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1. Exploratory Data Analysis
1.3. EDA Techniques
1.3.6. Probability Distributions
1.3.6.7. Tables for Probability Distributions

1.3.6.7.3.

Upper Critical Values of the F Distribution

How to Use This Table This table contains the upper critical values of the F distribution. This table is used for one-sided F tests at the α = 0.05, 0.10, and 0.01 levels.

More specifically, a test statistic is computed with ν1 and ν2 degrees of freedom, and the result is compared to this table. For a one-sided test, the null hypothesis is rejected when the test statistic is greater than the tabled value. This is demonstrated with the graph of an F distribution with ν1 = 10 and ν2 = 10. The shaded area of the graph indicates the rejection region at the α significance level. Since this is a one-sided test, we have α probability in the upper tail of exceeding the critical value and zero in the lower tail. Because the F distribution is asymmetric, a two-sided test requires a set of of tables (not included here) that contain the rejection regions for both the lower and upper tails.

plot for one-sided test at alpha = 0.05

Contents The following tables for ν2 from 1 to 100 are included:
  1. One sided, 5% significance level, ν1 = 1 - 10
  2. One sided, 5% significance level, ν1 = 11 - 20
  3. One sided, 10% significance level, ν1 = 1 - 10
  4. One sided, 10% significance level, ν1 = 11 - 20
  5. One sided, 1% significance level, ν1 = 1 - 10
  6. One sided, 1% significance level, ν1 = 11 - 20
Upper critical values of the F distribution
for ν1 numerator degrees of freedom and ν2 denominator degrees of freedom

5% significance level

\( F_{.05}(\nu_{1},\nu_{2}) \)

     \ ν1   1       2       3       4       5       6       7       8       9      10
   ν2

  1      161.448 199.500 215.707 224.583 230.162 233.986 236.768 238.882 240.543 241.882
  2       18.513  19.000  19.164  19.247  19.296  19.330  19.353  19.371  19.385  19.396
  3       10.128   9.552   9.277   9.117   9.013   8.941   8.887   8.845   8.812   8.786
  4        7.709   6.944   6.591   6.388   6.256   6.163   6.094   6.041   5.999   5.964
  5        6.608   5.786   5.409   5.192   5.050   4.950   4.876   4.818   4.772   4.735
  6        5.987   5.143   4.757   4.534   4.387   4.284   4.207   4.147   4.099   4.060
  7        5.591   4.737   4.347   4.120   3.972   3.866   3.787   3.726   3.677   3.637
  8        5.318   4.459   4.066   3.838   3.687   3.581   3.500   3.438   3.388   3.347
  9        5.117   4.256   3.863   3.633   3.482   3.374   3.293   3.230   3.179   3.137
 10        4.965   4.103   3.708   3.478   3.326   3.217   3.135   3.072   3.020   2.978
 11        4.844   3.982   3.587   3.357   3.204   3.095   3.012   2.948   2.896   2.854
 12        4.747   3.885   3.490   3.259   3.106   2.996   2.913   2.849   2.796   2.753
 13        4.667   3.806   3.411   3.179   3.025   2.915   2.832   2.767   2.714   2.671
 14        4.600   3.739   3.344   3.112   2.958   2.848   2.764   2.699   2.646   2.602
 15        4.543   3.682   3.287   3.056   2.901   2.790   2.707   2.641   2.588   2.544
 16        4.494   3.634   3.239   3.007   2.852   2.741   2.657   2.591   2.538   2.494
 17        4.451   3.592   3.197   2.965   2.810   2.699   2.614   2.548   2.494   2.450
 18        4.414   3.555   3.160   2.928   2.773   2.661   2.577   2.510   2.456   2.412
 19        4.381   3.522   3.127   2.895   2.740   2.628   2.544   2.477   2.423   2.378
 20        4.351   3.493   3.098   2.866   2.711   2.599   2.514   2.447   2.393   2.348
 21        4.325   3.467   3.072   2.840   2.685   2.573   2.488   2.420   2.366   2.321
 22        4.301   3.443   3.049   2.817   2.661   2.549   2.464   2.397   2.342   2.297
 23        4.279   3.422   3.028   2.796   2.640   2.528   2.442   2.375   2.320   2.275
 24        4.260   3.403   3.009   2.776   2.621   2.508   2.423   2.355   2.300   2.255
 25        4.242   3.385   2.991   2.759   2.603   2.490   2.405   2.337   2.282   2.236
 26        4.225   3.369   2.975   2.743   2.587   2.474   2.388   2.321   2.265   2.220
 27        4.210   3.354   2.960   2.728   2.572   2.459   2.373   2.305   2.250   2.204
 28        4.196   3.340   2.947   2.714   2.558   2.445   2.359   2.291   2.236   2.190
 29        4.183   3.328   2.934   2.701   2.545   2.432   2.346   2.278   2.223   2.177
 30        4.171   3.316   2.922   2.690   2.534   2.421   2.334   2.266   2.211   2.165
 31        4.160   3.305   2.911   2.679   2.523   2.409   2.323   2.255   2.199   2.153
 32        4.149   3.295   2.901   2.668   2.512   2.399   2.313   2.244   2.189   2.142
 33        4.139   3.285   2.892   2.659   2.503   2.389   2.303   2.235   2.179   2.133
 34        4.130   3.276   2.883   2.650   2.494   2.380   2.294   2.225   2.170   2.123
 35        4.121   3.267   2.874   2.641   2.485   2.372   2.285   2.217   2.161   2.114
 36        4.113   3.259   2.866   2.634   2.477   2.364   2.277   2.209   2.153   2.106
 37        4.105   3.252   2.859   2.626   2.470   2.356   2.270   2.201   2.145   2.098
 38        4.098   3.245   2.852   2.619   2.463   2.349   2.262   2.194   2.138   2.091
 39        4.091   3.238   2.845   2.612   2.456   2.342   2.255   2.187   2.131   2.084
 40        4.085   3.232   2.839   2.606   2.449   2.336   2.249   2.180   2.124   2.077
