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| The F Distribution: Values of F (alpha = 0.10) | |||||||||||
| 0.1 | |||||||||||
| see below for more | |||||||||||
| Degees of Freedom of the numerator | df1 | ||||||||||
| df2 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | df2 |
| 1 | 39.86361 | 49.50016 | 53.59334 | 55.83297 | 57.23996 | 58.20448 | 58.90615 | 59.43912 | 59.85748 | 60.19491 | 1 |
| 2 | 8.526342 | 9.000019 | 9.161795 | 9.243422 | 9.292648 | 9.325504 | 9.349094 | 9.366772 | 9.380528 | 9.391556 | 2 |
| 3 | 5.538311 | 5.462397 | 5.390774 | 5.342656 | 5.309147 | 5.284733 | 5.266202 | 5.251678 | 5.239997 | 5.230419 | 3 |
| 4 | 4.544773 | 4.324562 | 4.190866 | 4.10725 | 4.050577 | 4.009749 | 3.978968 | 3.954938 | 3.935668 | 3.91988 | 4 |
| 5 | 4.060411 | 3.779718 | 3.619476 | 3.520199 | 3.452982 | 3.404509 | 3.367902 | 3.339281 | 3.316281 | 3.297401 | 5 |
| 6 | 3.775952 | 3.463299 | 3.288761 | 3.180759 | 3.107516 | 3.054552 | 3.014456 | 2.983036 | 2.957741 | 2.936936 | 6 |
| 7 | 3.589435 | 3.257441 | 3.074071 | 2.960533 | 2.883347 | 2.827392 | 2.78493 | 2.751577 | 2.724676 | 2.702514 | 7 |
| 8 | 3.457913 | 3.113115 | 2.923798 | 2.806424 | 2.726445 | 2.668337 | 2.624134 | 2.589349 | 2.561237 | 2.538037 | 8 |
| 9 | 3.360299 | 3.006448 | 2.812861 | 2.69268 | 2.610612 | 2.550856 | 2.505313 | 2.469406 | 2.440338 | 2.416314 | 9 |
| 10 | 3.28501 | 2.924466 | 2.727674 | 2.60534 | 2.521638 | 2.460581 | 2.413962 | 2.377149 | 2.347306 | 2.322604 | 10 |
| 11 | 3.225196 | 2.859508 | 2.660229 | 2.53619 | 2.451184 | 2.389065 | 2.341565 | 2.303999 | 2.273502 | 2.248228 | 11 |
| 12 | 3.176552 | 2.806793 | 2.605525 | 2.4801 | 2.394025 | 2.331024 | 2.282782 | 2.244576 | 2.213525 | 2.187765 | 12 |
| 13 | 3.136208 | 2.763166 | 2.56027 | 2.433708 | 2.346724 | 2.282981 | 2.234103 | 2.19535 | 2.163819 | 2.137636 | 13 |
| 14 | 3.102215 | 2.726466 | 2.522221 | 2.394692 | 2.30694 | 2.242558 | 2.193133 | 2.153904 | 2.121954 | 2.095398 | 14 |
| 15 | 3.073183 | 2.695174 | 2.489788 | 2.361432 | 2.273023 | 2.208083 | 2.158178 | 2.118529 | 2.08621 | 2.05932 | 15 |
| 16 | 3.048115 | 2.668173 | 2.46181 | 2.332747 | 2.243759 | 2.178329 | 2.128004 | 2.087983 | 2.05533 | 2.028145 | 16 |
| 17 | 3.02623 | 2.64464 | 2.437432 | 2.307747 | 2.21825 | 2.15239 | 2.101689 | 2.061334 | 2.02839 | 2.000938 | 17 |
| 18 | 3.006974 | 2.623949 | 2.416005 | 2.285773 | 2.195826 | 2.129582 | 2.078544 | 2.03789 | 2.004676 | 1.976979 | 18 |
| 19 | 2.9899 | 2.60561 | 2.397023 | 2.266304 | 2.175955 | 2.109363 | 2.05802 | 2.017096 | 1.98364 | 1.955726 | 19 |
