|
|
|
|
| The F Distribution: Values of F (alpha = 0.05) | |||||||||||
| Enter a = | 0.05 | F-Stat | 19.29629 | 0.05 | |||||||
| Enter df1= | 5 | see below for more | |||||||||
| Enter df2= | 2 | Degees of Freedom of the numerator | df1 | ||||||||
| df2 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | df2 |
| 1 | 161.4462 | 199.4995 | 215.7067 | 224.5833 | 230.1604 | 233.9875 | 236.7669 | 238.8842 | 240.5432 | 241.8819 | 1 |
| 2 | 18.51276 | 19.00003 | 19.16419 | 19.24673 | 19.29629 | 19.32949 | 19.35314 | 19.37087 | 19.38474 | 19.39588 | 2 |
| 3 | 10.12796 | 9.552082 | 9.276619 | 9.117173 | 9.013434 | 8.940674 | 8.88673 | 8.845234 | 8.812322 | 8.785491 | 3 |
| 4 | 7.70865 | 6.944276 | 6.591392 | 6.388234 | 6.256073 | 6.163134 | 6.094211 | 6.041034 | 5.9988 | 5.964353 | 4 |
| 5 | 6.607877 | 5.786148 | 5.409447 | 5.192163 | 5.050339 | 4.950294 | 4.875858 | 4.818332 | 4.77246 | 4.735057 | 5 |
| 6 | 5.987374 | 5.143249 | 4.757055 | 4.533689 | 4.387374 | 4.283862 | 4.206669 | 4.146813 | 4.099007 | 4.059956 | 6 |
| 7 | 5.59146 | 4.737416 | 4.34683 | 4.120309 | 3.971522 | 3.865978 | 3.787051 | 3.725717 | 3.676675 | 3.636529 | 7 |
| 8 | 5.317645 | 4.458968 | 4.06618 | 3.837854 | 3.687504 | 3.580581 | 3.50046 | 3.438103 | 3.388124 | 3.347168 | 8 |
| 9 | 5.117357 | 4.256492 | 3.862539 | 3.63309 | 3.481659 | 3.373756 | 3.29274 | 3.229587 | 3.178897 | 3.137274 | 9 |
| 10 | 4.964591 | 4.102816 | 3.708266 | 3.47805 | 3.325837 | 3.217181 | 3.135469 | 3.071662 | 3.020382 | 2.97824 | 10 |
| 11 | 4.844338 | 3.982308 | 3.587431 | 3.356689 | 3.20388 | 3.094613 | 3.012332 | 2.947985 | 2.896222 | 2.853625 | 11 |
| 12 | 4.747221 | 3.88529 | 3.4903 | 3.25916 | 3.105875 | 2.996117 | 2.913353 | 2.848566 | 2.796376 | 2.753389 | 12 |
| 13 | 4.667186 | 3.805567 | 3.410534 | 3.179117 | 3.025434 | 2.915272 | 2.832095 | 2.76691 | 2.714359 | 2.671023 | 13 |
| 14 | 4.600111 | 3.73889 | 3.343885 | 3.112248 | 2.958245 | 2.847727 | 2.764196 | 2.69867 | 2.645791 | 2.602157 | 14 |
| 15 | 4.543068 | 3.682317 | 3.287383 | 3.055568 | 2.901295 | 2.790465 | 2.706628 | 2.640796 | 2.587626 | 2.543715 | 15 |
| 16 | 4.493998 | 3.633716 | 3.238867 | 3.006917 | 2.85241 | 2.741309 | 2.657195 | 2.591094 | 2.537668 | 2.493515 | 16 |
| 17 | 4.451323 | 3.591538 | 3.196774 | 2.964711 | 2.809998 | 2.698656 | 2.6143 | 2.547957 | 2.494289 | 2.449916 | 17 |
| 18 | 4.413863 | 3.554561 | 3.159911 | 2.927749 | 2.77285 | 2.661302 | 2.576719 | 2.510156 | 2.456282 | 2.411703 | 18 |
| 19 | 4.380752 | 3.52189 | 3.127354 | 2.895106 | 2.740059 | 2.628319 | 2.543537 | 2.476767 | 2.422702 | 2.377931 | 19 |
