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| The F Distribution: Values of F (alpha = 0.01) | |||||||||||
| 0.01 | |||||||||||
| see below for more | |||||||||||
| Degees of Freedom of the numerator | df1 | ||||||||||
| df2 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | df2 |
| 1 | 4052.185 | 4999.34 | 5403.534 | 5624.257 | 5763.955 | 5858.95 | 5928.334 | 5980.954 | 6022.397 | 6055.925 | 1 |
| 2 | 98.50191 | 99.00032 | 99.16403 | 99.25134 | 99.30227 | 99.33137 | 99.35684 | 99.37503 | 99.38958 | 99.39686 | 2 |
| 3 | 34.11606 | 30.81641 | 29.45671 | 28.71002 | 28.23708 | 27.91057 | 27.67138 | 27.48948 | 27.34487 | 27.22845 | 3 |
| 4 | 21.19759 | 17.99981 | 16.69423 | 15.97709 | 15.52189 | 15.20675 | 14.97574 | 14.79884 | 14.65924 | 14.546 | 4 |
| 5 | 16.25813 | 13.27408 | 12.0599 | 11.39188 | 10.96714 | 10.67224 | 10.45555 | 10.28934 | 10.15769 | 10.05105 | 5 |
| 6 | 13.74519 | 10.92485 | 9.779569 | 9.14838 | 8.745928 | 8.466031 | 8.260031 | 8.101665 | 7.976041 | 7.874178 | 6 |
| 7 | 12.24635 | 9.546511 | 8.451252 | 7.846666 | 7.460358 | 7.191375 | 6.992877 | 6.840082 | 6.718778 | 6.620098 | 7 |
| 8 | 11.25863 | 8.649067 | 7.590984 | 7.006065 | 6.631808 | 6.370669 | 6.177629 | 6.028813 | 5.910579 | 5.814286 | 8 |
| 9 | 10.56151 | 8.021516 | 6.991968 | 6.422056 | 6.056894 | 5.80178 | 5.612833 | 5.467086 | 5.351126 | 5.256538 | 9 |
| 10 | 10.04423 | 7.559493 | 6.552341 | 5.994366 | 5.636366 | 5.3858 | 5.20015 | 5.056677 | 4.942422 | 4.849142 | 10 |
| 11 | 9.646101 | 7.205699 | 6.216737 | 5.668312 | 5.315997 | 5.069182 | 4.886033 | 4.744493 | 4.631545 | 4.539288 | 11 |
| 12 | 9.330279 | 6.926598 | 5.952529 | 5.411948 | 5.064351 | 4.820549 | 4.639503 | 4.499384 | 4.387516 | 4.296055 | 12 |
| 13 | 9.073801 | 6.70093 | 5.739366 | 5.205322 | 4.86159 | 4.620347 | 4.441006 | 4.30208 | 4.191065 | 4.100286 | 13 |
| 14 | 8.861662 | 6.514938 | 5.563891 | 5.035417 | 4.694982 | 4.455842 | 4.277865 | 4.139963 | 4.029687 | 3.939419 | 14 |
| 15 | 8.683173 | 6.358846 | 5.41695 | 4.893195 | 4.555602 | 4.318281 | 4.141555 | 4.004448 | 3.894797 | 3.804928 | 15 |
| 16 | 8.530947 | 6.226287 | 5.292236 | 4.772573 | 4.437425 | 4.201638 | 4.025935 | 3.889568 | 3.780428 | 3.690928 | 16 |
| 17 | 8.399752 | 6.112145 | 5.185029 | 4.668948 | 4.335959 | 4.10148 | 3.926743 | 3.790944 | 3.68226 | 3.593073 | 17 |
| 18 | 8.285497 | 6.012897 | 5.09192 | 4.579022 | 4.247909 | 4.014623 | 3.840626 | 3.705424 | 3.597052 | 3.508148 | 18 |
| 19 | 8.184998 | 5.925926 | 5.010293 | 4.500237 | 4.170772 | 3.938567 | 3.765251 | 3.630532 | 3.522501 | 3.433797 | 19 |