| 20 | 2.974652 | 2.589253 | 2.380087 | 2.248935 | 2.158227 | 2.091323 | 2.039702 | 1.998533 | 1.964853 | 1.936737 | 20 |
| 21 | 2.960959 | 2.574566 | 2.364885 | 2.233342 | 2.142311 | 2.075122 | 2.023253 | 1.98186 | 1.947974 | 1.919673 | 21 |
| 22 | 2.948582 | 2.561315 | 2.351172 | 2.219274 | 2.127944 | 2.060496 | 2.008395 | 1.966797 | 1.932726 | 1.904255 | 22 |
| 23 | 2.937355 | 2.549292 | 2.338727 | 2.206512 | 2.114909 | 2.047226 | 1.994916 | 1.953126 | 1.918881 | 1.890253 | 23 |
| 24 | 2.927116 | 2.538329 | 2.32739 | 2.194881 | 2.103032 | 2.035133 | 1.982624 | 1.940659 | 1.906255 | 1.877481 | 24 |
| 25 | 2.917744 | 2.528303 | 2.317016 | 2.184244 | 2.092165 | 2.024063 | 1.971376 | 1.929244 | 1.894694 | 1.865782 | 25 |
| 26 | 2.909132 | 2.519094 | 2.307491 | 2.174467 | 2.082182 | 2.013891 | 1.961041 | 1.918757 | 1.884068 | 1.855028 | 26 |
| 27 | 2.901189 | 2.51061 | 2.298712 | 2.165464 | 2.07298 | 2.004519 | 1.951509 | 1.909086 | 1.874266 | 1.845109 | 27 |
| 28 | 2.893842 | 2.502759 | 2.290598 | 2.157137 | 2.064475 | 1.995851 | 1.942695 | 1.90014 | 1.8652 | 1.835929 | 28 |
| 30 | 2.880697 | 2.488719 | 2.276071 | 2.142237 | 2.049248 | 1.980332 | 1.926917 | 1.884121 | 1.848958 | 1.819487 | 30 |
| 40 | 2.83535 | 2.440366 | 2.226091 | 2.09095 | 1.99682 | 1.926878 | 1.872522 | 1.828862 | 1.792902 | 1.762686 | 40 |
| 50 | 2.808662 | 2.411955 | 2.196728 | 2.060816 | 1.966001 | 1.89543 | 1.840498 | 1.796298 | 1.759837 | 1.729148 | 50 |
| 60 | 2.791069 | 2.393257 | 2.177408 | 2.040984 | 1.945711 | 1.874721 | 1.819394 | 1.774829 | 1.73802 | 1.707008 | 60 |
| 120 | 2.747811 | 2.347338 | 2.12999 | 1.992301 | 1.895874 | 1.82381 | 1.767475 | 1.721959 | 1.684249 | 1.65238 | 120 |
| 100,000 | 2.70559 | 2.302638 | 2.083851 | 1.944915 | 1.847329 | 1.774165 | 1.71678 | 1.670257 | 1.63158 | 1.598782 | 100,000 |
| 0.1 | see below for more | ||||||||||
| Degees of Freedom of the numerator | df1 | ||||||||||
| df2 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | df2 |
| 1 | 60.47276 | 60.70513 | 60.90249 | 61.07257 | 61.22036 | 61.34997 | 61.46456 | 61.56642 | 61.65783 | 61.74014 | 1 |
| 2 | 9.400594 | 9.408154 | 9.414521 | 9.419978 | 9.424696 | 9.428845 | 9.43254 | 9.43578 | 9.438679 | 9.441294 | 2 |
| 3 | 5.222404 | 5.215611 | 5.209785 | 5.20474 | 5.20032 | 5.196398 | 5.192931 | 5.189818 | 5.187019 | 5.184489 | 3 |
| 4 | 3.906692 | 3.895522 | 3.885944 | 3.877631 | 3.870355 | 3.863931 | 3.858219 | 3.853103 | 3.848498 | 3.844335 | 4 |
| 5 | 3.281627 | 3.268241 | 3.256744 | 3.246761 | 3.238014 | 3.230284 | 3.223398 | 3.217238 | 3.211682 | 3.206651 | 5 |
