F distribution critical value landmarks

Table entries are critical values for F * with probably p in right tail of the distribution.

p 1 2 3 4 5 6 7 8 12 24 1000 1 0.100 39.86 49.50 53.59 55.83 57.24 58.20 58.91 59.44 60.71 62.00 63.30 0.050 161.4 199.5 215.7 224.6 230.2 234.0 236.8 238.9 243.9 249.1 254.2 0.025 647.8 799.5 864.2 899.6 921.8 937.1 948.2 956.6 976.7 997.3 1017.8 0.010 4052 4999 5404 5624 5764 5859 5928 5981 6107 6234 6363 0.001 405312 499725 540257 562668 576496 586033 593185 597954 610352 623703 636101

2 0.100 8.53 9.00 9.16 9.24 9.29 9.33 9.35 9.37 9.41 9.45 9.49 0.050 18.51 19.00 19.16 19.25 19.30 19.33 19.35 19.37 19.41 19.45 19.49 0.025 38.51 39.00 39.17 39.25 39.30 39.33 39.36 39.37 39.41 39.46 39.50 0.010 98.50 99.00 99.16 99.25 99.30 99.33 99.36 99.38 99.42 99.46 99.50 0.001 998.38 998.84 999.31 999.31 999.31 999.31 999.31 999.31 999.31 999.31 999.31

3 0.100 5.54 5.46 5.39 5.34 5.31 5.28 5.27 5.25 5.22 5.18 5.13 0.050 10.13 9.55 9.28 9.12 9.01 8.94 8.89 8.85 8.74 8.64 8.53 0.025 17.44 16.04 15.44 15.10 14.88 14.73 14.62 14.54 14.34 14.12 13.91 0.010 34.12 30.82 29.46 28.71 28.24 27.91 27.67 27.49 27.05 26.60 26.14 0.001 167.06 148.49 141.10 137.08 134.58 132.83 131.61 130.62 128.32 125.93 123.52

4 0.100 4.54 4.32 4.19 4.11 4.05 4.01 3.98 3.95 3.90 3.83 3.76 0.050 7.71 6.94 6.59 6.39 6.26 6.16 6.09 6.04 5.91 5.77 5.63 0.025 12.22 10.65 9.98 9.60 9.36 9.20 9.07 8.98 8.75 8.51 8.26 0.010 21.20 18.00 16.69 15.98 15.52 15.21 14.98 14.80 14.37 13.93 13.47 0.001 74.13 61.25 56.17 53.43 51.72 50.52 49.65 49.00 47.41 45.77 44.09

5 0.100 4.06 3.78 3.62 3.52 3.45 3.40 3.37 3.34 3.27 3.19 3.11 0.050 6.61 5.79 5.41 5.19 5.05 4.95 4.88 4.82 4.68 4.53 4.37 0.025 10.01 8.43 7.76 7.39 7.15 6.98 6.85 6.76 6.52 6.28 6.02 0.010 16.26 13.27 12.06 11.39 10.97 10.67 10.46 10.29 9.89 9.47 9.03 0.001 47.18 37.12 33.20 31.08 29.75 28.83 28.17 27.65 26.42 25.13 23.82

6 0.100 3.78 3.46 3.29 3.18 3.11 3.05 3.01 2.98 2.90 2.82 2.72 0.050 5.99 5.14 4.76 4.53 4.39 4.28 4.21 4.15 4.00 3.84 3.67 0.025 8.81 7.26 6.60 6.23 5.99 5.82 5.70 5.60 5.37 5.12 4.86 0.010 13.75 10.92 9.78 9.15 8.75 8.47 8.26 8.10 7.72 7.31 6.89 0.001 35.51 27.00 23.71 21.92 20.80 20.03 19.46 19.03 17.99 16.90 15.77