 41        4.079   3.226   2.833   2.600   2.443   2.330   2.243   2.174   2.118   2.071
 42        4.073   3.220   2.827   2.594   2.438   2.324   2.237   2.168   2.112   2.065
 43        4.067   3.214   2.822   2.589   2.432   2.318   2.232   2.163   2.106   2.059
 44        4.062   3.209   2.816   2.584   2.427   2.313   2.226   2.157   2.101   2.054
 45        4.057   3.204   2.812   2.579   2.422   2.308   2.221   2.152   2.096   2.049
 46        4.052   3.200   2.807   2.574   2.417   2.304   2.216   2.147   2.091   2.044
 47        4.047   3.195   2.802   2.570   2.413   2.299   2.212   2.143   2.086   2.039
 48        4.043   3.191   2.798   2.565   2.409   2.295   2.207   2.138   2.082   2.035
 49        4.038   3.187   2.794   2.561   2.404   2.290   2.203   2.134   2.077   2.030
 50        4.034   3.183   2.790   2.557   2.400   2.286   2.199   2.130   2.073   2.026
 51        4.030   3.179   2.786   2.553   2.397   2.283   2.195   2.126   2.069   2.022
 52        4.027   3.175   2.783   2.550   2.393   2.279   2.192   2.122   2.066   2.018
 53        4.023   3.172   2.779   2.546   2.389   2.275   2.188   2.119   2.062   2.015
 54        4.020   3.168   2.776   2.543   2.386   2.272   2.185   2.115   2.059   2.011
 55        4.016   3.165   2.773   2.540   2.383   2.269   2.181   2.112   2.055   2.008
 56        4.013   3.162   2.769   2.537   2.380   2.266   2.178   2.109   2.052   2.005
 57        4.010   3.159   2.766   2.534   2.377   2.263   2.175   2.106   2.049   2.001
 58        4.007   3.156   2.764   2.531   2.374   2.260   2.172   2.103   2.046   1.998
 59        4.004   3.153   2.761   2.528   2.371   2.257   2.169   2.100   2.043   1.995
 60        4.001   3.150   2.758   2.525   2.368   2.254   2.167   2.097   2.040   1.993
 61        3.998   3.148   2.755   2.523   2.366   2.251   2.164   2.094   2.037   1.990
 62        3.996   3.145   2.753   2.520   2.363   2.249   2.161   2.092   2.035   1.987
 63        3.993   3.143   2.751   2.518   2.361   2.246   2.159   2.089   2.032   1.985
 64        3.991   3.140   2.748   2.515   2.358   2.244   2.156   2.087   2.030   1.982
 65        3.989   3.138   2.746   2.513   2.356   2.242   2.154   2.084   2.027   1.980
 66        3.986   3.136   2.744   2.511   2.354   2.239   2.152   2.082   2.025   1.977
 67        3.984   3.134   2.742   2.509   2.352   2.237   2.150   2.080   2.023   1.975
 68        3.982   3.132   2.740   2.507   2.350   2.235   2.148   2.078   2.021   1.973
 69        3.980   3.130   2.737   2.505   2.348   2.233   2.145   2.076   2.019   1.971
 70        3.978   3.128   2.736   2.503   2.346   2.231   2.143   2.074   2.017   1.969
 71        3.976   3.126   2.734   2.501   2.344   2.229   2.142   2.072   2.015   1.967
 72        3.974   3.124   2.732   2.499   2.342   2.227   2.140   2.070   2.013   1.965
 73        3.972   3.122   2.730   2.497   2.340   2.226   2.138   2.068   2.011   1.963
 74        3.970   3.120   2.728   2.495   2.338   2.224   2.136   2.066   2.009   1.961
 75        3.968   3.119   2.727   2.494   2.337   2.222   2.134   2.064   2.007   1.959
 76        3.967   3.117   2.725   2.492   2.335   2.220   2.133   2.063   2.006   1.958
 77        3.965   3.115   2.723   2.490   2.333   2.219   2.131   2.061   2.004   1.956
 78        3.963   3.114   2.722   2.489   2.332   2.217   2.129   2.059   2.002   1.954
 79        3.962   3.112   2.720   2.487   2.330   2.216   2.128   2.058   2.001   1.953
 80        3.960   3.111   2.719   2.486   2.329   2.214   2.126   2.056   1.999   1.951
 81        3.959   3.109   2.717   2.484   2.327   2.213   2.125   2.055   1.998   1.950
 82        3.957   3.108   2.716   2.483   2.326   2.211   2.123   2.053   1.996   1.948
 83        3.956   3.107   2.715   2.482   2.324   2.210   2.122   2.052   1.995   1.947
 84        3.955   3.105   2.713   2.480   2.323   2.209   2.121   2.051   1.993   1.945
 85        3.953   3.104   2.712   2.479   2.322   2.207   2.119   2.049   1.992   1.944
 86        3.952   3.103   2.711   2.478   2.321   2.206   2.118   2.048   1.991   1.943
 87        3.951   3.101   2.709   2.476   2.319   2.205   2.117   2.047   1.989   1.941
 88        3.949   3.100   2.708   2.475   2.318   2.203   2.115   2.045   1.988   1.940
 89        3.948   3.099   2.707   2.474   2.317   2.202   2.114   2.044   1.987   1.939
 90        3.947   3.098   2.706   2.473   2.316   2.201   2.113   2.043   1.986   1.938
 91        3.946   3.097   2.705   2.472   2.315   2.200   2.112   2.042   1.984   1.936
 92        3.945   3.095   2.704   2.471   2.313   2.199   2.111   2.041   1.983   1.935
 93        3.943   3.094   2.703   2.470   2.312   2.198   2.110   2.040   1.982   1.934
 94        3.942   3.093   2.701   2.469   2.311   2.197   2.109   2.038   1.981   1.933
 95        3.941   3.092   2.700   2.467   2.310   2.196   2.108   2.037   1.980   1.932
 96        3.940   3.091   2.699   2.466   2.309   2.195   2.106   2.036   1.979   1.931
 97        3.939   3.090   2.698   2.465   2.308   2.194   2.105   2.035   1.978   1.930
 98        3.938   3.089   2.697   2.465   2.307   2.193   2.104   2.034   1.977   1.929
 99        3.937   3.088   2.696   2.464   2.306   2.192   2.103   2.033   1.976   1.928
100        3.936   3.087   2.696   2.463   2.305   2.191   2.103   2.032   1.975   1.927