| 6 | 2.919521 | 2.90472 | 2.891994 | 2.880931 | 2.871218 | 2.862635 | 2.854989 | 2.848125 | 2.841944 | 2.836337 | 6 |
| 7 | 2.683926 | 2.668109 | 2.654495 | 2.642643 | 2.632227 | 2.623011 | 2.614797 | 2.607422 | 2.600764 | 2.594732 | 7 |
| 8 | 2.518554 | 2.501956 | 2.487646 | 2.475176 | 2.464215 | 2.454499 | 2.44583 | 2.438046 | 2.431015 | 2.424635 | 8 |
| 9 | 2.396114 | 2.378883 | 2.364011 | 2.35104 | 2.339625 | 2.3295 | 2.320455 | 2.312333 | 2.30499 | 2.298322 | 9 |
| 10 | 2.30181 | 2.284054 | 2.268706 | 2.255312 | 2.243514 | 2.233044 | 2.223683 | 2.215266 | 2.207656 | 2.200743 | 10 |
| 11 | 2.22693 | 2.208726 | 2.19298 | 2.17922 | 2.167091 | 2.15632 | 2.146685 | 2.138016 | 2.130175 | 2.123045 | 11 |
| 12 | 2.166033 | 2.147438 | 2.13134 | 2.117268 | 2.104851 | 2.093813 | 2.083937 | 2.075048 | 2.066997 | 2.059679 | 12 |
| 13 | 2.11552 | 2.096588 | 2.080185 | 2.065832 | 2.053159 | 2.04189 | 2.031797 | 2.022706 | 2.014474 | 2.006981 | 13 |
| 14 | 2.072952 | 2.053714 | 2.037037 | 2.022432 | 2.009536 | 1.998053 | 1.987768 | 1.978499 | 1.970101 | 1.962452 | 14 |
| 15 | 2.036575 | 2.017071 | 2.000149 | 1.98532 | 1.972214 | 1.960547 | 1.950085 | 1.940652 | 1.932101 | 1.924313 | 15 |
| 16 | 2.005134 | 1.985388 | 1.968242 | 1.953211 | 1.93992 | 1.928079 | 1.91746 | 1.907878 | 1.899188 | 1.891273 | 16 |
| 17 | 1.977682 | 1.957716 | 1.940371 | 1.925155 | 1.911694 | 1.899696 | 1.888928 | 1.879211 | 1.870397 | 1.862361 | 17 |
| 18 | 1.953509 | 1.933341 | 1.915812 | 1.900428 | 1.886811 | 1.874668 | 1.863764 | 1.853923 | 1.844992 | 1.836845 | 18 |
| 19 | 1.932051 | 1.911701 | 1.894005 | 1.878465 | 1.864706 | 1.852428 | 1.841403 | 1.831445 | 1.822404 | 1.814154 | 19 |
| 20 | 1.912881 | 1.892364 | 1.874511 | 1.85883 | 1.844935 | 1.832534 | 1.821395 | 1.811328 | 1.802185 | 1.793843 | 20 |
| 21 | 1.89565 | 1.874973 | 1.85698 | 1.841165 | 1.827146 | 1.814632 | 1.803384 | 1.793218 | 1.783981 | 1.77555 | 21 |
| 22 | 1.880073 | 1.859256 | 1.841126 | 1.825189 | 1.811056 | 1.798433 | 1.787086 | 1.776826 | 1.767503 | 1.758988 | 22 |
| 23 | 1.865924 | 1.844974 | 1.826724 | 1.810669 | 1.79643 | 1.783707 | 1.772268 | 1.761919 | 1.752511 | 1.743921 | 23 |
| 24 | 1.853017 | 1.831943 | 1.813575 | 1.797416 | 1.783075 | 1.77026 | 1.758732 | 1.748301 | 1.738815 | 1.730152 | 24 |
| 25 | 1.841194 | 1.820002 | 1.801528 | 1.785267 | 1.770834 | 1.757931 | 1.746319 | 1.735811 | 1.726253 | 1.71752 | 25 |
| 26 | 1.830323 | 1.809024 | 1.790447 | 1.774092 | 1.75957 | 1.746585 | 1.734897 | 1.724315 | 1.714689 | 1.705889 | 26 |
