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Percentage Points for the F-Distribution


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Upper 5% points

ν 1

ν 2 12345678122440

1 161.4 199.5 215.7 224.6 230.2 234.0 236.8 238.9 243.9 249.1 251.1 254.3

2 18.51 19.00 19.16 19.25 19.30 19.33 19.35 19.37 19.41 19.45 19.47 19.50

3 10.13 9.55 9.28 9.12 9.01 8.94 8.89 8.85 8.74 8.64 8.59 8.53

4 7.71 6.94 6.59 6.39 6.26 6.16 6.09 6.04 5.91 5.77 5.72 5.63

5 6.61 5.79 5.41 5.19 5.05 4.95 4.88 4.82 4.68 4.53 4.46 4.36

6 5.99 5.14 4.76 4.53 4.39 4.28 4.21 4.15 4.00 3.84 3.77 3.67

7 5.59 4.74 4.35 4.12 3.97 3.87 3.79 3.73 3.57 3.41 3.34 3.23

8 5.32 4.46 4.07 3.84 3.69 3.58 3.50 3.44 3.28 3.12 3.04 2.93

9 5.12 4.26 3.86 3.63 3.48 3.37 3.29 3.23 3.07 2.90 2.83 2.71

10 4.96 4.10 3.71 3.48 3.33 3.22 3.14 3.07 2.91 2.74 2.66 2.54

12 4.75 3.89 3.49 3.26 3.11 3.00 2.91 2.85 2.69 2.51 2.43 2.30

15 4.54 3.68 3.29 3.06 2.90 2.79 2.71 2.64 2.48 2.29 2.20 2.07

18 4.41 3.55 3.16 2.93 2.77 2.66 2.58 2.51 2.34 2.15 2.06 1.92

20 4.35 3.49 3.10 2.87 2.71 2.60 2.51 2.45 2.28 2.08 1.99 1.84

25 4.24 3.39 2.99 2.76 2.60 2.49 2.40 2.34 2.16 1.96 1.87 1.71

30 4.17 3.32 2.92 2.69 2.53 2.42 2.33 2.27 2.09 1.89 1.79 1.62

40 4.08 3.23 2.84 2.61 2.45 2.34 2.25 2.18 2.00 1.79 1.69 1.51

60 4.00 3.15 2.76 2.53 2.37 2.25 2.17 2.10 1.92 1.70 1.59 1.39

∞ 3.84 3.00 2.60 2.37 2.21 2.10 2.01 1.94 1.75 1.52 1.39 1.00

NB. The lower 5% point of an Fν1, ν2 distribution is the reciprocal of the upper 5% point of an Fν2, ν1 distribution.

