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| The F Distribution: Values of F (alpha = 0.025) | |||||||||||
| 0.025 | |||||||||||
| see below for more | |||||||||||
| Degees of Freedom of the numerator | df1 | ||||||||||
| df2 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | df2 |
| 1 | 647.7931 | 799.4822 | 864.1509 | 899.5994 | 921.8347 | 937.1142 | 948.2028 | 956.6429 | 963.2786 | 968.6337 | 1 |
| 2 | 38.50619 | 39.00004 | 39.16557 | 39.24833 | 39.29836 | 39.3311 | 39.35565 | 39.37294 | 39.38658 | 39.3984 | 2 |
| 3 | 17.44343 | 16.04417 | 15.43913 | 15.10102 | 14.88479 | 14.73472 | 14.62445 | 14.53986 | 14.47302 | 14.4189 | 3 |
| 4 | 12.21792 | 10.64905 | 9.979203 | 9.604491 | 9.364499 | 9.197265 | 9.074142 | 8.979555 | 8.904635 | 8.843926 | 4 |
| 5 | 10.00694 | 8.433631 | 7.76356 | 7.387882 | 7.146355 | 6.9777 | 6.853043 | 6.757205 | 6.681034 | 6.619189 | 5 |
| 6 | 8.813117 | 7.259871 | 6.598782 | 6.22714 | 5.987545 | 5.819743 | 5.695483 | 5.599645 | 5.523418 | 5.461345 | 6 |
| 7 | 8.072675 | 6.541541 | 5.889831 | 5.522594 | 5.285244 | 5.118579 | 4.994888 | 4.899334 | 4.823221 | 4.761119 | 7 |
| 8 | 7.570861 | 6.059452 | 5.415984 | 5.052641 | 4.817281 | 4.651696 | 4.528545 | 4.433275 | 4.357219 | 4.295117 | 8 |
| 9 | 7.20928 | 5.714696 | 5.078107 | 4.718061 | 4.484406 | 4.31973 | 4.197034 | 4.101963 | 4.025992 | 3.963862 | 9 |
| 10 | 6.936716 | 5.4564 | 4.825608 | 4.468347 | 4.236085 | 4.07212 | 3.949822 | 3.854893 | 3.77895 | 3.716792 | 10 |
| 11 | 6.724122 | 5.255885 | 4.63001 | 4.27508 | 4.044011 | 3.880643 | 3.758629 | 3.663814 | 3.5879 | 3.52567 | 11 |
| 12 | 6.553762 | 5.09587 | 4.474202 | 4.121205 | 3.891131 | 3.728303 | 3.606516 | 3.511786 | 3.435844 | 3.373543 | 12 |
| 13 | 6.414268 | 4.965273 | 4.347186 | 3.995893 | 3.766672 | 3.604256 | 3.482668 | 3.387981 | 3.312039 | 3.249667 | 13 |
| 14 | 6.29791 | 4.856702 | 4.241713 | 3.891927 | 3.663416 | 3.501356 | 3.379938 | 3.285294 | 3.209294 | 3.146852 | 14 |
| 15 | 6.199514 | 4.765042 | 4.15281 | 3.804274 | 3.576417 | 3.414669 | 3.293366 | 3.198735 | 3.122707 | 3.060194 | 15 |
| 16 | 6.115101 | 4.686683 | 4.07681 | 3.729411 | 3.502123 | 3.340631 | 3.219441 | 3.124825 | 3.048754 | 2.986155 | 16 |
| 17 | 6.042001 | 4.618869 | 4.011156 | 3.664752 | 3.437947 | 3.276682 | 3.155577 | 3.060975 | 2.984862 | 2.922192 | 17 |
| 18 | 5.978052 | 4.559666 | 3.953858 | 3.608335 | 3.38197 | 3.220919 | 3.099871 | 3.005269 | 2.929113 | 2.866372 | 18 |
| 19 | 5.921606 | 4.507513 | 3.903438 | 3.558711 | 3.332715 | 3.171849 | 3.050872 | 2.956256 | 2.880057 | 2.817245 | 19 |