     \ ν1   11      12      13      14      15      16      17      18      19      20
   ν2


  1      242.983 243.906 244.690 245.364 245.950 246.464 246.918 247.323 247.686 248.013
  2       19.405  19.413  19.419  19.424  19.429  19.433  19.437  19.440  19.443  19.446
  3        8.763   8.745   8.729   8.715   8.703   8.692   8.683   8.675   8.667   8.660
  4        5.936   5.912   5.891   5.873   5.858   5.844   5.832   5.821   5.811   5.803
  5        4.704   4.678   4.655   4.636   4.619   4.604   4.590   4.579   4.568   4.558
  6        4.027   4.000   3.976   3.956   3.938   3.922   3.908   3.896   3.884   3.874
  7        3.603   3.575   3.550   3.529   3.511   3.494   3.480   3.467   3.455   3.445
  8        3.313   3.284   3.259   3.237   3.218   3.202   3.187   3.173   3.161   3.150
  9        3.102   3.073   3.048   3.025   3.006   2.989   2.974   2.960   2.948   2.936
 10        2.943   2.913   2.887   2.865   2.845   2.828   2.812   2.798   2.785   2.774
 11        2.818   2.788   2.761   2.739   2.719   2.701   2.685   2.671   2.658   2.646
 12        2.717   2.687   2.660   2.637   2.617   2.599   2.583   2.568   2.555   2.544
 13        2.635   2.604   2.577   2.554   2.533   2.515   2.499   2.484   2.471   2.459
 14        2.565   2.534   2.507   2.484   2.463   2.445   2.428   2.413   2.400   2.388
 15        2.507   2.475   2.448   2.424   2.403   2.385   2.368   2.353   2.340   2.328
 16        2.456   2.425   2.397   2.373   2.352   2.333   2.317   2.302   2.288   2.276
 17        2.413   2.381   2.353   2.329   2.308   2.289   2.272   2.257   2.243   2.230
 18        2.374   2.342   2.314   2.290   2.269   2.250   2.233   2.217   2.203   2.191
 19        2.340   2.308   2.280   2.256   2.234   2.215   2.198   2.182   2.168   2.155
 20        2.310   2.278   2.250   2.225   2.203   2.184   2.167   2.151   2.137   2.124
 21        2.283   2.250   2.222   2.197   2.176   2.156   2.139   2.123   2.109   2.096
 22        2.259   2.226   2.198   2.173   2.151   2.131   2.114   2.098   2.084   2.071
 23        2.236   2.204   2.175   2.150   2.128   2.109   2.091   2.075   2.061   2.048
 24        2.216   2.183   2.155   2.130   2.108   2.088   2.070   2.054   2.040   2.027
 25        2.198   2.165   2.136   2.111   2.089   2.069   2.051   2.035   2.021   2.007
 26        2.181   2.148   2.119   2.094   2.072   2.052   2.034   2.018   2.003   1.990
 27        2.166   2.132   2.103   2.078   2.056   2.036   2.018   2.002   1.987   1.974
 28        2.151   2.118   2.089   2.064   2.041   2.021   2.003   1.987   1.972   1.959
 29        2.138   2.104   2.075   2.050   2.027   2.007   1.989   1.973   1.958   1.945
 30        2.126   2.092   2.063   2.037   2.015   1.995   1.976   1.960   1.945   1.932
 31        2.114   2.080   2.051   2.026   2.003   1.983   1.965   1.948   1.933   1.920
 32        2.103   2.070   2.040   2.015   1.992   1.972   1.953   1.937   1.922   1.908
 33        2.093   2.060   2.030   2.004   1.982   1.961   1.943   1.926   1.911   1.898
 34        2.084   2.050   2.021   1.995   1.972   1.952   1.933   1.917   1.902   1.888
 35        2.075   2.041   2.012   1.986   1.963   1.942   1.924   1.907   1.892   1.878
 36        2.067   2.033   2.003   1.977   1.954   1.934   1.915   1.899   1.883   1.870
 37        2.059   2.025   1.995   1.969   1.946   1.926   1.907   1.890   1.875   1.861
 38        2.051   2.017   1.988   1.962   1.939   1.918   1.899   1.883   1.867   1.853
 39        2.044   2.010   1.981   1.954   1.931   1.911   1.892   1.875   1.860   1.846
 40        2.038   2.003   1.974   1.948   1.924   1.904   1.885   1.868   1.853   1.839
 41        2.031   1.997   1.967   1.941   1.918   1.897   1.879   1.862   1.846   1.832
 42        2.025   1.991   1.961   1.935   1.912   1.891   1.872   1.855   1.840   1.826
 43        2.020   1.985   1.955   1.929   1.906   1.885   1.866   1.849   1.834   1.820
 44        2.014   1.980   1.950   1.924   1.900   1.879   1.861   1.844   1.828   1.814
 45        2.009   1.974   1.945   1.918   1.895   1.874   1.855   1.838   1.823   1.808
 46        2.004   1.969   1.940   1.913   1.890   1.869   1.850   1.833   1.817   1.803
 47        1.999   1.965   1.935   1.908   1.885   1.864   1.845   1.828   1.812   1.798
 48        1.995   1.960   1.930   1.904   1.880   1.859   1.840   1.823   1.807   1.793
 49        1.990   1.956   1.926   1.899   1.876   1.855   1.836   1.819   1.803   1.789
 50        1.986   1.952   1.921   1.895   1.871   1.850   1.831   1.814   1.798   1.784
 51        1.982   1.947   1.917   1.891   1.867   1.846   1.827   1.810   1.794   1.780
 52        1.978   1.944   1.913   1.887   1.863   1.842   1.823   1.806   1.790   1.776
 53        1.975   1.940   1.910   1.883   1.859   1.838   1.819   1.802   1.786   1.772
 54        1.971   1.936   1.906   1.879   1.856   1.835   1.816   1.798   1.782   1.768
 55        1.968   1.933   1.903   1.876   1.852   1.831   1.812   1.795   1.779   1.764
 56        1.964   1.930   1.899   1.873   1.849   1.828   1.809   1.791   1.775   1.761
 57        1.961   1.926   1.896   1.869   1.846   1.824   1.805   1.788   1.772   1.757
 58        1.958   1.923   1.893   1.866   1.842   1.821   1.802   1.785   1.769   1.754
 59        1.955   1.920   1.890   1.863   1.839   1.818   1.799   1.781   1.766   1.751
 60        1.952   1.917   1.887   1.860   1.836   1.815   1.796   1.778   1.763   1.748
 61        1.949   1.915   1.884   1.857   1.834   1.812   1.793   1.776   1.760   1.745
 62        1.947   1.912   1.882   1.855   1.831   1.809   1.790   1.773   1.757   1.742
 63        1.944   1.909   1.879   1.852   1.828   1.807   1.787   1.770   1.754   1.739
 64        1.942   1.907   1.876   1.849   1.826   1.804   1.785   1.767   1.751   1.737
 65        1.939   1.904   1.874   1.847   1.823   1.802   1.782   1.765   1.749   1.734
 66        1.937   1.902   1.871   1.845   1.821   1.799   1.780   1.762   1.746   1.732
 67        1.935   1.900   1.869   1.842   1.818   1.797   1.777   1.760   1.744   1.729
 68        1.932   1.897   1.867   1.840   1.816   1.795   1.775   1.758   1.742   1.727
 69        1.930   1.895   1.865   1.838   1.814   1.792   1.773   1.755   1.739   1.725
 70        1.928   1.893   1.863   1.836   1.812   1.790   1.771   1.753   1.737   1.722
 71        1.926   1.891   1.861   1.834   1.810   1.788   1.769   1.751   1.735   1.720
 72        1.924   1.889   1.859   1.832   1.808   1.786   1.767   1.749   1.733   1.718
 73        1.922   1.887   1.857   1.830   1.806   1.784   1.765   1.747   1.731   1.716
 74        1.921   1.885   1.855   1.828   1.804   1.782   1.763   1.745   1.729   1.714
 75        1.919   1.884   1.853   1.826   1.802   1.780   1.761   1.743   1.727   1.712
 76        1.917   1.882   1.851   1.824   1.800   1.778   1.759   1.741   1.725   1.710
 77        1.915   1.880   1.849   1.822   1.798   1.777   1.757   1.739   1.723   1.708
 78        1.914   1.878   1.848   1.821   1.797   1.775   1.755   1.738   1.721   1.707
 79        1.912   1.877   1.846   1.819   1.795   1.773   1.754   1.736   1.720   1.705
 80        1.910   1.875   1.845   1.817   1.793   1.772   1.752   1.734   1.718   1.703
 81        1.909   1.874   1.843   1.816   1.792   1.770   1.750   1.733   1.716   1.702
 82        1.907   1.872   1.841   1.814   1.790   1.768   1.749   1.731   1.715   1.700
 83        1.906   1.871   1.840   1.813   1.789   1.767   1.747   1.729   1.713   1.698
 84        1.905   1.869   1.838   1.811   1.787   1.765   1.746   1.728   1.712   1.697
 85        1.903   1.868   1.837   1.810   1.786   1.764   1.744   1.726   1.710   1.695
 86        1.902   1.867   1.836   1.808   1.784   1.762   1.743   1.725   1.709   1.694
 87        1.900   1.865   1.834   1.807   1.783   1.761   1.741   1.724   1.707   1.692
 88        1.899   1.864   1.833   1.806   1.782   1.760   1.740   1.722   1.706   1.691
 89        1.898   1.863   1.832   1.804   1.780   1.758   1.739   1.721   1.705   1.690
 90        1.897   1.861   1.830   1.803   1.779   1.757   1.737   1.720   1.703   1.688
 91        1.895   1.860   1.829   1.802   1.778   1.756   1.736   1.718   1.702   1.687
 92        1.894   1.859   1.828   1.801   1.776   1.755   1.735   1.717   1.701   1.686
 93        1.893   1.858   1.827   1.800   1.775   1.753   1.734   1.716   1.699   1.684
 94        1.892   1.857   1.826   1.798   1.774   1.752   1.733   1.715   1.698   1.683
 95        1.891   1.856   1.825   1.797   1.773   1.751   1.731   1.713   1.697   1.682
 96        1.890   1.854   1.823   1.796   1.772   1.750   1.730   1.712   1.696   1.681
 97        1.889   1.853   1.822   1.795   1.771   1.749   1.729   1.711   1.695   1.680
 98        1.888   1.852   1.821   1.794   1.770   1.748   1.728   1.710   1.694   1.679
 99        1.887   1.851   1.820   1.793   1.769   1.747   1.727   1.709   1.693   1.678
100        1.886   1.850   1.819   1.792   1.768   1.746   1.726   1.708   1.691   1.676

Upper critical values of the F distribution
for ν1 numerator degrees of freedom and ν2 denominator degrees of freedom

10% significance level

\( F_{.10}(\nu_{1},\nu_{2}) \)

     \ ν1   1       2       3       4       5       6       7       8       9      10
   ν2

