
3.308 |
3.618 |
4.068 |
4.874 |
7.938 |
| 22 |
.193 |
.335 |
.479 |
.636 |
.814 |
1.03 |
1.298 |
1.682 |
2.351 |
3.049 |
3.281 |
3.586 |
4.028 |
4.817 |
7.796 |
| 23 |
.193 |
.335 |
.479 |
.635 |
.813 |
1.02 |
1.295 |
1.676 |
2.339 |
3.028 |
3.257 |
3.557 |
3.991 |
4.765 |
7.669 |
| 24 |
.193 |
.335 |
.479 |
.635 |
.812 |
1.02 |
1.292 |
1.670 |
2.327 |
3.009 |
3.234 |
3.530 |
3.958 |
4.718 |
7.554 |
| 25 |
.193 |
.335 |
.479 |
.634 |
.811 |
1.02 |
1.289 |
1.665 |
2.317 |
2.991 |
3.214 |
3.506 |
3.928 |
4.675 |
7.451 |
| 26 |
.193 |
.335 |
.479 |
.634 |
.810 |
1.02 |
1.286 |
1.660 |
2.307 |
2.975 |
3.196 |
3.484 |
3.900 |
4.637 |
7.357 |
| 27 |
.193 |
.335 |
.478 |
.633 |
.809 |
1.02 |
1.284 |
1.656 |
2.299 |
2.960 |
3.178 |
3.464 |
3.874 |
4.601 |
7.272 |
| 28 |
.193 |
.335 |
.478 |
.633 |
.808 |
1.02 |
1.281 |
1.652 |
2.291 |
2.947 |
3.163 |
3.445 |
3.851 |
4.568 |
7.193 |
| 29 |
.193 |
.335 |
.478 |
.633 |
.808 |
1.02 |
1.279 |
1.648 |
2.283 |
2.934 |
3.148 |
3.428 |
3.829 |
4.538 |
7.121 |
| 30 |
.193 |
.335 |
.478 |
.632 |
.807 |
1.01 |
1.277 |
1.645 |
2.276 |
2.922 |
3.135 |
3.412 |
3.809 |
4.510 |
7.054 |
| 35 |
.194 |
.335 |
.477 |
.631 |
.804 |
1.01 |
1.269 |
1.630 |
2.247 |
2.874 |
3.079 |
3.346 |
3.727 |
4.396 |
6.787 |
| 40 |
.194 |
.335 |
.477 |
.630 |
.802 |
1.01 |
1.263 |
1.620 |
2.226 |
2.839 |
3.038 |
3.298 |
3.667 |
4.313 |
6.595 |
| 45 |
.194 |
.335 |
.477 |
.629 |
.801 |
1.00 |
1.258 |
1.611 |
2.210 |
2.812 |
3.007 |
3.261 |
3.622 |
4.249 |
6.450 |
| 50 |
.194 |
.335 |
.477 |
.629 |
.800 |
1.00 |
1.255 |
1.605 |
2.197 |
2.790 |
2.982 |
3.231 |
3.585 |
4.199 |
6.336 |
| 55 |
.194 |
.335 |
.476 |
.628 |
.799 |
1.00 |
1.252 |
1.599 |
2.186 |
2.773 |
2.962 |
3.208 |
3.556 |
4.159 |
6.246 |
| 60 |
.194 |
.335 |
.476 |
.628 |
.798 |
.998 |
1.249 |
1.595 |
2.177 |
2.758 |
2.946 |
3.188 |
3.532 |
4.126 |
6.171 |
| 70 |
.194 |
.335 |
.476 |
.627 |
.796 |
.996 |
1.245 |
1.588 |
2.164 |
2.736 |
2.920 |
3.158 |
3.494 |
4.074 |
6.057 |
| 80 |
.194 |
.335 |
.476 |
.626 |
.795 |
.994 |
1.242 |
1.583 |
2.154 |
2.719 |
2.901 |
3.135 |
3.467 |
4.036 |
5.972 |
| 90 |
.194 |
.335 |
.476 |
.626 |
.795 |
.993 |
1.240 |
1.579 |
2.146 |
2.706 |
2.886 |
3.118 |
3.445 |
4.007 |
5.908 |
| 100 |
.194 |
.335 |
.476 |
.626 |
.794 |
.992 |
1.238 |
1.576 |
2.139 |
2.696 |
2.874 |
3.104 |
3.428 |
3.984 |
5.857 |
| 120 |
.194 |
.335 |
.475 |
.625 |
.793 |
.990 |
1.235 |
1.571 |
2.130 |
2.680 |
2.856 |
3.083 |
3.403 |
3.949 |
5.781 |
| 240 |
.195 |
.335 |
.475 |
.624 |
.791 |
.986 |
1.228 |
1.559 |
2.107 |
2.642 |
2.813 |
3.032 |
3.340 |
3.864 |
5.598 |
| ∞ |
.195 |
.335 |
.475 |
.623 |
.789 |
.982 |
1.222 |
1.547 |
2.084 |