| 20 | 5.87147 | 4.461242 | 3.858702 | 3.514685 | 3.28906 | 3.128349 | 3.007415 | 2.912799 | 2.836543 | 2.773675 | 20 |
| 21 | 5.826621 | 4.419917 | 3.818769 | 3.475407 | 3.250079 | 3.089511 | 2.968633 | 2.874003 | 2.797705 | 2.734765 | 21 |
| 22 | 5.786319 | 4.38277 | 3.782887 | 3.440135 | 3.215092 | 3.054637 | 2.933803 | 2.839158 | 2.762818 | 2.699807 | 22 |
| 23 | 5.749826 | 4.349204 | 3.750486 | 3.408275 | 3.183487 | 3.02316 | 2.90234 | 2.807695 | 2.731312 | 2.668244 | 23 |
| 24 | 5.716629 | 4.318736 | 3.721084 | 3.379355 | 3.15481 | 2.994582 | 2.873804 | 2.779132 | 2.702706 | 2.639595 | 24 |
| 25 | 5.686388 | 4.290939 | 3.694282 | 3.353009 | 3.12869 | 2.968548 | 2.847798 | 2.753112 | 2.676643 | 2.613461 | 25 |
| 26 | 5.658649 | 4.265473 | 3.669726 | 3.328893 | 3.104773 | 2.944716 | 2.823981 | 2.72928 | 2.652783 | 2.589552 | 26 |
| 27 | 5.633126 | 4.242082 | 3.647187 | 3.306738 | 3.082803 | 2.922832 | 2.802125 | 2.707395 | 2.630856 | 2.567575 | 27 |
| 28 | 5.609564 | 4.22051 | 3.626411 | 3.286317 | 3.062553 | 2.902652 | 2.78196 | 2.687216 | 2.610648 | 2.54731 | 28 |
| 30 | 5.567529 | 4.182056 | 3.589349 | 3.249923 | 3.026472 | 2.866699 | 2.74602 | 2.651262 | 2.574609 | 2.511186 | 30 |
| 40 | 5.423942 | 4.051003 | 3.463271 | 3.126118 | 2.903718 | 2.744386 | 2.623779 | 2.528864 | 2.451941 | 2.388163 | 40 |
| 50 | 5.340326 | 3.974918 | 3.390198 | 3.05441 | 2.83265 | 2.673559 | 2.552973 | 2.457938 | 2.380823 | 2.316796 | 50 |
| 60 | 5.285614 | 3.925265 | 3.342521 | 3.007656 | 2.786308 | 2.627374 | 2.506795 | 2.411667 | 2.334403 | 2.270198 | 60 |
| 120 | 5.152344 | 3.804644 | 3.226887 | 2.894311 | 2.673985 | 2.515407 | 2.394799 | 2.299409 | 2.221732 | 2.157009 | 120 |
| 100,000 | 5.024049 | 3.689024 | 3.11627 | 2.785953 | 2.566622 | 2.408356 | 2.287663 | 2.191946 | 2.113765 | 2.048445 | 100,000 |
| 0.025 | see below for more | ||||||||||
| Degees of Freedom of the numerator | df1 | ||||||||||
| df2 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | df2 |
| 1 | 973.0284 | 976.7246 | 979.8387 | 982.5453 | 984.8736 | 986.9109 | 988.7153 | 990.3451 | 991.8003 | 993.0809 | 1 |
| 2 | 39.40659 | 39.41477 | 39.42114 | 39.4266 | 39.43114 | 39.43569 | 39.43933 | 39.44206 | 39.44569 | 39.44751 | 2 |
| 3 | 14.37411 | 14.33659 | 14.30453 | 14.27679 | 14.25269 | 14.23155 | 14.21267 | 14.19608 | 14.18084 | 14.16743 | 3 |
| 4 | 8.793563 | 8.751158 | 8.715006 | 8.683742 | 8.656571 | 8.632583 | 8.611323 | 8.592338 | 8.575284 | 8.559937 | 4 |
| 5 | 6.567802 | 6.524544 | 6.487596 | 6.455593 | 6.42774 | 6.403184 | 6.381356 | 6.361915 | 6.344408 | 6.328548 | 5 |