  1       39.863  49.500  53.593  55.833  57.240  58.204  58.906  59.439  59.858  60.195
  2        8.526   9.000   9.162   9.243   9.293   9.326   9.349   9.367   9.381   9.392
  3        5.538   5.462   5.391   5.343   5.309   5.285   5.266   5.252   5.240   5.230
  4        4.545   4.325   4.191   4.107   4.051   4.010   3.979   3.955   3.936   3.920
  5        4.060   3.780   3.619   3.520   3.453   3.405   3.368   3.339   3.316   3.297
  6        3.776   3.463   3.289   3.181   3.108   3.055   3.014   2.983   2.958   2.937
  7        3.589   3.257   3.074   2.961   2.883   2.827   2.785   2.752   2.725   2.703
  8        3.458   3.113   2.924   2.806   2.726   2.668   2.624   2.589   2.561   2.538
  9        3.360   3.006   2.813   2.693   2.611   2.551   2.505   2.469   2.440   2.416
 10        3.285   2.924   2.728   2.605   2.522   2.461   2.414   2.377   2.347   2.323
 11        3.225   2.860   2.660   2.536   2.451   2.389   2.342   2.304   2.274   2.248
 12        3.177   2.807   2.606   2.480   2.394   2.331   2.283   2.245   2.214   2.188
 13        3.136   2.763   2.560   2.434   2.347   2.283   2.234   2.195   2.164   2.138
 14        3.102   2.726   2.522   2.395   2.307   2.243   2.193   2.154   2.122   2.095
 15        3.073   2.695   2.490   2.361   2.273   2.208   2.158   2.119   2.086   2.059
 16        3.048   2.668   2.462   2.333   2.244   2.178   2.128   2.088   2.055   2.028
 17        3.026   2.645   2.437   2.308   2.218   2.152   2.102   2.061   2.028   2.001
 18        3.007   2.624   2.416   2.286   2.196   2.130   2.079   2.038   2.005   1.977
 19        2.990   2.606   2.397   2.266   2.176   2.109   2.058   2.017   1.984   1.956
 20        2.975   2.589   2.380   2.249   2.158   2.091   2.040   1.999   1.965   1.937
 21        2.961   2.575   2.365   2.233   2.142   2.075   2.023   1.982   1.948   1.920
 22        2.949   2.561   2.351   2.219   2.128   2.060   2.008   1.967   1.933   1.904
 23        2.937   2.549   2.339   2.207   2.115   2.047   1.995   1.953   1.919   1.890
 24        2.927   2.538   2.327   2.195   2.103   2.035   1.983   1.941   1.906   1.877
 25        2.918   2.528   2.317   2.184   2.092   2.024   1.971   1.929   1.895   1.866
 26        2.909   2.519   2.307   2.174   2.082   2.014   1.961   1.919   1.884   1.855
 27        2.901   2.511   2.299   2.165   2.073   2.005   1.952   1.909   1.874   1.845
 28        2.894   2.503   2.291   2.157   2.064   1.996   1.943   1.900   1.865   1.836
 29        2.887   2.495   2.283   2.149   2.057   1.988   1.935   1.892   1.857   1.827
 30        2.881   2.489   2.276   2.142   2.049   1.980   1.927   1.884   1.849   1.819
 31        2.875   2.482   2.270   2.136   2.042   1.973   1.920   1.877   1.842   1.812
 32        2.869   2.477   2.263   2.129   2.036   1.967   1.913   1.870   1.835   1.805
 33        2.864   2.471   2.258   2.123   2.030   1.961   1.907   1.864   1.828   1.799
 34        2.859   2.466   2.252   2.118   2.024   1.955   1.901   1.858   1.822   1.793
 35        2.855   2.461   2.247   2.113   2.019   1.950   1.896   1.852   1.817   1.787
 36        2.850   2.456   2.243   2.108   2.014   1.945   1.891   1.847   1.811   1.781
 37        2.846   2.452   2.238   2.103   2.009   1.940   1.886   1.842   1.806   1.776
 38        2.842   2.448   2.234   2.099   2.005   1.935   1.881   1.838   1.802   1.772
 39        2.839   2.444   2.230   2.095   2.001   1.931   1.877   1.833   1.797   1.767
 40        2.835   2.440   2.226   2.091   1.997   1.927   1.873   1.829   1.793   1.763
 41        2.832   2.437   2.222   2.087   1.993   1.923   1.869   1.825   1.789   1.759
 42        2.829   2.434   2.219   2.084   1.989   1.919   1.865   1.821   1.785   1.755
 43        2.826   2.430   2.216   2.080   1.986   1.916   1.861   1.817   1.781   1.751
 44        2.823   2.427   2.213   2.077   1.983   1.913   1.858   1.814   1.778   1.747
 45        2.820   2.425   2.210   2.074   1.980   1.909   1.855   1.811   1.774   1.744
 46        2.818   2.422   2.207   2.071   1.977   1.906   1.852   1.808   1.771   1.741
 47        2.815   2.419   2.204   2.068   1.974   1.903   1.849   1.805   1.768   1.738
 48        2.813   2.417   2.202   2.066   1.971   1.901   1.846   1.802   1.765   1.735
 49        2.811   2.414   2.199   2.063   1.968   1.898   1.843   1.799   1.763   1.732
 50        2.809   2.412   2.197   2.061   1.966   1.895   1.840   1.796   1.760   1.729
 51        2.807   2.410   2.194   2.058   1.964   1.893   1.838   1.794   1.757   1.727
 52        2.805   2.408   2.192   2.056   1.961   1.891   1.836   1.791   1.755   1.724
 53        2.803   2.406   2.190   2.054   1.959   1.888   1.833   1.789   1.752   1.722
 54        2.801   2.404   2.188   2.052   1.957   1.886   1.831   1.787   1.750   1.719
 55        2.799   2.402   2.186   2.050   1.955   1.884   1.829   1.785   1.748   1.717
 56        2.797   2.400   2.184   2.048   1.953   1.882   1.827   1.782   1.746   1.715
 57        2.796   2.398   2.182   2.046   1.951   1.880   1.825   1.780   1.744   1.713
 58        2.794   2.396   2.181   2.044   1.949   1.878   1.823   1.779   1.742   1.711
 59        2.793   2.395   2.179   2.043   1.947   1.876   1.821   1.777   1.740   1.709
 60        2.791   2.393   2.177   2.041   1.946   1.875   1.819   1.775   1.738   1.707
 61        2.790   2.392   2.176   2.039   1.944   1.873   1.818   1.773   1.736   1.705
 62        2.788   2.390   2.174   2.038   1.942   1.871   1.816   1.771   1.735   1.703
 63        2.787   2.389   2.173   2.036   1.941   1.870   1.814   1.770   1.733   1.702
 64        2.786   2.387   2.171   2.035   1.939   1.868   1.813   1.768   1.731   1.700
 65        2.784   2.386   2.170   2.033   1.938   1.867   1.811   1.767   1.730   1.699
 66        2.783   2.385   2.169   2.032   1.937   1.865   1.810   1.765   1.728   1.697
 67        2.782   2.384   2.167   2.031   1.935   1.864   1.808   1.764   1.727   1.696
 68        2.781   2.382   2.166   2.029   1.934   1.863   1.807   1.762   1.725   1.694
 69        2.780   2.381   2.165   2.028   1.933   1.861   1.806   1.761   1.724   1.693
 70        2.779   2.380   2.164   2.027   1.931   1.860   1.804   1.760   1.723   1.691
 71        2.778   2.379   2.163   2.026   1.930   1.859   1.803   1.758   1.721   1.690
 72        2.777   2.378   2.161   2.025   1.929   1.858   1.802   1.757   1.720   1.689
 73        2.776   2.377   2.160   2.024   1.928   1.856   1.801   1.756   1.719   1.687
 74        2.775   2.376   2.159   2.022   1.927   1.855   1.800   1.755   1.718   1.686
 75        2.774   2.375   2.158   2.021   1.926   1.854   1.798   1.754   1.716   1.685
 76        2.773   2.374   2.157   2.020   1.925   1.853   1.797   1.752   1.715   1.684
 77        2.772   2.373   2.156   2.019   1.924   1.852   1.796   1.751   1.714   1.683
 78        2.771   2.372   2.155   2.018   1.923   1.851   1.795   1.750   1.713   1.682
 79        2.770   2.371   2.154   2.017   1.922   1.850   1.794   1.749   1.712   1.681
 80        2.769   2.370   2.154   2.016   1.921   1.849   1.793   1.748   1.711   1.680
 81        2.769   2.369   2.153   2.016   1.920   1.848   1.792   1.747   1.710   1.679
 82        2.768   2.368   2.152   2.015   1.919   1.847   1.791   1.746   1.709   1.678
 83        2.767   2.368   2.151   2.014   1.918   1.846   1.790   1.745   1.708   1.677
 84        2.766   2.367   2.150   2.013   1.917   1.845   1.790   1.744   1.707   1.676
 85        2.765   2.366   2.149   2.012   1.916   1.845   1.789   1.744   1.706   1.675
 86        2.765   2.365   2.149   2.011   1.915   1.844   1.788   1.743   1.705   1.674
 87        2.764   2.365   2.148   2.011   1.915   1.843   1.787   1.742   1.705   1.673
 88        2.763   2.364   2.147   2.010   1.914   1.842   1.786   1.741   1.704   1.672
 89        2.763   2.363   2.146   2.009   1.913   1.841   1.785   1.740   1.703   1.671
 90        2.762   2.363   2.146   2.008   1.912   1.841   1.785   1.739   1.702   1.670
 91        2.761   2.362   2.145   2.008   1.912   1.840   1.784   1.739   1.701   1.670
 92        2.761   2.361   2.144   2.007   1.911   1.839   1.783   1.738   1.701   1.669
 93        2.760   2.361   2.144   2.006   1.910   1.838   1.782   1.737   1.700   1.668
 94        2.760   2.360   2.143   2.006   1.910   1.838   1.782   1.736   1.699   1.667
 95        2.759   2.359   2.142   2.005   1.909   1.837   1.781   1.736   1.698   1.667
 96        2.759   2.359   2.142   2.004   1.908   1.836   1.780   1.735   1.698   1.666
 97        2.758   2.358   2.141   2.004   1.908   1.836   1.780   1.734   1.697   1.665
 98        2.757   2.358   2.141   2.003   1.907   1.835   1.779   1.734   1.696   1.665
 99        2.757   2.357   2.140   2.003   1.906   1.835   1.778   1.733   1.696   1.664
100        2.756   2.356   2.139   2.002   1.906   1.834   1.778   1.732   1.695   1.663