| 27 | 1.820293 | 1.798892 | 1.780222 | 1.763777 | 1.749171 | 1.736108 | 1.724345 | 1.713696 | 1.704004 | 1.695145 | 27 |
| 28 | 1.811014 | 1.789513 | 1.770754 | 1.754227 | 1.739544 | 1.726406 | 1.714573 | 1.703858 | 1.694104 | 1.685187 | 28 |
| 30 | 1.79438 | 1.772705 | 1.753779 | 1.737099 | 1.722272 | 1.708997 | 1.697039 | 1.686203 | 1.676336 | 1.66731 | 30 |
| 40 | 1.736886 | 1.714563 | 1.69503 | 1.677776 | 1.662411 | 1.648628 | 1.636186 | 1.624894 | 1.614591 | 1.605152 | 40 |
| 50 | 1.702908 | 1.680167 | 1.660242 | 1.642615 | 1.626896 | 1.612776 | 1.600016 | 1.588418 | 1.577824 | 1.568107 | 50 |
| 60 | 1.68046 | 1.65743 | 1.637227 | 1.619338 | 1.603368 | 1.589012 | 1.576021 | 1.564207 | 1.553405 | 1.543485 | 60 |
| 120 | 1.625015 | 1.601205 | 1.580258 | 1.561656 | 1.545002 | 1.529987 | 1.516367 | 1.503943 | 1.492555 | 1.482071 | 120 |
| 100,000 | 1.57052 | 1.545844 | 1.524061 | 1.504651 | 1.487211 | 1.471435 | 1.457073 | 1.443929 | 1.43184 | 1.420673 | 100,000 |
| 0.1 | |||||||||||
| Degees of Freedom of the numerator | df1 | ||||||||||
| df2 | 21 | 22 | 23 | 24 | 25 | 30 | 40 | 60 | 120 | 10000 | df2 |
| 1 | 61.81472 | 61.88293 | 61.94477 | 62.00207 | 62.05482 | 62.26492 | 62.52912 | 62.79424 | 63.06072 | 63.32493 | 1 |
| 2 | 9.443681 | 9.445841 | 9.447831 | 9.449593 | 9.451298 | 9.457949 | 9.466248 | 9.474547 | 9.482903 | 9.491146 | 2 |
| 3 | 5.182187 | 5.18007 | 5.178151 | 5.176361 | 5.174726 | 5.168118 | 5.15972 | 5.151179 | 5.14251 | 5.133813 | 3 |
| 4 | 3.840555 | 3.837087 | 3.833918 | 3.830991 | 3.828305 | 3.817419 | 3.803621 | 3.789566 | 3.77527 | 3.760903 | 4 |
| 5 | 3.202075 | 3.19789 | 3.194053 | 3.190522 | 3.18726 | 3.17408 | 3.157325 | 3.140229 | 3.122793 | 3.105214 | 5 |
| 6 | 2.831236 | 2.826575 | 2.82229 | 2.818346 | 2.814701 | 2.799958 | 2.781171 | 2.761951 | 2.74229 | 2.722409 | 6 |
| 7 | 2.589232 | 2.584201 | 2.579583 | 2.575327 | 2.57139 | 2.55546 | 2.535096 | 2.51422 | 2.49279 | 2.471054 | 7 |
| 8 | 2.418822 | 2.413501 | 2.408605 | 2.404096 | 2.399922 | 2.383018 | 2.361361 | 2.3391 | 2.316181 | 2.292854 | 8 |
| 9 | 2.292239 | 2.286672 | 2.281553 | 2.276828 | 2.272458 | 2.254719 | 2.231957 | 2.208495 | 2.184272 | 2.159531 | 9 |
| 10 | 2.194433 | 2.188653 | 2.183334 | 2.178425 | 2.173884 | 2.155424 | 2.131692 | 2.107161 | 2.081766 | 2.055742 | 10 |
| 11 | 2.116536 | 2.110568 | 2.105075 | 2.100006 | 2.095309 | 2.076213 | 2.05161 | 2.02612 | 1.999652 | 1.972445 | 11 |
| 12 | 2.052989 | 2.046857 | 2.041208 | 2.035993 | 2.031161 | 2.011493 | 1.986102 | 1.959734 | 1.932278 | 1.903967 | 12 |
| 13 | 2.000135 | 1.99385 | 1.988063 | 1.982716 | 1.97776 | 1.957574 | 1.931465 | 1.904287 | 1.875915 | 1.846562 | 13 |
