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 |
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