     \ ν1   11      12      13      14      15      16      17      18      19      20
   ν2


  1       60.473  60.705  60.903  61.073  61.220  61.350  61.464  61.566  61.658  61.740
  2        9.401   9.408   9.415   9.420   9.425   9.429   9.433   9.436   9.439   9.441
  3        5.222   5.216   5.210   5.205   5.200   5.196   5.193   5.190   5.187   5.184
  4        3.907   3.896   3.886   3.878   3.870   3.864   3.858   3.853   3.849   3.844
  5        3.282   3.268   3.257   3.247   3.238   3.230   3.223   3.217   3.212   3.207
  6        2.920   2.905   2.892   2.881   2.871   2.863   2.855   2.848   2.842   2.836
  7        2.684   2.668   2.654   2.643   2.632   2.623   2.615   2.607   2.601   2.595
  8        2.519   2.502   2.488   2.475   2.464   2.455   2.446   2.438   2.431   2.425
  9        2.396   2.379   2.364   2.351   2.340   2.329   2.320   2.312   2.305   2.298
 10        2.302   2.284   2.269   2.255   2.244   2.233   2.224   2.215   2.208   2.201
 11        2.227   2.209   2.193   2.179   2.167   2.156   2.147   2.138   2.130   2.123
 12        2.166   2.147   2.131   2.117   2.105   2.094   2.084   2.075   2.067   2.060
 13        2.116   2.097   2.080   2.066   2.053   2.042   2.032   2.023   2.014   2.007
 14        2.073   2.054   2.037   2.022   2.010   1.998   1.988   1.978   1.970   1.962
 15        2.037   2.017   2.000   1.985   1.972   1.961   1.950   1.941   1.932   1.924
 16        2.005   1.985   1.968   1.953   1.940   1.928   1.917   1.908   1.899   1.891
 17        1.978   1.958   1.940   1.925   1.912   1.900   1.889   1.879   1.870   1.862
 18        1.954   1.933   1.916   1.900   1.887   1.875   1.864   1.854   1.845   1.837
 19        1.932   1.912   1.894   1.878   1.865   1.852   1.841   1.831   1.822   1.814
 20        1.913   1.892   1.875   1.859   1.845   1.833   1.821   1.811   1.802   1.794
 21        1.896   1.875   1.857   1.841   1.827   1.815   1.803   1.793   1.784   1.776
 22        1.880   1.859   1.841   1.825   1.811   1.798   1.787   1.777   1.768   1.759
 23        1.866   1.845   1.827   1.811   1.796   1.784   1.772   1.762   1.753   1.744
 24        1.853   1.832   1.814   1.797   1.783   1.770   1.759   1.748   1.739   1.730
 25        1.841   1.820   1.802   1.785   1.771   1.758   1.746   1.736   1.726   1.718
 26        1.830   1.809   1.790   1.774   1.760   1.747   1.735   1.724   1.715   1.706
 27        1.820   1.799   1.780   1.764   1.749   1.736   1.724   1.714   1.704   1.695
 28        1.811   1.790   1.771   1.754   1.740   1.726   1.715   1.704   1.694   1.685
 29        1.802   1.781   1.762   1.745   1.731   1.717   1.705   1.695   1.685   1.676
 30        1.794   1.773   1.754   1.737   1.722   1.709   1.697   1.686   1.676   1.667
 31        1.787   1.765   1.746   1.729   1.714   1.701   1.689   1.678   1.668   1.659
 32        1.780   1.758   1.739   1.722   1.707   1.694   1.682   1.671   1.661   1.652
 33        1.773   1.751   1.732   1.715   1.700   1.687   1.675   1.664   1.654   1.645
 34        1.767   1.745   1.726   1.709   1.694   1.680   1.668   1.657   1.647   1.638
 35        1.761   1.739   1.720   1.703   1.688   1.674   1.662   1.651   1.641   1.632
 36        1.756   1.734   1.715   1.697   1.682   1.669   1.656   1.645   1.635   1.626
 37        1.751   1.729   1.709   1.692   1.677   1.663   1.651   1.640   1.630   1.620
 38        1.746   1.724   1.704   1.687   1.672   1.658   1.646   1.635   1.624   1.615
 39        1.741   1.719   1.700   1.682   1.667   1.653   1.641   1.630   1.619   1.610
 40        1.737   1.715   1.695   1.678   1.662   1.649   1.636   1.625   1.615   1.605
 41        1.733   1.710   1.691   1.673   1.658   1.644   1.632   1.620   1.610   1.601
 42        1.729   1.706   1.687   1.669   1.654   1.640   1.628   1.616   1.606   1.596
 43        1.725   1.703   1.683   1.665   1.650   1.636   1.624   1.612   1.602   1.592
 44        1.721   1.699   1.679   1.662   1.646   1.632   1.620   1.608   1.598   1.588
 45        1.718   1.695   1.676   1.658   1.643   1.629   1.616   1.605   1.594   1.585
 46        1.715   1.692   1.672   1.655   1.639   1.625   1.613   1.601   1.591   1.581
 47        1.712   1.689   1.669   1.652   1.636   1.622   1.609   1.598   1.587   1.578
 48        1.709   1.686   1.666   1.648   1.633   1.619   1.606   1.594   1.584   1.574
 49        1.706   1.683   1.663   1.645   1.630   1.616   1.603   1.591   1.581   1.571
 50        1.703   1.680   1.660   1.643   1.627   1.613   1.600   1.588   1.578   1.568
 51        1.700   1.677   1.658   1.640   1.624   1.610   1.597   1.586   1.575   1.565
 52        1.698   1.675   1.655   1.637   1.621   1.607   1.594   1.583   1.572   1.562
 53        1.695   1.672   1.652   1.635   1.619   1.605   1.592   1.580   1.570   1.560
 54        1.693   1.670   1.650   1.632   1.616   1.602   1.589   1.578   1.567   1.557
 55        1.691   1.668   1.648   1.630   1.614   1.600   1.587   1.575   1.564   1.555
 56        1.688   1.666   1.645   1.628   1.612   1.597   1.585   1.573   1.562   1.552
 57        1.686   1.663   1.643   1.625   1.610   1.595   1.582   1.571   1.560   1.550
 58        1.684   1.661   1.641   1.623   1.607   1.593   1.580   1.568   1.558   1.548
 59        1.682   1.659   1.639   1.621   1.605   1.591   1.578   1.566   1.555   1.546
 60        1.680   1.657   1.637   1.619   1.603   1.589   1.576   1.564   1.553   1.543
 61        1.679   1.656   1.635   1.617   1.601   1.587   1.574   1.562   1.551   1.541
 62        1.677   1.654   1.634   1.616   1.600   1.585   1.572   1.560   1.549   1.540
 63        1.675   1.652   1.632   1.614   1.598   1.583   1.570   1.558   1.548   1.538
 64        1.673   1.650   1.630   1.612   1.596   1.582   1.569   1.557   1.546   1.536
 65        1.672   1.649   1.628   1.610   1.594   1.580   1.567   1.555   1.544   1.534
 66        1.670   1.647   1.627   1.609   1.593   1.578   1.565   1.553   1.542   1.532
 67        1.669   1.646   1.625   1.607   1.591   1.577   1.564   1.552   1.541   1.531
 68        1.667   1.644   1.624   1.606   1.590   1.575   1.562   1.550   1.539   1.529
 69        1.666   1.643   1.622   1.604   1.588   1.574   1.560   1.548   1.538   1.527
 70        1.665   1.641   1.621   1.603   1.587   1.572   1.559   1.547   1.536   1.526
 71        1.663   1.640   1.619   1.601   1.585   1.571   1.557   1.545   1.535   1.524
 72        1.662   1.639   1.618   1.600   1.584   1.569   1.556   1.544   1.533   1.523
 73        1.661   1.637   1.617   1.599   1.583   1.568   1.555   1.543   1.532   1.522
 74        1.659   1.636   1.616   1.597   1.581   1.567   1.553   1.541   1.530   1.520
 75        1.658   1.635   1.614   1.596   1.580   1.565   1.552   1.540   1.529   1.519
 76        1.657   1.634   1.613   1.595   1.579   1.564   1.551   1.539   1.528   1.518
 77        1.656   1.632   1.612   1.594   1.578   1.563   1.550   1.538   1.527   1.516
 78        1.655   1.631   1.611   1.593   1.576   1.562   1.548   1.536   1.525   1.515
 79        1.654   1.630   1.610   1.592   1.575   1.561   1.547   1.535   1.524   1.514
 80        1.653   1.629   1.609   1.590   1.574   1.559   1.546   1.534   1.523   1.513
 81        1.652   1.628   1.608   1.589   1.573   1.558   1.545   1.533   1.522   1.512
 82        1.651   1.627   1.607   1.588   1.572   1.557   1.544   1.532   1.521   1.511
 83        1.650   1.626   1.606   1.587   1.571   1.556   1.543   1.531   1.520   1.509
 84        1.649   1.625   1.605   1.586   1.570   1.555   1.542   1.530   1.519   1.508
 85        1.648   1.624   1.604   1.585   1.569   1.554   1.541   1.529   1.518   1.507
 86        1.647   1.623   1.603   1.584   1.568   1.553   1.540   1.528   1.517   1.506
 87        1.646   1.622   1.602   1.583   1.567   1.552   1.539   1.527   1.516   1.505
 88        1.645   1.622   1.601   1.583   1.566   1.551   1.538   1.526   1.515   1.504
 89        1.644   1.621   1.600   1.582   1.565   1.550   1.537   1.525   1.514   1.503
 90        1.643   1.620   1.599   1.581   1.564   1.550   1.536   1.524   1.513   1.503
 91        1.643   1.619   1.598   1.580   1.564   1.549   1.535   1.523   1.512   1.502
 92        1.642   1.618   1.598   1.579   1.563   1.548   1.534   1.522   1.511   1.501
 93        1.641   1.617   1.597   1.578   1.562   1.547   1.534   1.521   1.510   1.500
 94        1.640   1.617   1.596   1.578   1.561   1.546   1.533   1.521   1.509   1.499
 95        1.640   1.616   1.595   1.577   1.560   1.545   1.532   1.520   1.509   1.498
 96        1.639   1.615   1.594   1.576   1.560   1.545   1.531   1.519   1.508   1.497
 97        1.638   1.614   1.594   1.575   1.559   1.544   1.530   1.518   1.507   1.497
 98        1.637   1.614   1.593   1.575   1.558   1.543   1.530   1.517   1.506   1.496
 99        1.637   1.613   1.592   1.574   1.557   1.542   1.529   1.517   1.505   1.495
100        1.636   1.612   1.592   1.573   1.557   1.542   1.528   1.516   1.505   1.494

