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F - Distribution Tables

The F distributions are a family of distributions with two parameters, the degrees of freedom of the sample variances in the numerator and denominator of the F statistic. The numerator degrees of freedom are always given first. The F distributions are not symmetric but are right skewed. The density curve figure illustrates the shape. Because sample variances cannot be negative, the F statistic takes only positive values and the F distribution has no probability below zero.The peak of the F density curve is near one; values far from one in either direction provide evidence against the hypothesis of equal standard deviations.

Table of the Upper Percentage Points of the F distribution

   

1

2

3

4

5

6

7

8

9

10

11

12

15

1

.05
.01

161
4052

200
4999

216
5403

225
5625

230
5764

234
5859

237
5928

239
5981

241
6022

242
6056

243
6082

244
6106

246
6157

2

.05
.01

18.51
98.49

19.00
99.01

19.16
99.17

19.25
99.25

19.39
99.30

19.33
99.33

19.36
99.34

19.37
99.36

19.38
99.38

19.39
99.40

19.4
99.4

19.4
99.4

19.4
99.4

3

.05
.01

10.13
34.12

9.55
30.81

9.28
29.46

9.12
28.71

9.01
28.24

8.94
27.91

8.88
27.67

8.84
27.49

8.81
27.34

8.78
27.23

8.76
27.13

8.74
27.05

8.70
26.87

4

.05
.01

7.71
21.20

6.94
18.00

6.59
16.69

6.39
15.98

6.26
15.52

6.16
15.21

6.09
14.98

6.04
14.80

6.00
14.66

5.96
14.54

5.93
14.95

5.91
14.37

5.86
14.2

5

.05
.01

6.61
16.26

5.79
13.27

5.41
12.06

5.19
11.39

5.05
10.97

4.95
10.67

4.88
10.45

4.82
10.27

4.78
10.15

4.74
10.05

4.70
9.96

4.68
9.89

4.62
9.72

6

.05
.01

5.99
13.74

5.14
10.92

4.76
9.78

4.53
9.15

4.39
8.75

4.28
8.47

4.21
8.26

4.15
8.10

4.10
7.98

4.06
7.87

4.03
7.79

4.00
7.72

3.94
7.56

7

.05
.01

5.59
12.25

4.74
9.55

4.35
8.45

4.12
7.85

3.97
7.46

3.87
7.19

3.79
7.00

3.73
6.84

3.68
6.71

3.63
6.62

3.60
6.54

3.57
6.47

3.51
6.31

8

.05
.01

5.32
11.26

4.46
8.65

4.07
7.59

3.84
7.01

3.69
6.63

3.58
6.37

3.50
6.19

3.44
6.03

3.39
5.91

3.34
5.82

3.31
5.74

3.28
5.67

3.22
5.52

9

.05
.01

5.12
10.56

4.26
8.02

3.86
6.99

3.63
6.42

3.48
6.06

3.37
5.80

3.29
5.61

3.23
5.47

3.18
5.35

3.14
5.26

3.10
5.18

3.07
5.11

3.01
4.96

10

.05
.01

4.96
10.04

4.10
7.56

3.71
6.55

3.48
5.99

3.33
5.64

3.22
5.39

3.14
5.21

3.07
5.06

3.02
4.95

2.97
4.85

2.94
4.78

2.91
4.71

2.85
4.56

20

.05
.01

4.30
7.95

3.44
5.72

3.05
4.82

2.82
4.31

2.66
3.99

2.55
3.76

2.46
3.59

2.40
3.45

2.34
3.35

2.30
3.26

2.31
3.30

2.28
3.23

2.20
3.09

30

.05
.01

4.17
7.56

3.32
5.39

2.92
4.51

2.69
4.02

2.53
3.70

2.42
3.47

2.33
3.30

2.27
3.17

2.21
3.07

2.16
2.98

2.12
2.90

2.09
2.84

2.01
2.70

40

.05
.01

4.08
7.31

3.23
5.18

2.84
4.31

2.61
3.83

2.45
3.51

2.34
3.29

2.25
3.12

2.18
2.99

2.12
2.89

2.08
2.80

2.04
2.73

2.00
2.66

1.92
2.52

50

.05
.01

4.03
7.17

3.18
5.06

2.79
4.20

2.56
3.72

2.40
3.41

2.29
3.19

2.20
3.02

2.13
2.89

2.07
2.78

2.03
2.70

1.98
2.62

1.95
2.56

1.87
2.42

60

.05
.01

4.00
7.08

3.15
4.98

2.76
4.13

2.53
3.65

2.37
3.34

2.25
3.12

2.17
2.95

2.10
2.82

2.04
2.72

1.99
2.63

1.95
2.56

1.92
2.50

1.84
2.35

70

.05
.01

3.98
7.01

3.13
4.92

2.74
4.08

2.50
3.60

2.35
3.29

2.23
3.07

2.14
2.91

2.07
2.77

2.01
2.67

1.97
2.59

1.93
2.51

1.89
2.45

1.82
2.32

80

.05
.01

3.96
6.96

3.11
4.88

2.72
4.04

2.48
3.56

2.33
3.25

2.21
3.04

2.12
2.87

2.05
2.74

1.99
2.64

1.95
2.55

1.91
2.48

1.88
2.41

1.80
2.28

100

.05
.01

3.94
6.90

3.09
4.82

2.70
3.98

2.46
3.51

2.31
3.21

2.19
2.99

2.10
2.82

2.03
2.69

1.97
2.59

1.93
2.50

1.88
2.43

1.85
2.36

1.77
2.22

200

.05
.01

3.89
6.76

3.04
4.71

2.65
3.88

2.42
3.41

2.26
3.11

2.14
2.89

2.06
2.73

1.98
2.60

1.93
2.50

1.88
2.41

1.83
2.34

1.80
2.28

1.72
2.13

400

.05
.01

3.86
6.70

3.02
4.66

2.62
3.83

2.39
3.36

2.23
3.06

2.12
2.85

2.03
2.69

1.96
2.55

1.90
2.46

1.85
2.37

1.81
2.29

1.78
2.23

1.70
2.08

1000

.05
.01

3.85
6.66

3.00
4.63

2.61
3.80

2.38
3.34

2.22
3.04

2.11
2.82

2.02
2.66

1.95
2.53

1.89
2.43

1.84
2.34

1.80
2.26

1.76
2.20

1.68
2.06

Inf

.05
.01

3.85
6.64

2.99
4.60

2.60
3.78

2.37
3.32

2.21
3.02

2.09
2.80

2.01
2.64

1.94
2.51

1.88
2.41

1.83
2.32

1.79
2.24

1.75
2.18

1.66
2.03