| 14 | 1.95546 | 1.949044 | 1.943128 | 1.937664 | 1.932595 | 1.911932 | 1.885162 | 1.857234 | 1.828001 | 1.797662 | 14 |
| 15 | 1.91719 | 1.910649 | 1.90462 | 1.899043 | 1.893874 | 1.872774 | 1.845393 | 1.816764 | 1.78672 | 1.755442 | 15 |
| 16 | 1.884029 | 1.877371 | 1.871236 | 1.865562 | 1.860295 | 1.838792 | 1.810841 | 1.781556 | 1.750747 | 1.718572 | 16 |
| 17 | 1.855003 | 1.848246 | 1.842011 | 1.836241 | 1.830887 | 1.80901 | 1.780528 | 1.750626 | 1.719091 | 1.686054 | 17 |
| 18 | 1.829385 | 1.822528 | 1.816204 | 1.810349 | 1.804914 | 1.782684 | 1.753705 | 1.723222 | 1.690992 | 1.657131 | 18 |
| 19 | 1.806601 | 1.799652 | 1.793243 | 1.787306 | 1.781796 | 1.75924 | 1.729793 | 1.698758 | 1.665869 | 1.631211 | 19 |
| 20 | 1.786198 | 1.779167 | 1.772676 | 1.766667 | 1.761084 | 1.738222 | 1.708333 | 1.676776 | 1.643256 | 1.607827 | 20 |
| 21 | 1.767823 | 1.760714 | 1.754149 | 1.748067 | 1.742418 | 1.719268 | 1.688962 | 1.656908 | 1.622782 | 1.586608 | 21 |
| 22 | 1.751182 | 1.743999 | 1.737364 | 1.731218 | 1.725505 | 1.702084 | 1.671381 | 1.638853 | 1.604148 | 1.567251 | 22 |
| 23 | 1.736041 | 1.72879 | 1.722087 | 1.715879 | 1.710106 | 1.686427 | 1.655351 | 1.622372 | 1.587107 | 1.549511 | 23 |
| 24 | 1.722203 | 1.714884 | 1.708123 | 1.701855 | 1.696026 | 1.672104 | 1.640672 | 1.60726 | 1.571458 | 1.533181 | 24 |
| 25 | 1.709507 | 1.702126 | 1.695305 | 1.688981 | 1.683102 | 1.658947 | 1.627177 | 1.593349 | 1.557032 | 1.518092 | 25 |
| 26 | 1.697813 | 1.690376 | 1.6835 | 1.677122 | 1.671191 | 1.646818 | 1.614724 | 1.580501 | 1.543683 | 1.5041 | 26 |
| 27 | 1.68701 | 1.679517 | 1.672587 | 1.666161 | 1.660181 | 1.6356 | 1.603198 | 1.568594 | 1.531294 | 1.491081 | 27 |
| 28 | 1.676998 | 1.66945 | 1.662471 | 1.655996 | 1.649973 | 1.625192 | 1.592495 | 1.557527 | 1.519759 | 1.478933 | 28 |
| 30 | 1.659018 | 1.651372 | 1.644301 | 1.637737 | 1.63163 | 1.606479 | 1.573229 | 1.537568 | 1.498911 | 1.456904 | 30 |
| 40 | 1.596467 | 1.588447 | 1.581016 | 1.574112 | 1.567674 | 1.541077 | 1.505625 | 1.467157 | 1.424757 | 1.377527 | 40 |
| 50 | 1.559156 | 1.550882 | 1.543206 | 1.536065 | 1.529404 | 1.501798 | 1.464779 | 1.424239 | 1.37894 | 1.327343 | 50 |
| 60 | 1.534342 | 1.525883 | 1.51803 | 1.510719 | 1.503892 | 1.47554 | 1.437343 | 1.3952 | 1.347568 | 1.292209 | 60 |
| 120 | 1.472383 | 1.463395 | 1.455032 | 1.447226 | 1.43992 | 1.409379 | 1.367602 | 1.32034 | 1.264572 | 1.193596 | 120 |
| 100,000 | 1.410317 | 1.40068 | 1.391681 | 1.383254 | 1.375342 | 1.34195 | 1.295215 | 1.240052 | 1.168734 | 1.01908 | 100,000 |