Upper critical values of the F distribution
for ν1 numerator degrees of freedom and ν2 denominator degrees of freedom

1% significance level

\( F_{.01}(\nu_{1},\nu_{2}) \)

     \ ν1   1       2       3       4       5       6       7       8       9      10
   ν2

  1      4052.19 4999.52 5403.34 5624.62 5763.65 5858.97 5928.33 5981.10 6022.50 6055.85
  2       98.502  99.000  99.166  99.249  99.300  99.333  99.356  99.374  99.388  99.399
  3       34.116  30.816  29.457  28.710  28.237  27.911  27.672  27.489  27.345  27.229
  4       21.198  18.000  16.694  15.977  15.522  15.207  14.976  14.799  14.659  14.546
  5       16.258  13.274  12.060  11.392  10.967  10.672  10.456  10.289  10.158  10.051
  6       13.745  10.925   9.780   9.148   8.746   8.466   8.260   8.102   7.976   7.874
  7       12.246   9.547   8.451   7.847   7.460   7.191   6.993   6.840   6.719   6.620
  8       11.259   8.649   7.591   7.006   6.632   6.371   6.178   6.029   5.911   5.814
  9       10.561   8.022   6.992   6.422   6.057   5.802   5.613   5.467   5.351   5.257
 10       10.044   7.559   6.552   5.994   5.636   5.386   5.200   5.057   4.942   4.849
 11        9.646   7.206   6.217   5.668   5.316   5.069   4.886   4.744   4.632   4.539
 12        9.330   6.927   5.953   5.412   5.064   4.821   4.640   4.499   4.388   4.296
 13        9.074   6.701   5.739   5.205   4.862   4.620   4.441   4.302   4.191   4.100
 14        8.862   6.515   5.564   5.035   4.695   4.456   4.278   4.140   4.030   3.939
 15        8.683   6.359   5.417   4.893   4.556   4.318   4.142   4.004   3.895   3.805
 16        8.531   6.226   5.292   4.773   4.437   4.202   4.026   3.890   3.780   3.691
 17        8.400   6.112   5.185   4.669   4.336   4.102   3.927   3.791   3.682   3.593
 18        8.285   6.013   5.092   4.579   4.248   4.015   3.841   3.705   3.597   3.508
 19        8.185   5.926   5.010   4.500   4.171   3.939   3.765   3.631   3.523   3.434
 20        8.096   5.849   4.938   4.431   4.103   3.871   3.699   3.564   3.457   3.368
 21        8.017   5.780   4.874   4.369   4.042   3.812   3.640   3.506   3.398   3.310
 22        7.945   5.719   4.817   4.313   3.988   3.758   3.587   3.453   3.346   3.258
 23        7.881   5.664   4.765   4.264   3.939   3.710   3.539   3.406   3.299   3.211
 24        7.823   5.614   4.718   4.218   3.895   3.667   3.496   3.363   3.256   3.168
 25        7.770   5.568   4.675   4.177   3.855   3.627   3.457   3.324   3.217   3.129
 26        7.721   5.526   4.637   4.140   3.818   3.591   3.421   3.288   3.182   3.094
 27        7.677   5.488   4.601   4.106   3.785   3.558   3.388   3.256   3.149   3.062
 28        7.636   5.453   4.568   4.074   3.754   3.528   3.358   3.226   3.120   3.032
 29        7.598   5.420   4.538   4.045   3.725   3.499   3.330   3.198   3.092   3.005
 30        7.562   5.390   4.510   4.018   3.699   3.473   3.305   3.173   3.067   2.979
 31        7.530   5.362   4.484   3.993   3.675   3.449   3.281   3.149   3.043   2.955
 32        7.499   5.336   4.459   3.969   3.652   3.427   3.258   3.127   3.021   2.934
 33        7.471   5.312   4.437   3.948   3.630   3.406   3.238   3.106   3.000   2.913
 34        7.444   5.289   4.416   3.927   3.611   3.386   3.218   3.087   2.981   2.894
 35        7.419   5.268   4.396   3.908   3.592   3.368   3.200   3.069   2.963   2.876
 36        7.396   5.248   4.377   3.890   3.574   3.351   3.183   3.052   2.946   2.859
 37        7.373   5.229   4.360   3.873   3.558   3.334   3.167   3.036   2.930   2.843
 38        7.353   5.211   4.343   3.858   3.542   3.319   3.152   3.021   2.915   2.828
 39        7.333   5.194   4.327   3.843   3.528   3.305   3.137   3.006   2.901   2.814
 40        7.314   5.179   4.313   3.828   3.514   3.291   3.124   2.993   2.888   2.801
 41        7.296   5.163   4.299   3.815   3.501   3.278   3.111   2.980   2.875   2.788
 42        7.280   5.149   4.285   3.802   3.488   3.266   3.099   2.968   2.863   2.776
 43        7.264   5.136   4.273   3.790   3.476   3.254   3.087   2.957   2.851   2.764
 44        7.248   5.123   4.261   3.778   3.465   3.243   3.076   2.946   2.840   2.754
 45        7.234   5.110   4.249   3.767   3.454   3.232   3.066   2.935   2.830   2.743
 46        7.220   5.099   4.238   3.757   3.444   3.222   3.056   2.925   2.820   2.733
 47        7.207   5.087   4.228   3.747   3.434   3.213   3.046   2.916   2.811   2.724
 48        7.194   5.077   4.218   3.737   3.425   3.204   3.037   2.907   2.802   2.715
 49        7.182   5.066   4.208   3.728   3.416   3.195   3.028   2.898   2.793   2.706
