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Percentage Points for the F-Distribution

Source:
A Dictionary of Statistics

Percentage Points for the F-Distribution

Upper 5% points

ν 1

ν 2

1

2

3

4

5

6

7

8

12

24

40

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

1

2

3

4

5

6

7

8

12

24

40

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

1

2

3

4

5

6

7

8

12

24

40

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.