7 0.100 3.59 3.26 3.07 2.96 2.88 2.83 2.78 2.75 2.67 2.58 2.47 0.050 5.59 4.74 4.35 4.12 3.97 3.87 3.79 3.73 3.57 3.41 3.23 0.025 8.07 6.54 5.89 5.52 5.29 5.12 4.99 4.90 4.67 4.41 4.15 0.010 12.25 9.55 8.45 7.85 7.46 7.19 6.99 6.84 6.47 6.07 5.66 0.001 29.25 21.69 18.77 17.20 16.21 15.52 15.02 14.63 13.71 12.73 11.72

8 0.100 3.46 3.11 2.92 2.81 2.73 2.67 2.62 2.59 2.50 2.40 2.30 0.050 5.32 4.46 4.07 3.84 3.69 3.58 3.50 3.44 3.28 3.12 2.93 0.025 7.57 6.06 5.42 5.05 4.82 4.65 4.53 4.43 4.20 3.95 3.68 0.010 11.26 8.65 7.59 7.01 6.63 6.37 6.18 6.03 5.67 5.28 4.87 0.001 25.41 18.49 15.83 14.39 13.48 12.86 12.40 12.05 11.19 10.30 9.36

9 0.100 3.36 3.01 2.81 2.69 2.61 2.55 2.51 2.47 2.38 2.28 2.16 0.050 5.12 4.26 3.86 3.63 3.48 3.37 3.29 3.23 3.07 2.90 2.71 0.025 7.21 5.71 5.08 4.72 4.48 4.32 4.20 4.10 3.87 3.61 3.34 0.010 10.56 8.02 6.99 6.42 6.06 5.80 5.61 5.47 5.11 4.73 4.32 0.001 22.86 16.39 13.90 12.56 11.71 11.13 10.70 10.37 9.57 8.72 7.84 Critical values computed with Excel 9.0 Figure of F distribution (like in Moore, 2004, p. 656)

here.

Degrees of freedom in numerator (df1)

F-table.xls 1 of 2 12/24/2005

Degrees of freedom in numerator (df1) p 1 2 3 4 5 6 7 8 12 24 1000 10 0.100 3.29 2.92 2.73 2.61 2.52 2.46 2.41 2.38 2.28 2.18 2.06 0.050 4.96 4.10 3.71 3.48 3.33 3.22 3.14 3.07 2.91 2.74 2.54 0.025 6.94 5.46 4.83 4.47 4.24 4.07 3.95 3.85 3.62 3.37 3.09 0.010 10.04 7.56 6.55 5.99 5.64 5.39 5.20 5.06 4.71 4.33 3.92 0.001 21.04 14.90 12.55 11.28 10.48 9.93 9.52 9.20 8.45 7.64 6.78

12 0.100 3.18 2.81 2.61 2.48 2.39 2.33 2.28 2.24 2.15 2.04 1.91 0.050 4.75 3.89 3.49 3.26 3.11 3.00 2.91 2.85 2.69 2.51 2.30 0.025 6.55 5.10 4.47 4.12 3.89 3.73 3.61 3.51 3.28 3.02 2.73 0.010 9.33 6.93 5.95 5.41 5.06 4.82 4.64 4.50 4.16 3.78 3.37 0.001 18.64 12.97 10.80 9.63 8.89 8.38 8.00 7.71 7.00 6.25 5.44

14 0.100 3.10 2.73 2.52 2.39 2.31 2.24 2.19 2.15 2.05 1.94 1.80 0.050 4.60 3.74 3.34 3.11 2.96 2.85 2.76 2.70 2.53 2.35 2.14 0.025 6.30 4.86 4.24 3.89 3.66 3.50 3.38 3.29 3.05 2.79 2.50 0.010 8.86 6.51 5.56 5.04 4.69 4.46 4.28 4.14 3.80 3.43 3.02 0.001 17.14 11.78 9.73 8.62 7.92 7.44 7.08 6.80 6.13 5.41 4.62

16 0.100 3.05 2.67 2.46 2.33 2.24 2.18 2.13 2.09 1.99 1.87 1.72 0.050 4.49 3.63 3.24 3.01 2.85 2.74 2.66 2.59 2.42 2.24 2.02 0.025 6.12 4.69 4.08 3.73 3.50 3.34 3.22 3.12 2.89 2.63 2.32 0.010 8.53 6.23 5.29 4.77 4.44 4.20 4.03 3.89 3.55 3.18 2.76 0.001 16.12 10.97 9.01 7.94 7.27 6.80 6.46 6.20 5.55 4.85 4.08