 50        7.171   5.057   4.199   3.720   3.408   3.186   3.020   2.890   2.785   2.698
 51        7.159   5.047   4.191   3.711   3.400   3.178   3.012   2.882   2.777   2.690
 52        7.149   5.038   4.182   3.703   3.392   3.171   3.005   2.874   2.769   2.683
 53        7.139   5.030   4.174   3.695   3.384   3.163   2.997   2.867   2.762   2.675
 54        7.129   5.021   4.167   3.688   3.377   3.156   2.990   2.860   2.755   2.668
 55        7.119   5.013   4.159   3.681   3.370   3.149   2.983   2.853   2.748   2.662
 56        7.110   5.006   4.152   3.674   3.363   3.143   2.977   2.847   2.742   2.655
 57        7.102   4.998   4.145   3.667   3.357   3.136   2.971   2.841   2.736   2.649
 58        7.093   4.991   4.138   3.661   3.351   3.130   2.965   2.835   2.730   2.643
 59        7.085   4.984   4.132   3.655   3.345   3.124   2.959   2.829   2.724   2.637
 60        7.077   4.977   4.126   3.649   3.339   3.119   2.953   2.823   2.718   2.632
 61        7.070   4.971   4.120   3.643   3.333   3.113   2.948   2.818   2.713   2.626
 62        7.062   4.965   4.114   3.638   3.328   3.108   2.942   2.813   2.708   2.621
 63        7.055   4.959   4.109   3.632   3.323   3.103   2.937   2.808   2.703   2.616
 64        7.048   4.953   4.103   3.627   3.318   3.098   2.932   2.803   2.698   2.611
 65        7.042   4.947   4.098   3.622   3.313   3.093   2.928   2.798   2.693   2.607
 66        7.035   4.942   4.093   3.618   3.308   3.088   2.923   2.793   2.689   2.602
 67        7.029   4.937   4.088   3.613   3.304   3.084   2.919   2.789   2.684   2.598
 68        7.023   4.932   4.083   3.608   3.299   3.080   2.914   2.785   2.680   2.593
 69        7.017   4.927   4.079   3.604   3.295   3.075   2.910   2.781   2.676   2.589
 70        7.011   4.922   4.074   3.600   3.291   3.071   2.906   2.777   2.672   2.585
 71        7.006   4.917   4.070   3.596   3.287   3.067   2.902   2.773   2.668   2.581
 72        7.001   4.913   4.066   3.591   3.283   3.063   2.898   2.769   2.664   2.578
 73        6.995   4.908   4.062   3.588   3.279   3.060   2.895   2.765   2.660   2.574
 74        6.990   4.904   4.058   3.584   3.275   3.056   2.891   2.762   2.657   2.570
 75        6.985   4.900   4.054   3.580   3.272   3.052   2.887   2.758   2.653   2.567
 76        6.981   4.896   4.050   3.577   3.268   3.049   2.884   2.755   2.650   2.563
 77        6.976   4.892   4.047   3.573   3.265   3.046   2.881   2.751   2.647   2.560
 78        6.971   4.888   4.043   3.570   3.261   3.042   2.877   2.748   2.644   2.557
 79        6.967   4.884   4.040   3.566   3.258   3.039   2.874   2.745   2.640   2.554
 80        6.963   4.881   4.036   3.563   3.255   3.036   2.871   2.742   2.637   2.551
 81        6.958   4.877   4.033   3.560   3.252   3.033   2.868   2.739   2.634   2.548
 82        6.954   4.874   4.030   3.557   3.249   3.030   2.865   2.736   2.632   2.545
 83        6.950   4.870   4.027   3.554   3.246   3.027   2.863   2.733   2.629   2.542
 84        6.947   4.867   4.024   3.551   3.243   3.025   2.860   2.731   2.626   2.539
 85        6.943   4.864   4.021   3.548   3.240   3.022   2.857   2.728   2.623   2.537
 86        6.939   4.861   4.018   3.545   3.238   3.019   2.854   2.725   2.621   2.534
 87        6.935   4.858   4.015   3.543   3.235   3.017   2.852   2.723   2.618   2.532
 88        6.932   4.855   4.012   3.540   3.233   3.014   2.849   2.720   2.616   2.529
 89        6.928   4.852   4.010   3.538   3.230   3.012   2.847   2.718   2.613   2.527
 90        6.925   4.849   4.007   3.535   3.228   3.009   2.845   2.715   2.611   2.524
 91        6.922   4.846   4.004   3.533   3.225   3.007   2.842   2.713   2.609   2.522
 92        6.919   4.844   4.002   3.530   3.223   3.004   2.840   2.711   2.606   2.520
 93        6.915   4.841   3.999   3.528   3.221   3.002   2.838   2.709   2.604   2.518
 94        6.912   4.838   3.997   3.525   3.218   3.000   2.835   2.706   2.602   2.515
 95        6.909   4.836   3.995   3.523   3.216   2.998   2.833   2.704   2.600   2.513
 96        6.906   4.833   3.992   3.521   3.214   2.996   2.831   2.702   2.598   2.511
 97        6.904   4.831   3.990   3.519   3.212   2.994   2.829   2.700   2.596   2.509
 98        6.901   4.829   3.988   3.517   3.210   2.992   2.827   2.698   2.594   2.507
 99        6.898   4.826   3.986   3.515   3.208   2.990   2.825   2.696   2.592   2.505
100        6.895   4.824   3.984   3.513   3.206   2.988   2.823   2.694   2.590   2.503


     \ ν1   11      12      13      14      15      16      17      18      19      20
   ν2