| 20 | 8.095981 | 5.84896 | 4.938215 | 4.430717 | 4.102674 | 3.871435 | 3.698744 | 3.564423 | 3.456677 | 3.3682 | 20 |
| 21 | 8.016627 | 5.780407 | 4.874039 | 4.368815 | 4.042136 | 3.811749 | 3.63957 | 3.505647 | 3.398156 | 3.309822 | 21 |
| 22 | 7.945346 | 5.719016 | 4.816627 | 4.313449 | 3.987964 | 3.758316 | 3.586649 | 3.453039 | 3.345775 | 3.257611 | 22 |
| 23 | 7.881113 | 5.663708 | 4.764843 | 4.263541 | 3.939192 | 3.710227 | 3.539014 | 3.405688 | 3.298624 | 3.210602 | 23 |
| 24 | 7.822905 | 5.613629 | 4.718061 | 4.218464 | 3.895082 | 3.666713 | 3.495927 | 3.362857 | 3.255991 | 3.168054 | 24 |
| 25 | 7.769813 | 5.56804 | 4.675485 | 4.177423 | 3.85495 | 3.627179 | 3.456762 | 3.323919 | 3.217224 | 3.129401 | 25 |
| 26 | 7.721269 | 5.526317 | 4.636547 | 4.139963 | 3.818343 | 3.591083 | 3.421007 | 3.288392 | 3.18181 | 3.094101 | 26 |
| 27 | 7.676704 | 5.488118 | 4.600906 | 4.10563 | 3.784749 | 3.558 | 3.388209 | 3.255821 | 3.149381 | 3.061757 | 27 |
| 28 | 7.635663 | 5.452932 | 4.568108 | 4.074025 | 3.753883 | 3.52756 | 3.358082 | 3.225864 | 3.119538 | 3.032 | 28 |
| 30 | 7.562448 | 5.390348 | 4.509729 | 4.017863 | 3.699029 | 3.473474 | 3.304507 | 3.17263 | 3.066532 | 2.979107 | 30 |
| 40 | 7.314156 | 5.178492 | 4.312597 | 3.828291 | 3.513833 | 3.291007 | 3.123773 | 2.992977 | 2.88756 | 2.800533 | 40 |
| 50 | 7.17057 | 5.05662 | 4.199364 | 3.719549 | 3.407678 | 3.186443 | 3.020176 | 2.890005 | 2.784958 | 2.69813 | 50 |
| 60 | 7.077119 | 4.977437 | 4.125894 | 3.649063 | 3.338869 | 3.118686 | 2.953044 | 2.823271 | 2.718451 | 2.631751 | 60 |
| 120 | 6.850883 | 4.7865 | 3.949083 | 3.479528 | 3.17354 | 2.955858 | 2.791765 | 2.662915 | 2.558579 | 2.472078 | 120 |
| 100,000 | 6.635105 | 4.605397 | 3.781821 | 3.319371 | 3.017448 | 2.802153 | 2.63951 | 2.511456 | 2.407518 | 2.321102 | 100,000 |
| 0.01 | see below for more | ||||||||||
| Degees of Freedom of the numerator | df1 | ||||||||||
| df2 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | df2 |
| 1 | 6083.399 | 6106.682 | 6125.774 | 6143.004 | 6156.974 | 6170.012 | 6181.188 | 6191.432 | 6200.746 | 6208.662 | 1 |
| 2 | 99.40777 | 99.41868 | 99.42232 | 99.42596 | 99.43324 | 99.43687 | 99.44051 | 99.44415 | 99.44779 | 99.44779 | 2 |
| 3 | 27.13205 | 27.05201 | 26.98289 | 26.92377 | 26.87193 | 26.82646 | 26.78644 | 26.75097 | 26.71914 | 26.69003 | 3 |
| 4 | 14.45233 | 14.37365 | 14.30635 | 14.2486 | 14.19812 | 14.15401 | 14.11445 | 14.07943 | 14.04806 | 14.01941 | 4 |
| 5 | 9.962605 | 9.888254 | 9.824817 | 9.770019 | 9.722271 | 9.680207 | 9.642918 | 9.609494 | 9.579708 | 9.55265 | 5 |