18 0.100 3.01 2.62 2.42 2.29 2.20 2.13 2.08 2.04 1.93 1.81 1.66 0.050 4.41 3.55 3.16 2.93 2.77 2.66 2.58 2.51 2.34 2.15 1.92 0.025 5.98 4.56 3.95 3.61 3.38 3.22 3.10 3.01 2.77 2.50 2.20 0.010 8.29 6.01 5.09 4.58 4.25 4.01 3.84 3.71 3.37 3.00 2.58 0.001 15.38 10.39 8.49 7.46 6.81 6.35 6.02 5.76 5.13 4.45 3.69

20 0.100 2.97 2.59 2.38 2.25 2.16 2.09 2.04 2.00 1.89 1.77 1.61 0.050 4.35 3.49 3.10 2.87 2.71 2.60 2.51 2.45 2.28 2.08 1.85 0.025 5.87 4.46 3.86 3.51 3.29 3.13 3.01 2.91 2.68 2.41 2.09 0.010 8.10 5.85 4.94 4.43 4.10 3.87 3.70 3.56 3.23 2.86 2.43 0.001 14.82 9.95 8.10 7.10 6.46 6.02 5.69 5.44 4.82 4.15 3.40

30 0.100 2.88 2.49 2.28 2.14 2.05 1.98 1.93 1.88 1.77 1.64 1.46 0.050 4.17 3.32 2.92 2.69 2.53 2.42 2.33 2.27 2.09 1.89 1.63 0.025 5.57 4.18 3.59 3.25 3.03 2.87 2.75 2.65 2.41 2.14 1.80 0.010 7.56 5.39 4.51 4.02 3.70 3.47 3.30 3.17 2.84 2.47 2.02 0.001 13.29 8.77 7.05 6.12 5.53 5.12 4.82 4.58 4.00 3.36 2.61

50 0.100 2.81 2.41 2.20 2.06 1.97 1.90 1.84 1.80 1.68 1.54 1.33 0.050 4.03 3.18 2.79 2.56 2.40 2.29 2.20 2.13 1.95 1.74 1.45 0.025 5.34 3.97 3.39 3.05 2.83 2.67 2.55 2.46 2.22 1.93 1.56 0.010 7.17 5.06 4.20 3.72 3.41 3.19 3.02 2.89 2.56 2.18 1.70 0.001 12.22 7.96 6.34 5.46 4.90 4.51 4.22 4.00 3.44 2.82 2.05

100 0.100 2.76 2.36 2.14 2.00 1.91 1.83 1.78 1.73 1.61 1.46 1.22 0.050 3.94 3.09 2.70 2.46 2.31 2.19 2.10 2.03 1.85 1.63 1.30 0.025 5.18 3.83 3.25 2.92 2.70 2.54 2.42 2.32 2.08 1.78 1.36 0.010 6.90 4.82 3.98 3.51 3.21 2.99 2.82 2.69 2.37 1.98 1.45 0.001 11.50 7.41 5.86 5.02 4.48 4.11 3.83 3.61 3.07 2.46 1.64

1000 0.100 2.71 2.31 2.09 1.95 1.85 1.78 1.72 1.68 1.55 1.39 1.08 0.050 3.85 3.00 2.61 2.38 2.22 2.11 2.02 1.95 1.76 1.53 1.11 0.025 5.04 3.70 3.13 2.80 2.58 2.42 2.30 2.20 1.96 1.65 1.13 0.010 6.66 4.63 3.80 3.34 3.04 2.82 2.66 2.53 2.20 1.81 1.16 0.001 10.89 6.96 5.46 4.65 4.14 3.78 3.51 3.30 2.77 2.16 1.22 Use StaTable, WinPepi > WhatIs, or other reliable software to determine specific p values

F-table.xls 2 of 2 12/24/2005