|
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
|
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