| 6 | 7.789595 | 7.718313 | 7.657491 | 7.604967 | 7.559038 | 7.518565 | 7.48264 | 7.450581 | 7.421932 | 7.395784 | 6 |
| 7 | 6.53813 | 6.469122 | 6.410005 | 6.35896 | 6.314394 | 6.275059 | 6.240043 | 6.208893 | 6.180812 | 6.15546 | 7 |
| 8 | 5.73425 | 5.66672 | 5.608911 | 5.558832 | 5.515176 | 5.476522 | 5.442303 | 5.411607 | 5.384095 | 5.359084 | 8 |
| 9 | 5.177867 | 5.111474 | 5.054517 | 5.005177 | 4.962089 | 4.924004 | 4.890182 | 4.859885 | 4.832657 | 4.807987 | 9 |
| 10 | 4.77155 | 4.705839 | 4.649621 | 4.600849 | 4.55816 | 4.520416 | 4.486935 | 4.456922 | 4.429864 | 4.405365 | 10 |
| 11 | 4.462436 | 4.397407 | 4.341643 | 4.29327 | 4.250865 | 4.213462 | 4.180151 | 4.150309 | 4.123422 | 4.099036 | 11 |
| 12 | 4.219828 | 4.155254 | 4.099832 | 4.051742 | 4.009621 | 3.972389 | 3.939192 | 3.90952 | 3.88269 | 3.858418 | 12 |
| 13 | 4.024514 | 3.960338 | 3.9052 | 3.857338 | 3.815387 | 3.778268 | 3.745185 | 3.71557 | 3.688854 | 3.66461 | 13 |
| 14 | 3.864045 | 3.800153 | 3.745242 | 3.697551 | 3.655714 | 3.61868 | 3.585683 | 3.556124 | 3.529408 | 3.505221 | 14 |
| 15 | 3.729895 | 3.66623 | 3.611518 | 3.56394 | 3.522189 | 3.485241 | 3.452328 | 3.42277 | 3.396082 | 3.371895 | 15 |
| 16 | 3.616151 | 3.552685 | 3.498087 | 3.450623 | 3.408957 | 3.372065 | 3.339153 | 3.309594 | 3.282935 | 3.25872 | 16 |
| 17 | 3.518494 | 3.455199 | 3.400714 | 3.353307 | 3.311698 | 3.274806 | 3.241922 | 3.212392 | 3.185733 | 3.161517 | 17 |
| 18 | 3.433797 | 3.370616 | 3.316217 | 3.268894 | 3.227285 | 3.190451 | 3.157538 | 3.128008 | 3.10132 | 3.077105 | 18 |
| 19 | 3.359617 | 3.29652 | 3.242207 | 3.194913 | 3.153332 | 3.116497 | 3.083613 | 3.054055 | 3.027367 | 3.003095 | 19 |
| 20 | 3.294105 | 3.231122 | 3.176865 | 3.1296 | 3.088047 | 3.051184 | 3.0183 | 2.988742 | 2.961997 | 2.937725 | 20 |
| 21 | 3.235868 | 3.172943 | 3.118743 | 3.071506 | 3.029953 | 2.99309 | 2.960178 | 2.930619 | 2.903846 | 2.879545 | 21 |
| 22 | 3.183743 | 3.120874 | 3.066702 | 3.019494 | 2.977941 | 2.941078 | 2.908166 | 2.878551 | 2.851777 | 2.827448 | 22 |
| 23 | 3.136819 | 3.074035 | 3.019863 | 2.972655 | 2.931131 | 2.89424 | 2.861299 | 2.831683 | 2.804882 | 2.780496 | 23 |
| 24 | 3.094357 | 3.03163 | 2.977487 | 2.930278 | 2.888726 | 2.851863 | 2.818894 | 2.789221 | 2.762391 | 2.738005 | 24 |
| 25 | 3.05576 | 2.993062 | 2.938947 | 2.891738 | 2.850186 | 2.813294 | 2.780297 | 2.750625 | 2.723766 | 2.699323 | 25 |
| 26 | 3.020546 | 2.957847 | 2.903761 | 2.856552 | 2.814971 | 2.77808 | 2.745054 | 2.715353 | 2.688452 | 2.663995 | 26 |
| 27 | 2.98823 | 2.92556 | 2.871502 | 2.824294 | 2.782713 | 2.745765 | 2.712738 | 2.682995 | 2.656066 | 2.63158 | 27 |