2.605 |
2.770 |
2.983 |
3.279 |
3.782 |
5.422 |
F Statistics for the Given Two-Tailed Probabilities (p) and dfEFFECT = 4
| dfERROR |
.90 |
.80 |
.70 |
.60 |
.50 |
.40 |
.30 |
.20 |
.10 |
.05 |
.04 |
.03 |
.02 |
.01 |
.001 |
| 2 |
.231 |
.405 |
.606 |
.860 |
1.21 |
1.72 |
2.561 |
4.236 |
9.243 |
19.25 |
24.25 |
32.58 |
49.25 |
99.25 |
999.25 |
| 3 |
.239 |
.402 |
.581 |
.793 |
1.06 |
1.43 |
1.985 |
2.956 |
5.343 |
9.117 |
10.75 |
13.25 |
17.69 |
28.71 |
137.10 |
| 4 |
.243 |
.403 |
.570 |
.763 |
1.00 |
1.31 |
1.753 |
2.483 |
4.107 |
6.388 |
7.305 |
8.648 |
10.90 |
15.98 |
53.436 |
| 5 |
.247 |
.404 |
.565 |
.747 |
.965 |
1.24 |
1.629 |
2.240 |
3.520 |
5.192 |
5.835 |
6.751 |
8.233 |
11.39 |
31.085 |
| 6 |
.249 |
.404 |
.562 |
.736 |
.942 |
1.20 |
1.551 |
2.092 |
3.181 |
4.534 |
5.038 |
5.744 |
6.859 |
9.148 |
21.924 |
| 7 |
.251 |
.405 |
.559 |
.729 |
.926 |
1.17 |
1.499 |
1.994 |
2.961 |
4.120 |
4.543 |
5.127 |
6.035 |
7.847 |
17.198 |
| 8 |
.253 |
.406 |
.558 |
.723 |
.915 |
1.15 |
1.460 |
1.923 |
2.806 |
3.838 |
4.207 |
4.713 |
5.489 |
7.006 |
14.392 |
| 9 |
.254 |
.406 |
.556 |
.719 |
.906 |
1.13 |
1.431 |
1.870 |
2.693 |
3.633 |
3.965 |
4.417 |
5.103 |
6.422 |
12.560 |
| 10 |
.255 |
.407 |
.556 |
.716 |
.899 |
1.12 |
1.408 |
1.829 |
2.605 |
3.478 |
3.783 |
4.195 |
4.816 |
5.994 |
11.283 |
| 11 |
.256 |
.407 |
.555 |
.713 |
.893 |
1.11 |
1.390 |
1.796 |
2.536 |
3.357 |
3.641 |
4.023 |
4.594 |
5.668 |
10.346 |
| 12 |
.257 |
.407 |
.554 |
.711 |
.888 |
1.10 |
1.375 |
1.768 |
2.480 |
3.259 |
3.527 |
3.886 |
4.419 |
5.412 |
9.633 |
| 13 |
.257 |
.408 |
.554 |
.709 |
.885 |
1.09 |
1.362 |
1.746 |
2.434 |
3.179 |
3.434 |
3.773 |
4.276 |
5.205 |
9.073 |
| 14 |
.258 |
.408 |
.553 |
.708 |
.881 |
1.09 |
1.352 |
1.727 |
2.395 |
3.112 |
3.356 |
3.680 |
4.158 |
5.035 |
8.622 |
| 15 |
.258 |
.408 |
.553 |
.706 |
.878 |
1.08 |
1.342 |
1.710 |
2.361 |
3.056 |
3.290 |
3.602 |
4.058 |
4.893 |
8.253 |
| 16 |
.259 |
.408 |
.553 |
.705 |
.876 |
1.08 |
1.334 |
1.696 |
2.333 |
3.007 |
3.234 |
3.534 |
3.974 |
4.773 |
7.944 |
| 17 |
.259 |
.409 |
.552 |
.704 |
.874 |
1.07 |
1.327 |
1.684 |
2.308 |
2.965 |
3.185 |
3.476 |
3.901 |
4.669 |
7.683 |
| 18 |
.260 |
.409 |
.552 |
.703 |
.872 |
1.07 |
1.321 |
1.673 |
2.286 |
2.928 |
3.142 |
3.425 |
3.837 |
4.579 |
7.459 |
| 19 |
.260 |
.409 |
.552 |
.702 |
.870 |
1.07 |
1.316 |
1.663 |
2.266 |
2.895 |
3.105 |
3.380 |
3.781 |
4.500 |
7.265 |
| 20 |
.260 |
.409 |
.552 |
.702 |
.868 |
1.06 |
1.311 |
1.654 |
2.249 |
2.866 |
3.071 |
3.341 |
3.731 |
4.431 |
7.096 |
| 21 |
.260 |
.409 |
.552 |
.701 |
.867 |
1.06 |
1.306 |
1.646 |
2.233 |
2.840 |
3.041 |
3.305 |
3.687 |
4.369 |
6.947 |
| 22 |