| 20 | 4.35125 | 3.492829 | 3.098393 | 2.866081 | 2.710891 | 2.598981 | 2.514014 | 2.447067 | 2.392817 | 2.347875 | 20 |
| 21 | 4.324789 | 3.466795 | 3.072472 | 2.840096 | 2.684779 | 2.572712 | 2.487582 | 2.420464 | 2.36605 | 2.320952 | 21 |
| 22 | 4.300944 | 3.443361 | 3.049124 | 2.816705 | 2.661274 | 2.549058 | 2.463771 | 2.396504 | 2.341935 | 2.296694 | 22 |
| 23 | 4.279343 | 3.42213 | 3.027999 | 2.795538 | 2.64 | 2.527656 | 2.442228 | 2.374811 | 2.320107 | 2.274724 | 23 |
| 24 | 4.259675 | 3.402832 | 3.008786 | 2.776289 | 2.620652 | 2.508187 | 2.422631 | 2.35508 | 2.300244 | 2.254737 | 24 |
| 25 | 4.241699 | 3.385196 | 2.991243 | 2.758711 | 2.602988 | 2.49041 | 2.404725 | 2.33706 | 2.2821 | 2.236476 | 25 |
| 26 | 4.2252 | 3.36901 | 2.975156 | 2.742595 | 2.586788 | 2.47411 | 2.388312 | 2.320526 | 2.265452 | 2.219718 | 26 |
| 27 | 4.210008 | 3.354131 | 2.960348 | 2.727766 | 2.571888 | 2.45911 | 2.373206 | 2.305313 | 2.250133 | 2.204295 | 27 |
| 28 | 4.195982 | 3.340389 | 2.946685 | 2.714074 | 2.558124 | 2.445262 | 2.359258 | 2.291266 | 2.235979 | 2.190042 | 28 |
| 30 | 4.170886 | 3.315833 | 2.922278 | 2.689632 | 2.533554 | 2.420521 | 2.334346 | 2.266162 | 2.210697 | 2.16458 | 30 |
| 40 | 4.08474 | 3.231733 | 2.838746 | 2.605972 | 2.449468 | 2.335852 | 2.249024 | 2.180172 | 2.124029 | 2.07725 | 40 |
| 50 | 4.03432 | 3.182606 | 2.79001 | 2.557179 | 2.400412 | 2.286434 | 2.199201 | 2.129923 | 2.073349 | 2.026141 | 50 |
| 60 | 4.001194 | 3.150411 | 2.758078 | 2.525212 | 2.368267 | 2.254055 | 2.166541 | 2.096968 | 2.040096 | 1.992593 | 60 |
| 120 | 3.920121 | 3.071776 | 2.680167 | 2.447237 | 2.289852 | 2.175007 | 2.086772 | 2.016428 | 1.958764 | 1.910461 | 120 |
| 100,000 | 3.841549 | 2.995819 | 2.604999 | 2.372019 | 2.214186 | 2.098687 | 2.009685 | 1.938506 | 1.879979 | 1.830799 | 100,000 |
| 0.05 | see below for more | ||||||||||
| Degees of Freedom of the numerator | df1 | ||||||||||
| df2 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | df2 |
| 1 | 242.9806 | 243.9047 | 244.6905 | 245.3635 | 245.9492 | 246.4658 | 246.9169 | 247.3244 | 247.6881 | 248.0156 | 1 |
| 2 | 19.40498 | 19.41248 | 19.41885 | 19.42431 | 19.42908 | 19.43317 | 19.43704 | 19.44022 | 19.44318 | 19.44568 | 2 |
| 3 | 8.763323 | 8.744678 | 8.728648 | 8.714892 | 8.702841 | 8.692268 | 8.682889 | 8.674533 | 8.666973 | 8.660209 | 3 |
| 4 | 5.935817 | 5.911716 | 5.891138 | 5.873346 | 5.8578 | 5.844129 | 5.831964 | 5.821107 | 5.811359 | 5.802548 | 4 |
| 5 | 4.703963 | 4.677702 | 4.65522 | 4.63578 | 4.618755 | 4.603777 | 4.590447 | 4.578538 | 4.567823 | 4.558132 | 5 |