| 6 | 5.40976 | 5.366246 | 5.329014 | 5.296812 | 5.268646 | 5.243862 | 5.221807 | 5.202139 | 5.184404 | 5.168403 | 6 |
| 7 | 4.709477 | 4.665822 | 4.628475 | 4.596075 | 4.567795 | 4.542812 | 4.520643 | 4.500777 | 4.482899 | 4.466756 | 7 |
| 8 | 4.243418 | 4.199677 | 4.16216 | 4.129674 | 4.101224 | 4.076099 | 4.05376 | 4.033751 | 4.01576 | 3.999446 | 8 |
| 9 | 3.912078 | 3.868223 | 3.830593 | 3.797965 | 3.769344 | 3.744105 | 3.721624 | 3.701473 | 3.68334 | 3.666912 | 9 |
| 10 | 3.664923 | 3.620954 | 3.583182 | 3.550412 | 3.521677 | 3.496268 | 3.473644 | 3.45338 | 3.435105 | 3.418535 | 10 |
| 11 | 3.473701 | 3.429619 | 3.391733 | 3.358821 | 3.329944 | 3.304393 | 3.281642 | 3.261235 | 3.242832 | 3.226148 | 11 |
| 12 | 3.321475 | 3.277279 | 3.239265 | 3.20621 | 3.177206 | 3.151527 | 3.128633 | 3.108113 | 3.089582 | 3.07277 | 12 |
| 13 | 3.197499 | 3.153175 | 3.115034 | 3.081851 | 3.052719 | 3.026912 | 3.00389 | 2.983242 | 2.964583 | 2.947672 | 13 |
| 14 | 3.094584 | 3.050161 | 3.011891 | 2.978595 | 2.949321 | 2.9234 | 2.900265 | 2.879489 | 2.860716 | 2.843692 | 14 |
| 15 | 3.007827 | 2.963276 | 2.924907 | 2.891483 | 2.862095 | 2.836046 | 2.812797 | 2.791907 | 2.773035 | 2.755897 | 15 |
| 16 | 2.933703 | 2.889053 | 2.850555 | 2.817018 | 2.787516 | 2.761354 | 2.738005 | 2.717002 | 2.69803 | 2.680792 | 16 |
| 17 | 2.869641 | 2.824891 | 2.786294 | 2.752643 | 2.723027 | 2.696765 | 2.673303 | 2.6522 | 2.633129 | 2.615799 | 17 |
| 18 | 2.813735 | 2.768886 | 2.730189 | 2.696424 | 2.666724 | 2.640348 | 2.616787 | 2.595598 | 2.576428 | 2.559005 | 18 |
| 19 | 2.764523 | 2.719574 | 2.680778 | 2.646928 | 2.617114 | 2.590653 | 2.566992 | 2.545704 | 2.526448 | 2.508941 | 19 |
| 20 | 2.720867 | 2.675833 | 2.636938 | 2.603002 | 2.573103 | 2.546543 | 2.522789 | 2.501416 | 2.482075 | 2.464489 | 20 |
| 21 | 2.681873 | 2.636767 | 2.597787 | 2.563752 | 2.533767 | 2.507122 | 2.483283 | 2.461832 | 2.442405 | 2.424734 | 21 |
| 22 | 2.646857 | 2.601652 | 2.562601 | 2.528481 | 2.49841 | 2.47168 | 2.447763 | 2.426226 | 2.406722 | 2.388987 | 22 |
| 23 | 2.615209 | 2.569941 | 2.530804 | 2.496606 | 2.46645 | 2.439648 | 2.415646 | 2.394039 | 2.374463 | 2.35665 | 23 |
| 24 | 2.586489 | 2.541142 | 2.501935 | 2.467658 | 2.437432 | 2.410545 | 2.386479 | 2.3648 | 2.345153 | 2.327269 | 24 |
| 25 | 2.560299 | 2.514895 | 2.475602 | 2.441254 | 2.410957 | 2.383999 | 2.359869 | 2.338112 | 2.318401 | 2.300453 | 25 |
| 26 | 2.536325 | 2.49085 | 2.4515 | 2.417082 | 2.386706 | 2.359684 | 2.335483 | 2.313662 | 2.293888 | 2.275883 | 26 |