.261 |
.409 |
.551 |
.700 |
.866 |
1.06 |
1.302 |
1.639 |
2.219 |
2.817 |
3.014 |
3.273 |
3.647 |
4.313 |
6.814 |
| 23 |
.261 |
.409 |
.551 |
.700 |
.864 |
1.06 |
1.298 |
1.633 |
2.207 |
2.796 |
2.990 |
3.244 |
3.611 |
4.264 |
6.696 |
| 24 |
.261 |
.409 |
.551 |
.699 |
.863 |
1.06 |
1.295 |
1.627 |
2.195 |
2.776 |
2.968 |
3.218 |
3.579 |
4.218 |
6.589 |
| 25 |
.261 |
.410 |
.551 |
.699 |
.862 |
1.05 |
1.292 |
1.622 |
2.184 |
2.759 |
2.948 |
3.194 |
3.549 |
4.177 |
6.493 |
| 26 |
.261 |
.410 |
.551 |
.698 |
.861 |
1.05 |
1.289 |
1.617 |
2.174 |
2.743 |
2.929 |
3.173 |
3.522 |
4.140 |
6.406 |
| 27 |
.262 |
.410 |
.551 |
.698 |
.861 |
1.05 |
1.286 |
1.612 |
2.165 |
2.728 |
2.912 |
3.153 |
3.498 |
4.106 |
6.326 |
| 28 |
.262 |
.410 |
.551 |
.698 |
.860 |
1.05 |
1.284 |
1.608 |
2.157 |
2.714 |
2.896 |
3.134 |
3.475 |
4.074 |
6.253 |
| 29 |
.262 |
.410 |
.551 |
.697 |
.859 |
1.05 |
1.282 |
1.604 |
2.149 |
2.701 |
2.882 |
3.117 |
3.453 |
4.045 |
6.186 |
| 30 |
.262 |
.410 |
.551 |
.697 |
.858 |
1.05 |
1.280 |
1.600 |
2.142 |
2.690 |
2.868 |
3.101 |
3.434 |
4.018 |
6.125 |
| 35 |
.262 |
.410 |
.550 |
.696 |
.856 |
1.04 |
1.271 |
1.585 |
2.113 |
2.641 |
2.813 |
3.036 |
3.354 |
3.908 |
5.876 |
| 40 |
.263 |
.410 |
.550 |
.695 |
.854 |
1.04 |
1.264 |
1.574 |
2.091 |
2.606 |
2.773 |
2.989 |
3.295 |
3.828 |
5.698 |
| 45 |
.263 |
.411 |
.550 |
.694 |
.852 |
1.03 |
1.259 |
1.565 |
2.074 |
2.579 |
2.742 |
2.952 |
3.251 |
3.767 |
5.564 |
| 50 |
.263 |
.411 |
.550 |
.693 |
.851 |
1.03 |
1.255 |
1.558 |
2.061 |
2.557 |
2.717 |
2.923 |
3.215 |
3.720 |
5.459 |
| 55 |
.264 |
.411 |
.550 |
.693 |
.850 |
1.03 |
1.252 |
1.552 |
2.050 |
2.540 |
2.697 |
2.900 |
3.187 |
3.681 |
5.375 |
| 60 |
.264 |
.411 |
.550 |
.693 |
.849 |
1.03 |
1.249 |
1.548 |
2.041 |
2.525 |
2.680 |
2.881 |
3.163 |
3.649 |
5.307 |
| 70 |
.264 |
.411 |
.549 |
.692 |
.847 |
1.03 |
1.245 |
1.540 |
2.027 |
2.503 |
2.655 |
2.851 |
3.127 |
3.600 |
5.201 |
| 80 |
.264 |
.411 |
.549 |
.691 |
.846 |
1.02 |
1.242 |
1.535 |
2.016 |
2.486 |
2.636 |
2.828 |
3.100 |
3.563 |
5.123 |
| 90 |
.265 |
.411 |
.549 |
.691 |
.846 |
1.02 |
1.239 |
1.531 |
2.008 |
2.473 |
2.621 |
2.811 |
3.079 |
3.535 |
5.064 |
| 100 |
.265 |
.411 |
.549 |
.691 |
.845 |
1.02 |
1.237 |
1.527 |
2.002 |
2.463 |
2.609 |
2.798 |
3.062 |
3.513 |
5.017 |
| 120 |
.265 |
.412 |
.549 |
.690 |
.844 |
1.02 |
1.234 |
1.522 |
1.992 |
2.447 |
2.592 |
2.777 |
3.037 |
3.480 |
4.947 |
| 240 |
.265 |
.412 |
.549 |
.689 |
.842 |
1.02 |
1.227 |
1.510 |
1.968 |
2.409 |
2.549 |
2.727 |
2.976 |
3.398 |
4.778 |
| ∞ |
.266 |
.412 |
.549 |
.688 |
.839 |
1.01 |
1.220 |
1.497 |
1.945 |
2.372 |
2.506 |
2.678 |
2.917 |
3.319 |
4.617 |