F - Distribution Tables

The Fdistributions are a family of distributions with two paramenters, thedegrees of freedom of the sample variances in the numerator anddenominator of the F statistic. The numerator degrees of freedom arealways given first. The F distributions are not symmetric but areright skewed. The density curve figure illustrates the shape. Becausesample variances cannot be negative, the F statistic takes onlypositive values and the F distribution has no probability below zero.The peak of the F density curve is near one; values far from one ineither direction provide evidence against the hypothesis of equalstandard 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