| 6 | 4.027441 | 3.999929 | 3.976368 | 3.955932 | 3.938055 | 3.922281 | 3.908269 | 3.895707 | 3.884409 | 3.874192 | 6 |
| 7 | 3.603034 | 3.574684 | 3.55034 | 3.529237 | 3.510735 | 3.494407 | 3.479869 | 3.466866 | 3.455142 | 3.444526 | 7 |
| 8 | 3.312948 | 3.283944 | 3.259018 | 3.237375 | 3.218403 | 3.201635 | 3.186699 | 3.173312 | 3.161247 | 3.150319 | 8 |
| 9 | 3.102485 | 3.072941 | 3.047546 | 3.025477 | 3.006107 | 2.988969 | 2.973692 | 2.960007 | 2.947651 | 2.93646 | 9 |
| 10 | 2.942954 | 2.912977 | 2.887177 | 2.864724 | 2.845013 | 2.827562 | 2.812008 | 2.798046 | 2.785441 | 2.774016 | 10 |
| 11 | 2.817927 | 2.787573 | 2.761418 | 2.738645 | 2.718636 | 2.700915 | 2.685098 | 2.670902 | 2.658084 | 2.646445 | 11 |
| 12 | 2.717329 | 2.686633 | 2.66018 | 2.637123 | 2.616851 | 2.598881 | 2.582837 | 2.568427 | 2.55541 | 2.543587 | 12 |
| 13 | 2.63465 | 2.603663 | 2.576925 | 2.55362 | 2.533113 | 2.514923 | 2.498673 | 2.484072 | 2.47087 | 2.458883 | 13 |
| 14 | 2.5655 | 2.534243 | 2.507264 | 2.483723 | 2.463004 | 2.444615 | 2.42818 | 2.413401 | 2.400036 | 2.387893 | 14 |
| 15 | 2.506809 | 2.475311 | 2.448111 | 2.424365 | 2.403446 | 2.384873 | 2.368267 | 2.353332 | 2.339817 | 2.327532 | 15 |
| 16 | 2.456368 | 2.424663 | 2.397258 | 2.373319 | 2.352223 | 2.333486 | 2.316725 | 2.30164 | 2.287983 | 2.27557 | 16 |
| 17 | 2.412563 | 2.380652 | 2.353062 | 2.328953 | 2.307694 | 2.2888 | 2.271893 | 2.25667 | 2.242892 | 2.230355 | 17 |
| 18 | 2.374158 | 2.34207 | 2.314302 | 2.290029 | 2.268621 | 2.249585 | 2.232547 | 2.217199 | 2.203297 | 2.190646 | 18 |
| 19 | 2.340208 | 2.307956 | 2.280032 | 2.255611 | 2.23406 | 2.214897 | 2.19773 | 2.182261 | 2.16825 | 2.155495 | 19 |
| 20 | 2.309989 | 2.277581 | 2.249514 | 2.224958 | 2.203272 | 2.183981 | 2.166701 | 2.151125 | 2.137007 | 2.124153 | 20 |
| 21 | 2.282917 | 2.25036 | 2.222158 | 2.197474 | 2.175668 | 2.156263 | 2.138872 | 2.123194 | 2.10898 | 2.096034 | 21 |
| 22 | 2.258517 | 2.225832 | 2.197503 | 2.172698 | 2.150777 | 2.131266 | 2.113772 | 2.097995 | 2.083688 | 2.070657 | 22 |
| 23 | 2.236419 | 2.203606 | 2.17516 | 2.150241 | 2.128218 | 2.1086 | 2.091014 | 2.075147 | 2.060752 | 2.047639 | 23 |
| 24 | 2.216311 | 2.183377 | 2.15482 | 2.129795 | 2.107676 | 2.087965 | 2.070284 | 2.054328 | 2.039858 | 2.026663 | 24 |
| 25 | 2.197929 | 2.164889 | 2.136229 | 2.111108 | 2.088889 | 2.069086 | 2.051323 | 2.035289 | 2.020741 | 2.007472 | 25 |
| 26 | 2.181068 | 2.147928 | 2.119165 | 2.093948 | 2.071644 | 2.051756 | 2.033914 | 2.017799 | 2.003176 | 1.989839 | 26 |