| 27 | 2.514298 | 2.468752 | 2.429331 | 2.394856 | 2.364416 | 2.33733 | 2.313058 | 2.291173 | 2.271342 | 2.253273 | 27 |
| 28 | 2.493977 | 2.448374 | 2.408896 | 2.37435 | 2.343846 | 2.316696 | 2.292367 | 2.270426 | 2.250538 | 2.232412 | 28 |
| 30 | 2.457753 | 2.412037 | 2.372438 | 2.337771 | 2.307154 | 2.27989 | 2.255447 | 2.233392 | 2.21339 | 2.195158 | 30 |
| 40 | 2.334311 | 2.288161 | 2.248107 | 2.212985 | 2.181906 | 2.154181 | 2.129291 | 2.106795 | 2.086367 | 2.067715 | 40 |
| 50 | 2.262666 | 2.216211 | 2.175845 | 2.140411 | 2.109012 | 2.080974 | 2.055771 | 2.032969 | 2.012236 | 1.993293 | 50 |
| 60 | 2.215863 | 2.169195 | 2.128601 | 2.092939 | 2.061306 | 2.03304 | 2.00761 | 1.984581 | 1.963631 | 1.944471 | 60 |
| 120 | 2.102105 | 2.054819 | 2.013593 | 1.977277 | 1.94499 | 1.916071 | 1.88998 | 1.866304 | 1.844711 | 1.824919 | 120 |
| 100,000 | 1.992859 | 1.944851 | 1.902869 | 1.865772 | 1.832692 | 1.802967 | 1.776076 | 1.751602 | 1.729205 | 1.708617 | 100,000 |
| 0.025 | |||||||||||
| Degees of Freedom of the numerator | df1 | ||||||||||
| df2 | 21 | 22 | 23 | 24 | 25 | 30 | 40 | 60 | 120 | 10000 | df2 |
| 1 | 994.3033 | 995.351 | 996.3405 | 997.2719 | 998.0868 | 1001.405 | 1005.596 | 1009.787 | 1014.036 | 1018.227 | 1 |
| 2 | 39.45024 | 39.45206 | 39.45479 | 39.45661 | 39.45752 | 39.46479 | 39.47298 | 39.48117 | 39.48935 | 39.49754 | 2 |
| 3 | 14.15515 | 14.14378 | 14.13355 | 14.12423 | 14.11536 | 14.08057 | 14.03646 | 13.99212 | 13.94733 | 13.90254 | 3 |
| 4 | 8.545953 | 8.53322 | 8.521624 | 8.510824 | 8.501047 | 8.461257 | 8.411121 | 8.360416 | 8.309144 | 8.257985 | 4 |
| 5 | 6.314167 | 6.301093 | 6.289042 | 6.278015 | 6.26784 | 6.226855 | 6.175071 | 6.122548 | 6.069286 | 6.015966 | 5 |
| 6 | 5.153822 | 5.140578 | 5.128385 | 5.117215 | 5.10687 | 5.065203 | 5.012453 | 4.958906 | 4.90445 | 4.849767 | 6 |
| 7 | 4.452033 | 4.438618 | 4.426312 | 4.415 | 4.404541 | 4.362391 | 4.308873 | 4.254389 | 4.19891 | 4.143033 | 7 |
| 8 | 3.98461 | 3.971081 | 3.958661 | 3.947207 | 3.936663 | 3.894002 | 3.839773 | 3.784436 | 3.727934 | 3.670891 | 8 |
| 9 | 3.651962 | 3.638291 | 3.625743 | 3.61419 | 3.603532 | 3.560416 | 3.505477 | 3.449301 | 3.39179 | 3.333568 | 9 |
| 10 | 3.403471 | 3.389687 | 3.377025 | 3.365358 | 3.354586 | 3.311015 | 3.255394 | 3.198409 | 3.139917 | 3.080515 | 10 |
| 11 | 3.210943 | 3.197044 | 3.184283 | 3.172516 | 3.161645 | 3.11762 | 3.061331 | 3.003535 | 2.944077 | 2.883539 | 11 |
| 12 | 3.057465 | 3.043453 | 3.030578 | 3.018712 | 3.007742 | 2.963276 | 2.906347 | 2.84777 | 2.78736 | 2.725685 | 12 |
| 13 | 2.932239 | 2.918128 | 2.905153 | 2.893188 | 2.882132 | 2.837254 | 2.7797 | 2.720355 | 2.659021 | 2.596238 | 13 |