| 28 | 2.958501 | 2.895888 | 2.841801 | 2.794593 | 2.753012 | 2.716035 | 2.682981 | 2.653223 | 2.62628 | 2.601752 | 28 |
| 30 | 2.905693 | 2.843109 | 2.789022 | 2.741814 | 2.700176 | 2.663199 | 2.630088 | 2.600245 | 2.573245 | 2.54866 | 30 |
| 40 | 2.727347 | 2.664819 | 2.610733 | 2.563411 | 2.521617 | 2.484427 | 2.451088 | 2.421018 | 2.393733 | 2.368878 | 40 |
| 50 | 2.625029 | 2.562501 | 2.50833 | 2.460894 | 2.418957 | 2.381597 | 2.348074 | 2.317805 | 2.290321 | 2.265239 | 50 |
| 60 | 2.558664 | 2.496108 | 2.44188 | 2.394344 | 2.352294 | 2.314806 | 2.281126 | 2.250701 | 2.223047 | 2.197808 | 60 |
| 120 | 2.398991 | 2.336293 | 2.281809 | 2.233946 | 2.191499 | 2.15357 | 2.119435 | 2.088512 | 2.060347 | 2.034582 | 120 |
| 100,000 | 2.247901 | 2.184919 | 2.130037 | 2.081691 | 2.038703 | 2.000178 | 1.965397 | 1.933813 | 1.904965 | 1.87849 | 100,000 |
| 0.01 | |||||||||||
| Degees of Freedom of the numerator | df1 | ||||||||||
| df2 | 21 | 22 | 23 | 24 | 25 | 30 | 40 | 60 | 120 | 10000 | df2 |
| 1 | 6216.113 | 6223.097 | 6228.685 | 6234.273 | 6239.861 | 6260.35 | 6286.427 | 6312.97 | 6339.513 | 6365.59 | 1 |
| 2 | 99.45143 | 99.45506 | 99.45506 | 99.45506 | 99.4587 | 99.46598 | 99.47689 | 99.48417 | 99.49144 | 99.49872 | 2 |
| 3 | 26.66366 | 26.6391 | 26.61727 | 26.59726 | 26.57907 | 26.50449 | 26.41082 | 26.31623 | 26.22073 | 26.12614 | 3 |
| 4 | 13.99394 | 13.97029 | 13.94892 | 13.92891 | 13.91072 | 13.83751 | 13.74519 | 13.6522 | 13.55829 | 13.46416 | 4 |
| 5 | 9.528094 | 9.505811 | 9.485348 | 9.466476 | 9.449195 | 9.379391 | 9.29117 | 9.20204 | 9.111773 | 9.021505 | 5 |
| 6 | 7.372137 | 7.35065 | 7.330868 | 7.312792 | 7.295966 | 7.22855 | 7.143171 | 7.056769 | 6.969003 | 6.881123 | 6 |
| 7 | 6.132382 | 6.11135 | 6.092023 | 6.074288 | 6.057917 | 5.991978 | 5.908419 | 5.823608 | 5.73732 | 5.650577 | 7 |
| 8 | 5.33646 | 5.315712 | 5.296727 | 5.279276 | 5.263132 | 5.198103 | 5.115567 | 5.031609 | 4.94606 | 4.859885 | 8 |
| 9 | 4.785534 | 4.76507 | 4.746312 | 4.729031 | 4.713002 | 4.648598 | 4.566687 | 4.48307 | 4.397748 | 4.311573 | 9 |
| 10 | 4.383139 | 4.362789 | 4.344088 | 4.326921 | 4.311062 | 4.246942 | 4.165258 | 4.081869 | 3.99649 | 3.910031 | 10 |
| 11 | 4.076867 | 4.056631 | 4.038043 | 4.020933 | 4.005074 | 3.941125 | 3.859554 | 3.776051 | 3.690445 | 3.603532 | 11 |
| 12 | 3.836305 | 3.816126 | 3.797595 | 3.780485 | 3.764683 | 3.700791 | 3.619164 | 3.53549 | 3.449429 | 3.36189 | 12 |
| 13 | 3.642526 | 3.622347 | 3.603816 | 3.586763 | 3.57096 | 3.50704 | 3.425271 | 3.341285 | 3.25474 | 3.166491 | 13 |