| 27 | 2.165542 | 2.132303 | 2.103448 | 2.078146 | 2.055756 | 2.03579 | 2.01787 | 2.001684 | 1.986994 | 1.973589 | 27 |
| 28 | 2.151197 | 2.117872 | 2.088932 | 2.06354 | 2.04107 | 2.021032 | 2.003038 | 1.986784 | 1.972026 | 1.958561 | 28 |
| 30 | 2.12556 | 2.092065 | 2.062961 | 2.037421 | 2.014804 | 1.994621 | 1.976495 | 1.960117 | 1.945235 | 1.931653 | 30 |
| 40 | 2.037581 | 2.003461 | 1.973756 | 1.947633 | 1.924462 | 1.90375 | 1.885113 | 1.868241 | 1.852893 | 1.83886 | 40 |
| 50 | 1.986056 | 1.951527 | 1.921428 | 1.894925 | 1.871385 | 1.850314 | 1.831335 | 1.814133 | 1.798465 | 1.784123 | 50 |
| 60 | 1.952213 | 1.917396 | 1.887017 | 1.860244 | 1.836437 | 1.815113 | 1.795886 | 1.778446 | 1.762547 | 1.747985 | 60 |
| 120 | 1.869289 | 1.833694 | 1.802555 | 1.775032 | 1.750497 | 1.728463 | 1.708543 | 1.690431 | 1.673879 | 1.65868 | 120 |
| 100,000 | 1.788745 | 1.752269 | 1.720254 | 1.69187 | 1.666486 | 1.643615 | 1.622873 | 1.603954 | 1.586606 | 1.570626 | 100,000 |
| 0.05 | |||||||||||
| Degees of Freedom of the numerator | df1 | ||||||||||
| df2 | 21 | 22 | 23 | 24 | 25 | 30 | 40 | 60 | 120 | 10000 | df2 |
| 1 | 248.3066 | 248.5795 | 248.8232 | 249.0524 | 249.2598 | 250.0965 | 251.1442 | 252.1956 | 253.2543 | 254.302 | 1 |
| 2 | 19.44818 | 19.45023 | 19.45227 | 19.45409 | 19.45568 | 19.4625 | 19.47069 | 19.4791 | 19.48729 | 19.4957 | 2 |
| 3 | 8.654013 | 8.648385 | 8.643269 | 8.638494 | 8.634117 | 8.616553 | 8.594384 | 8.571988 | 8.549364 | 8.52674 | 3 |
| 4 | 5.794533 | 5.787228 | 5.780521 | 5.774382 | 5.768698 | 5.745875 | 5.716998 | 5.687752 | 5.658109 | 5.628436 | 4 |
| 5 | 4.549321 | 4.541278 | 4.533916 | 4.527152 | 4.520899 | 4.495718 | 4.4638 | 4.431371 | 4.398458 | 4.365404 | 5 |
| 6 | 3.864898 | 3.8564 | 3.848612 | 3.84145 | 3.834842 | 3.808168 | 3.774289 | 3.7398 | 3.70467 | 3.6693 | 6 |
| 7 | 3.434863 | 3.426038 | 3.417952 | 3.410491 | 3.403613 | 3.375803 | 3.340432 | 3.304322 | 3.267445 | 3.230213 | 7 |
| 8 | 3.140372 | 3.131277 | 3.122935 | 3.11524 | 3.108134 | 3.079407 | 3.042778 | 3.005297 | 2.966928 | 2.928054 | 8 |
| 9 | 2.926257 | 2.916934 | 2.908365 | 2.900478 | 2.893174 | 2.863658 | 2.825928 | 2.787246 | 2.747527 | 2.707168 | 9 |
| 10 | 2.763599 | 2.754071 | 2.745317 | 2.737252 | 2.729784 | 2.699551 | 2.660855 | 2.621078 | 2.580123 | 2.538393 | 10 |
| 11 | 2.635836 | 2.626123 | 2.617199 | 2.608971 | 2.601361 | 2.570488 | 2.530903 | 2.490125 | 2.448026 | 2.405002 | 11 |
| 12 | 2.532808 | 2.522931 | 2.513858 | 2.50548 | 2.497728 | 2.46628 | 2.425878 | 2.384169 | 2.340997 | 2.296744 | 12 |
| 13 | 2.447941 | 2.437922 | 2.428699 | 2.420194 | 2.412321 | 2.380332 | 2.339178 | 2.296595 | 2.252413 | 2.206995 | 13 |