Upper 2.5% points

ν 1

ν 2 12345678122440

1 647.8 799.5 864.2 899.6 921.8 937.1 948.2 956.7 967.7 997.2 1006 1018

2 38.51 39.00 39.17 39.25 39.30 39.33 39.36 39.37 39.41 39.46 39.47 39.50

3 17.44 16.04 15.44 15.10 14.88 14.73 14.62 14.54 14.34 14.12 14.04 13.90

4 12.22 10.65 9.98 9.60 9.36 9.20 9.07 8.98 8.75 8.51 8.41 8.26

5 10.01 8.43 7.76 7.39 7.15 6.98 6.85 6.76 6.52 6.28 6.18 6.02

6 8.81 7.26 6.60 6.23 5.99 5.82 5.70 5.60 5.37 5.12 5.01 4.85

7 8.07 6.54 5.89 5.52 5.29 5.12 4.99 4.90 4.67 4.42 4.31 4.14

8 7.57 6.06 5.42 5.05 4.82 4.65 4.53 4.43 4.20 3.95 3.84 3.67

9 7.21 5.71 5.08 4.72 4.48 4.32 4.20 4.10 3.87 3.61 3.51 3.33

10 6.94 5.46 4.83 4.47 4.24 4.07 3.95 3.85 3.62 3.37 3.26 3.08

12 6.55 5.10 4.47 4.12 3.89 3.73 3.61 3.51 3.28 3.02 2.91 2.72

15 6.20 4.77 4.15 3.80 3.58 3.41 3.29 3.20 2.96 2.70 2.59 2.40

18 5.98 4.56 3.95 3.61 3.38 3.22 3.10 3.01 2.77 2.50 2.38 2.19

20 5.87 4.46 3.86 3.51 3.29 3.13 3.01 2.91 2.68 2.41 2.29 2.09

25 5.69 4.29 3.69 3.35 3.13 2.97 2.85 2.75 2.51 2.24 2.12 1.91

30 5.57 4.18 3.59 3.25 3.03 2.87 2.75 2.65 2.41 2.14 2.01 1.79

40 5.42 4.05 3.46 3.13 2.90 2.74 2.62 2.53 2.29 2.01 1.88 1.64

60 5.29 3.93 3.34 3.01 2.79 2.63 2.51 2.41 2.17 1.88 1.74 1.48

∞ 5.02 3.69 3.12 2.79 2.57 2.41 2.29 2.19 1.94 1.64 1.48 1.00

NB. The lower 2.5% point of an Fν1, ν2 distribution is the reciprocal of the upper 2.5% point of an Fν2, ν1 distribution.

Upper 1% points

ν 1

ν 2 12345678122440

1 4052 4999 5403 5625 5764 5859 5928 5981 6106 6235 6287 6366

2 98.50 99.00 99.17 99.25 99.30 99.33 99.36 99.37 99.42 99.46 99.47 99.50

3 34.12 30.82 29.46 28.71 28.24 27.91 27.67 27.49 27.05 26.60 26.41 26.13

4 21.20 18.00 16.69 15.98 15.52 15.21 14.98 14.80 14.37 13.93 13.75 13.46

5 16.26 13.27 12.06 11.39 10.97 10.67 10.46 10.29 9.89 9.47 9.29 9.02

6 13.75 10.92 9.78 9.15 8.75 8.47 8.26 8.10 7.72 7.31 7.14 6.88

7 12.25 9.55 8.45 7.85 7.46 7.19 6.99 6.84 6.47 6.07 5.91 5.65

8 11.26 8.65 7.59 7.01 6.63 6.37 6.18 6.03 5.67 5.28 5.12 4.86

9 10.56 8.02 6.99 6.42 6.06 5.80 5.61 5.47 5.11 4.73 4.57 4.31

10 10.04 7.56 6.55 5.99 5.64 5.39 5.20 5.06 4.71 4.33 4.17 3.91

12 9.33 6.93 5.95 5.41 5.06 4.82 4.64 4.50 4.16 3.78 3.62 3.36

15 8.68 6.36 5.42 4.89 4.56 4.32 4.14 4.00 3.67 3.29 3.13 2.87

18 8.29 6.01 5.09 4.58 4.25 4.01 3.84 3.71 3.37 3.00 2.84 2.57

20 8.10 5.85 4.94 4.43 4.10 3.87 3.70 3.56 3.23 2.86 2.69 2.42

25 7.77 5.57 4.68 4.18 3.85 3.63 3.46 3.32 2.99 2.62 2.45 2.17

30 7.56 5.39 4.51 4.02 3.70 3.47 3.30 3.17 2.84 2.47 2.30 2.01

40 7.31 5.18 4.31 3.83 3.51 3.29 3.12 2.99 2.66 2.29 2.11 1.80

60 7.08 4.98 4.13 3.65 3.34 3.12 2.95 2.82 2.50 2.12 1.94 1.60

∞ 6.63 4.61 3.78 3.32 3.02 2.80 2.64 2.51 2.18 1.79 1.59 1.00

NB. The lower 1% point of an Fν1, ν2 distribution is the reciprocal of the upper 1% point of an Fν2, ν1 distribution.

From A Dictionary of Statistics in Oxford Reference.

Subjects: Probability and Statistics.



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