| 14 | 2.828159 | 2.813948 | 2.800874 | 2.788809 | 2.777654 | 2.732378 | 2.674227 | 2.614158 | 2.551928 | 2.488036 | 14 |
| 15 | 2.740265 | 2.725955 | 2.712781 | 2.700645 | 2.68939 | 2.643731 | 2.585011 | 2.524231 | 2.461121 | 2.396149 | 15 |
| 16 | 2.665061 | 2.650651 | 2.637393 | 2.625171 | 2.613845 | 2.567816 | 2.508528 | 2.447067 | 2.383111 | 2.317094 | 16 |
| 17 | 2.599975 | 2.58548 | 2.572136 | 2.55983 | 2.548418 | 2.502041 | 2.442228 | 2.380105 | 2.315325 | 2.248271 | 17 |
| 18 | 2.543089 | 2.528509 | 2.515094 | 2.502702 | 2.49122 | 2.444509 | 2.384184 | 2.321421 | 2.255838 | 2.187775 | 18 |
| 19 | 2.492953 | 2.478288 | 2.464787 | 2.452325 | 2.440771 | 2.393733 | 2.332925 | 2.269552 | 2.203194 | 2.134129 | 19 |
| 20 | 2.448417 | 2.433673 | 2.420101 | 2.40756 | 2.395936 | 2.3486 | 2.287322 | 2.223359 | 2.156241 | 2.08621 | 20 |
| 21 | 2.408591 | 2.393776 | 2.380133 | 2.367528 | 2.35584 | 2.308212 | 2.24648 | 2.181949 | 2.114092 | 2.043116 | 21 |
| 22 | 2.372765 | 2.357879 | 2.344173 | 2.331504 | 2.319752 | 2.27184 | 2.209674 | 2.144596 | 2.076028 | 2.004121 | 22 |
| 23 | 2.340364 | 2.325415 | 2.311637 | 2.298904 | 2.287095 | 2.23892 | 2.176343 | 2.110724 | 2.041475 | 1.968651 | 23 |
| 24 | 2.310919 | 2.295906 | 2.282071 | 2.269275 | 2.257408 | 2.208978 | 2.146002 | 2.079872 | 2.009948 | 1.936236 | 24 |
| 25 | 2.28404 | 2.268962 | 2.255071 | 2.242224 | 2.230301 | 2.181622 | 2.118263 | 2.051635 | 1.981057 | 1.906471 | 25 |
| 26 | 2.259405 | 2.244271 | 2.230323 | 2.217419 | 2.205446 | 2.156526 | 2.092804 | 2.0257 | 1.954483 | 1.879037 | 26 |
| 27 | 2.236746 | 2.221554 | 2.20755 | 2.194597 | 2.182574 | 2.133426 | 2.069342 | 2.001784 | 1.929948 | 1.853657 | 27 |
| 28 | 2.215828 | 2.200579 | 2.186525 | 2.173522 | 2.16145 | 2.112088 | 2.047663 | 1.97965 | 1.907217 | 1.830102 | 28 |
| 30 | 2.178467 | 2.163134 | 2.14898 | 2.135877 | 2.12372 | 2.073946 | 2.008875 | 1.940009 | 1.866418 | 1.787697 | 30 |
| 40 | 2.050612 | 2.034881 | 2.020343 | 2.006871 | 1.994344 | 1.942915 | 1.8752 | 1.802768 | 1.724203 | 1.638238 | 40 |
| 50 | 1.975906 | 1.95989 | 1.945082 | 1.93134 | 1.918558 | 1.865942 | 1.796273 | 1.721144 | 1.638622 | 1.54645 | 50 |
| 60 | 1.926871 | 1.910649 | 1.895636 | 1.881695 | 1.86872 | 1.815202 | 1.744048 | 1.666791 | 1.581036 | 1.483446 | 60 |
| 120 | 1.806701 | 1.789864 | 1.77425 | 1.759723 | 1.746173 | 1.689944 | 1.614147 | 1.529941 | 1.432676 | 1.312163 | 120 |
| 100,000 | 1.68961 | 1.671992 | 1.655604 | 1.640313 | 1.626002 | 1.566125 | 1.483702 | 1.38847 | 1.268646 | 1.029319 | 100,000 |