| 14 | 2.376815 | 2.366654 | 2.357304 | 2.348678 | 2.340691 | 2.308205 | 2.266347 | 2.222947 | 2.177813 | 2.131273 | 14 |
| 15 | 2.31632 | 2.306031 | 2.296566 | 2.287827 | 2.279727 | 2.246786 | 2.204274 | 2.160107 | 2.114056 | 2.066439 | 15 |
| 16 | 2.26423 | 2.253827 | 2.244249 | 2.235403 | 2.22721 | 2.193843 | 2.150713 | 2.105814 | 2.058897 | 2.010239 | 16 |
| 17 | 2.218897 | 2.208388 | 2.198711 | 2.189765 | 2.18148 | 2.147708 | 2.103999 | 2.05841 | 2.010662 | 1.961006 | 17 |
| 18 | 2.179085 | 2.168473 | 2.1587 | 2.149662 | 2.141292 | 2.107143 | 2.062883 | 2.016641 | 1.9681 | 1.917474 | 18 |
| 19 | 2.143835 | 2.133127 | 2.123265 | 2.114142 | 2.105686 | 2.071186 | 2.026411 | 1.979544 | 1.930239 | 1.878671 | 19 |
| 20 | 2.112401 | 2.101601 | 2.091653 | 2.082452 | 2.073918 | 2.039087 | 1.993818 | 1.946358 | 1.896318 | 1.843837 | 20 |
| 21 | 2.084189 | 2.073307 | 2.063281 | 2.054005 | 2.045397 | 2.010246 | 1.964516 | 1.916487 | 1.86574 | 1.812374 | 21 |
| 22 | 2.058727 | 2.04777 | 2.037666 | 2.028319 | 2.019647 | 1.984194 | 1.93802 | 1.889447 | 1.838018 | 1.783789 | 22 |
| 23 | 2.035634 | 2.024599 | 2.014424 | 2.005009 | 1.99627 | 1.960537 | 1.913939 | 1.864844 | 1.812761 | 1.757691 | 23 |
| 24 | 2.014584 | 2.003482 | 1.993239 | 1.983757 | 1.974961 | 1.938957 | 1.891955 | 1.842359 | 1.789644 | 1.733756 | 24 |
| 25 | 1.995321 | 1.984152 | 1.973845 | 1.964306 | 1.955449 | 1.919187 | 1.8718 | 1.821725 | 1.768395 | 1.711708 | 25 |
| 26 | 1.977625 | 1.966391 | 1.956025 | 1.946429 | 1.937515 | 1.901011 | 1.853255 | 1.802718 | 1.748795 | 1.69133 | 26 |
| 27 | 1.961311 | 1.950017 | 1.939593 | 1.929941 | 1.920974 | 1.884235 | 1.836128 | 1.78515 | 1.730651 | 1.672422 | 27 |
| 28 | 1.946223 | 1.934872 | 1.924391 | 1.914685 | 1.905669 | 1.86871 | 1.820265 | 1.768857 | 1.713801 | 1.654826 | 28 |
| 30 | 1.919204 | 1.907743 | 1.897163 | 1.887361 | 1.878249 | 1.840871 | 1.79179 | 1.739572 | 1.683453 | 1.623036 | 30 |
| 40 | 1.825978 | 1.814104 | 1.803123 | 1.792937 | 1.783459 | 1.744432 | 1.692797 | 1.637252 | 1.576609 | 1.50977 | 40 |
| 50 | 1.770946 | 1.758789 | 1.747534 | 1.737078 | 1.727344 | 1.687157 | 1.633682 | 1.575653 | 1.511472 | 1.43921 | 50 |
| 60 | 1.734591 | 1.722224 | 1.710767 | 1.700116 | 1.690191 | 1.649141 | 1.594273 | 1.534314 | 1.467267 | 1.390303 | 60 |
| 120 | 1.644668 | 1.631697 | 1.619656 | 1.608438 | 1.597957 | 1.554342 | 1.495202 | 1.429013 | 1.351887 | 1.255252 | 120 |
| 100,000 | 1.555847 | 1.542126 | 1.529346 | 1.517403 | 1.50621 | 1.459213 | 1.394086 | 1.318171 | 1.221569 | 1.024554 | 100,000 |