  1.     6083.35 6106.35 6125.86 6142.70 6157.28 6170.12 6181.42 6191.52 6200.58 6208.74
  2.      99.408  99.416  99.422  99.428  99.432  99.437  99.440  99.444  99.447  99.449
  3.      27.133  27.052  26.983  26.924  26.872  26.827  26.787  26.751  26.719  26.690
  4.      14.452  14.374  14.307  14.249  14.198  14.154  14.115  14.080  14.048  14.020
  5.       9.963   9.888   9.825   9.770   9.722   9.680   9.643   9.610   9.580   9.553
  6.       7.790   7.718   7.657   7.605   7.559   7.519   7.483   7.451   7.422   7.396
  7.       6.538   6.469   6.410   6.359   6.314   6.275   6.240   6.209   6.181   6.155
  8.       5.734   5.667   5.609   5.559   5.515   5.477   5.442   5.412   5.384   5.359
  9.       5.178   5.111   5.055   5.005   4.962   4.924   4.890   4.860   4.833   4.808
 10.       4.772   4.706   4.650   4.601   4.558   4.520   4.487   4.457   4.430   4.405
 11.       4.462   4.397   4.342   4.293   4.251   4.213   4.180   4.150   4.123   4.099
 12.       4.220   4.155   4.100   4.052   4.010   3.972   3.939   3.909   3.883   3.858
 13.       4.025   3.960   3.905   3.857   3.815   3.778   3.745   3.716   3.689   3.665
 14.       3.864   3.800   3.745   3.698   3.656   3.619   3.586   3.556   3.529   3.505
 15.       3.730   3.666   3.612   3.564   3.522   3.485   3.452   3.423   3.396   3.372
 16.       3.616   3.553   3.498   3.451   3.409   3.372   3.339   3.310   3.283   3.259
 17.       3.519   3.455   3.401   3.353   3.312   3.275   3.242   3.212   3.186   3.162
 18.       3.434   3.371   3.316   3.269   3.227   3.190   3.158   3.128   3.101   3.077
 19.       3.360   3.297   3.242   3.195   3.153   3.116   3.084   3.054   3.027   3.003
 20.       3.294   3.231   3.177   3.130   3.088   3.051   3.018   2.989   2.962   2.938
 21.       3.236   3.173   3.119   3.072   3.030   2.993   2.960   2.931   2.904   2.880
 22.       3.184   3.121   3.067   3.019   2.978   2.941   2.908   2.879   2.852   2.827
 23.       3.137   3.074   3.020   2.973   2.931   2.894   2.861   2.832   2.805   2.781
 24.       3.094   3.032   2.977   2.930   2.889   2.852   2.819   2.789   2.762   2.738
 25.       3.056   2.993   2.939   2.892   2.850   2.813   2.780   2.751   2.724   2.699
 26.       3.021   2.958   2.904   2.857   2.815   2.778   2.745   2.715   2.688   2.664
 27.       2.988   2.926   2.871   2.824   2.783   2.746   2.713   2.683   2.656   2.632
 28.       2.959   2.896   2.842   2.795   2.753   2.716   2.683   2.653   2.626   2.602
 29.       2.931   2.868   2.814   2.767   2.726   2.689   2.656   2.626   2.599   2.574
 30.       2.906   2.843   2.789   2.742   2.700   2.663   2.630   2.600   2.573   2.549
 31.       2.882   2.820   2.765   2.718   2.677   2.640   2.606   2.577   2.550   2.525
 32.       2.860   2.798   2.744   2.696   2.655   2.618   2.584   2.555   2.527   2.503
 33.       2.840   2.777   2.723   2.676   2.634   2.597   2.564   2.534   2.507   2.482
 34.       2.821   2.758   2.704   2.657   2.615   2.578   2.545   2.515   2.488   2.463
 35.       2.803   2.740   2.686   2.639   2.597   2.560   2.527   2.497   2.470   2.445
 36.       2.786   2.723   2.669   2.622   2.580   2.543   2.510   2.480   2.453   2.428
 37.       2.770   2.707   2.653   2.606   2.564   2.527   2.494   2.464   2.437   2.412
 38.       2.755   2.692   2.638   2.591   2.549   2.512   2.479   2.449   2.421   2.397
 39.       2.741   2.678   2.624   2.577   2.535   2.498   2.465   2.434   2.407   2.382
 40.       2.727   2.665   2.611   2.563   2.522   2.484   2.451   2.421   2.394   2.369
 41.       2.715   2.652   2.598   2.551   2.509   2.472   2.438   2.408   2.381   2.356
 42.       2.703   2.640   2.586   2.539   2.497   2.460   2.426   2.396   2.369   2.344
 43.       2.691   2.629   2.575   2.527   2.485   2.448   2.415   2.385   2.357   2.332
 44.       2.680   2.618   2.564   2.516   2.475   2.437   2.404   2.374   2.346   2.321
 45.       2.670   2.608   2.553   2.506   2.464   2.427   2.393   2.363   2.336   2.311
 46.       2.660   2.598   2.544   2.496   2.454   2.417   2.384   2.353   2.326   2.301
 47.       2.651   2.588   2.534   2.487   2.445   2.408   2.374   2.344   2.316   2.291
 48.       2.642   2.579   2.525   2.478   2.436   2.399   2.365   2.335   2.307   2.282
 49.       2.633   2.571   2.517   2.469   2.427   2.390   2.356   2.326   2.299   2.274
 50.       2.625   2.562   2.508   2.461   2.419   2.382   2.348   2.318   2.290   2.265
 51.       2.617   2.555   2.500   2.453   2.411   2.374   2.340   2.310   2.282   2.257
 52.       2.610   2.547   2.493   2.445   2.403   2.366   2.333   2.302   2.275   2.250
 53.       2.602   2.540   2.486   2.438   2.396   2.359   2.325   2.295   2.267   2.242
 54.       2.595   2.533   2.479   2.431   2.389   2.352   2.318   2.288   2.260   2.235
 55.       2.589   2.526   2.472   2.424   2.382   2.345   2.311   2.281   2.253   2.228
 56.       2.582   2.520   2.465   2.418   2.376   2.339   2.305   2.275   2.247   2.222
 57.       2.576   2.513   2.459   2.412   2.370   2.332   2.299   2.268   2.241   2.215
 58.       2.570   2.507   2.453   2.406   2.364   2.326   2.293   2.262   2.235   2.209
 59.       2.564   2.502   2.447   2.400   2.358   2.320   2.287   2.256   2.229   2.203
 60.       2.559   2.496   2.442   2.394   2.352   2.315   2.281   2.251   2.223   2.198
 61.       2.553   2.491   2.436   2.389   2.347   2.309   2.276   2.245   2.218   2.192
 62.       2.548   2.486   2.431   2.384   2.342   2.304   2.270   2.240   2.212   2.187
 63.       2.543   2.481   2.426   2.379   2.337   2.299   2.265   2.235   2.207   2.182
 64.       2.538   2.476   2.421   2.374   2.332   2.294   2.260   2.230   2.202   2.177
 65.       2.534   2.471   2.417   2.369   2.327   2.289   2.256   2.225   2.198   2.172
 66.       2.529   2.466   2.412   2.365   2.322   2.285   2.251   2.221   2.193   2.168
 67.       2.525   2.462   2.408   2.360   2.318   2.280   2.247   2.216   2.188   2.163
 68.       2.520   2.458   2.403   2.356   2.314   2.276   2.242   2.212   2.184   2.159
 69.       2.516   2.454   2.399   2.352   2.310   2.272   2.238   2.208   2.180   2.155
 70.       2.512   2.450   2.395   2.348   2.306   2.268   2.234   2.204   2.176   2.150
 71.       2.508   2.446   2.391   2.344   2.302   2.264   2.230   2.200   2.172   2.146
 72.       2.504   2.442   2.388   2.340   2.298   2.260   2.226   2.196   2.168   2.143
 73.       2.501   2.438   2.384   2.336   2.294   2.256   2.223   2.192   2.164   2.139
 74.       2.497   2.435   2.380   2.333   2.290   2.253   2.219   2.188   2.161   2.135
 75.       2.494   2.431   2.377   2.329   2.287   2.249   2.215   2.185   2.157   2.132
 76.       2.490   2.428   2.373   2.326   2.284   2.246   2.212   2.181   2.154   2.128
 77.       2.487   2.424   2.370   2.322   2.280   2.243   2.209   2.178   2.150   2.125
 78.       2.484   2.421   2.367   2.319   2.277   2.239   2.206   2.175   2.147   2.122
 79.       2.481   2.418   2.364   2.316   2.274   2.236   2.202   2.172   2.144   2.118
 80.       2.478   2.415   2.361   2.313   2.271   2.233   2.199   2.169   2.141   2.115
 81.       2.475   2.412   2.358   2.310   2.268   2.230   2.196   2.166   2.138   2.112
 82.       2.472   2.409   2.355   2.307   2.265   2.227   2.193   2.163   2.135   2.109
 83.       2.469   2.406   2.352   2.304   2.262   2.224   2.191   2.160   2.132   2.106
 84.       2.466   2.404   2.349   2.302   2.259   2.222   2.188   2.157   2.129   2.104
 85.       2.464   2.401   2.347   2.299   2.257   2.219   2.185   2.154   2.126   2.101
 86.       2.461   2.398   2.344   2.296   2.254   2.216   2.182   2.152   2.124   2.098
 87.       2.459   2.396   2.342   2.294   2.252   2.214   2.180   2.149   2.121   2.096
 88.       2.456   2.393   2.339   2.291   2.249   2.211   2.177   2.147   2.119   2.093
 89.       2.454   2.391   2.337   2.289   2.247   2.209   2.175   2.144   2.116   2.091
 90.       2.451   2.389   2.334   2.286   2.244   2.206   2.172   2.142   2.114   2.088
 91.       2.449   2.386   2.332   2.284   2.242   2.204   2.170   2.139   2.111   2.086
 92.       2.447   2.384   2.330   2.282   2.240   2.202   2.168   2.137   2.109   2.083
 93.       2.444   2.382   2.327   2.280   2.237   2.200   2.166   2.135   2.107   2.081
 94.       2.442   2.380   2.325   2.277   2.235   2.197   2.163   2.133   2.105   2.079
 95.       2.440   2.378   2.323   2.275   2.233   2.195   2.161   2.130   2.102   2.077
 96.       2.438   2.375   2.321   2.273   2.231   2.193   2.159   2.128   2.100   2.075
 97.       2.436   2.373   2.319   2.271   2.229   2.191   2.157   2.126   2.098   2.073
 98.       2.434   2.371   2.317   2.269   2.227   2.189   2.155   2.124   2.096   2.071
 99.       2.432   2.369   2.315   2.267   2.225   2.187   2.153   2.122   2.094   2.069
100.       2.430   2.368   2.313   2.265   2.223   2.185   2.151   2.120   2.092   2.067

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