Consider $K$ independent mean squares, each with $df$ degrees of freedom. Under the null hypothesis each has a chi-square distribution divided by the degrees of freedom times the same fixed constant. The test statistic is the largest mean square divided by the smallest mean square. The column headings are values of $K$; the table entries are the upper critical values.
Table 1: Critical values for the maximum $F$ ratio.
  Upper 0.05 significance level critical values
df 2 3 4 5 6 7 8 9 10 11 12
2 39.0 87.5 142 202 266 333 403 475 550 626 704
3 15.4 27.8 39.2 50.7 62.0 72.9 83.5 93.9 104 114 124
4 9.60 15.5 20.6 25.2 29.5 33.6 37.5 41.1 44.6 48.0 51.4
5 7.15 10.8 13.7 16.3 18.7 20.8 22.9 24.7 26.5 28.2 29.9
6 5.82 8.38 10.4 12.1 13.7 15.0 16.3 17.5 18.6 19.7 20.7
7 4.99 6.94 8.44 9.70 10.8 11.8 12.7 13.5 14.3 15.1 15.8
8 4.43 6.00 7.18 8.12 9.03 9.78 10.5 11.1 11.7 12.2 12.7
9 4.03 5.34 6.31 7.11 7.80 8.41 8.95 9.45 9.91 10.3 10.7
10 3.72 4.85 5.67 6.34 6.92 7.42 7.87 8.28 8.66 9.01 9.34
12 3.28 4.16 4.79 5.30 5.72 6.09 6.42 6.72 7.00 7.25 7.48
15 2.86 3.54 4.01 4.37 4.68 4.95 5.19 5.40 5.59 5.77 5.93
20 2.46 2.95 3.29 3.54 3.76 3.94 4.10 4.24 4.37 4.49 4.59
30 2.07 2.40 2.61 2.78 2.91 3.02 3.12 3.21 3.29 3.36 3.39
$\infty$ 1.67 1.85 1.96 2.04 2.11 2.17 2.22 2.26 2.30 2.33 2.36
  Upper 0.01 significance level critical values$^{*}$
df 2 3 4 5 6 7 8 9 10 11 12
2 199 448 729 1036 1362 1705 2063 2432 2813 3204 3605
3 47.5 85 120 151 184 21(6) 24(9) 28(1) 31(0) 33(7) 36(1)
4 23.2 37 49 59 69 79 89 97 106 113 120
5 14.9 22 28 33 38 42 46 50 54 57 60
6 11.1 15.5 19.1 22 25 27 30 32 34 36 37
7 8.89 12.1 14.5 16.5 18.4 20 22 23 24 26 27
8 7.50 9.9 11.7 13.2 14.5 15.8 16.9 17.9 18.9 19.8 21
9 6.54 8.5 9.9 11.1 12.1 13.1 13.9 14.7 15.3 16.0 16.6
10 5.85 7.4 8.6 9.6 10.4 11.1 11.8 12.4 12.9 13.4 13.9
12 4.91 6.1 6.9 7.6 8.2 8.7 9.1 9.5 9.9 10.2 10.6
15 4.07 4.9 5.5 6.0 6.4 6.7 7.1 7.3 7.5 7.8 8.0
20 3.32 3.8 4.3 4.6 4.9 5.1 5.3 5.5 5.6 5.8 5.9
30 2.63 3.0 3.3 3.4 3.6 3.7 3.8 3.9 4.0 4.1 4.2
$\infty$ 1.96 2.2 2.3 2.4 2.4 2.5 2.5 2.6 2.6 2.7 2.7
$^{*}$The figures in parentheses are uncertain. In general the third digit may be in error by a few units.