| 14 | 3.483194 | 3.463015 | 3.444484 | 3.427374 | 3.411571 | 3.347594 | 3.265654 | 3.18127 | 3.094186 | 3.005113 | 14 |
| 15 | 3.34984 | 3.32966 | 3.311129 | 3.294019 | 3.278217 | 3.214097 | 3.131902 | 3.047148 | 2.959439 | 2.869541 | 15 |
| 16 | 3.236664 | 3.216485 | 3.197925 | 3.180816 | 3.164985 | 3.100723 | 3.018243 | 2.933035 | 2.844729 | 2.75395 | 16 |
| 17 | 3.139434 | 3.119226 | 3.100638 | 3.0835 | 3.06764 | 3.003237 | 2.920444 | 2.83481 | 2.74585 | 2.654161 | 17 |
| 18 | 3.054993 | 3.034756 | 3.01614 | 2.998974 | 2.983086 | 2.918512 | 2.835407 | 2.749317 | 2.659704 | 2.567106 | 18 |
| 19 | 2.980983 | 2.960718 | 2.942073 | 2.924878 | 2.908934 | 2.844189 | 2.7608 | 2.674199 | 2.583931 | 2.490452 | 19 |
| 20 | 2.915584 | 2.895291 | 2.876618 | 2.859366 | 2.843393 | 2.778478 | 2.694748 | 2.60772 | 2.516771 | 2.422368 | 20 |
| 21 | 2.857377 | 2.837027 | 2.818325 | 2.801045 | 2.785043 | 2.719958 | 2.635886 | 2.548404 | 2.456815 | 2.361489 | 21 |
| 22 | 2.805223 | 2.784873 | 2.766114 | 2.748806 | 2.732776 | 2.667491 | 2.583107 | 2.495142 | 2.402913 | 2.306678 | 22 |
| 23 | 2.758242 | 2.737849 | 2.719077 | 2.701711 | 2.685653 | 2.620197 | 2.535501 | 2.447081 | 2.354199 | 2.257067 | 23 |
| 24 | 2.715723 | 2.695273 | 2.676444 | 2.659078 | 2.642963 | 2.577337 | 2.492328 | 2.403453 | 2.309946 | 2.21192 | 24 |
| 25 | 2.677012 | 2.65652 | 2.637677 | 2.620254 | 2.604111 | 2.538314 | 2.452992 | 2.363691 | 2.269559 | 2.170637 | 25 |
| 26 | 2.641627 | 2.621135 | 2.602235 | 2.584784 | 2.568612 | 2.502617 | 2.417011 | 2.327283 | 2.232539 | 2.132737 | 26 |
| 27 | 2.609198 | 2.588649 | 2.56972 | 2.552241 | 2.536012 | 2.469875 | 2.383956 | 2.293802 | 2.198462 | 2.097792 | 27 |
| 28 | 2.579327 | 2.55875 | 2.539792 | 2.52227 | 2.506027 | 2.439691 | 2.353502 | 2.262937 | 2.166999 | 2.065462 | 28 |
| 30 | 2.526178 | 2.505544 | 2.486502 | 2.468923 | 2.452595 | 2.385974 | 2.299203 | 2.207855 | 2.110767 | 2.007539 | 30 |
| 40 | 2.346113 | 2.32518 | 2.305882 | 2.288004 | 2.271392 | 2.203379 | 2.114234 | 2.019405 | 1.917186 | 1.806136 | 40 |
| 50 | 2.24226 | 2.221114 | 2.201588 | 2.183484 | 2.166658 | 2.097593 | 2.006587 | 1.909029 | 1.802597 | 1.684661 | 50 |
| 60 | 2.174659 | 2.153342 | 2.133632 | 2.115371 | 2.098375 | 2.028472 | 1.936016 | 1.836256 | 1.72632 | 1.602288 | 60 |
| 120 | 2.010907 | 1.989051 | 1.968822 | 1.950013 | 1.932492 | 1.860002 | 1.762849 | 1.655692 | 1.532992 | 1.382666 | 120 |
| 100,000 | 1.854097 | 1.831523 | 1.810548 | 1.791015 | 1.772754 | 1.696598 | 1.592475 | 1.473214 | 1.324857 | 1.034879 | 100,000 |