Appendix G: F Distribution Table

Appendix G: F Distribution Table How to Use the F Distribution Table The table is divided into two separate sections. The first section (Table G.1) gi...

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Appendix G: F Distribution Table



How to Use the F Distribution Table The table is divided into two separate sections. The first section (Table G.1) gives critical values of F for the .05 level of significance; the second section (Table G.2) gives critical values of F for the .01 level of significance. First, decide the appropriate level of significance for your test. That determines which of the two sections of the table you will use. The top row of each section lists various values for df1 (df1 = k – 1), where k equals the number of groups or categories of the independent variable. Find the appropriate df for your data in the top row. That determines the column of the table you will use. Next, calculate the value of df2 (df2 = n – k) for your data and locate it in the left-hand column of the table. That determines the row of the table you will use. The quantity in the cell corresponding to the intersection of the row and column you have identified is the critical value of F for your test. If the F you have calculated for your data is equal to or greater than this quantity, your results are statistically significant at the level you have chosen. Table G.1  Distribution of F (p = .05) df1

1

2

3

4

5

6

8

10

161.4

199.5

215.7

224.6

230.2

234.0

238.9

241.9

df2 1 2

18.51

19.00

19.16

19.25

19.30

19.33

19.37

19.40

3

10.13

9.55

9.28

9.12

9.01

8.94

8.85

8.79

4

7.71

6.94

6.59

6.39

6.26

6.16

6.04

5.96

5

6.61

5.79

5.41

5.19

5.05

4.95

4.82

4.74

6

5.99

5.14

4.76

4.53

4.39

4.28

4.15

4.06

7

5.59

4.74

4.35

4.12

3.97

3.87

3.73

3.64 (Continued)

28   ❖  STATISTICS FOR CRIMINAL JUSTICE AND CRIMINOLOGY

Table G.1  Distribution of F (p = .05) (Continued) 1

2

3

4

5

6

8

10

8

5.32

4.46

4.07

3.84

3.69

3.58

3.44

3.35

9

5.12

4.26

3.86

3.63

3.48

3.37

3.23

3.14

10

4.96

4.10

3.71

3.48

3.33

3.22

3.07

2.98

11

4.84

3.98

3.59

3.36

3.20

3.09

2.95

2.85

12

4.75

3.89

3.49

3.26

3.11

3.00

2.85

2.75

13

4.67

3.81

3.41

3.18

3.03

2.92

2.77

2.67

14

4.60

3.74

3.34

3.11

2.96

2.85

2.70

2.60

15

4.54

3.68

3.29

3.06

2.90

2.79

2.64

2.54

16

4.49

3.63

3.24

3.01

2.85

2.74

2.59

2.49

17

4.45

3.59

3.20

2.96

2.81

2.70

2.55

2.45

18

4.41

3.55

3.16

2.93

2.77

2.66

2.51

2.41

19

4.38

3.52

3.13

2.90

2.74

2.63

2.48

2.38

20

4.35

3.49

3.10

2.87

2.71

2.60

2.45

2.35

21

4.32

3.47

3.07

2.84

2.68

2.57

2.42

2.32

22

4.30

3.44

3.05

2.82

2.66

2.55

2.40

2.30

23

4.28

3.42

3.03

2.80

2.64

2.53

2.37

2.27

24

4.26

3.40

3.01

2.78

2.62

2.51

2.36

2.25

25

4.24

3.39

2.99

2.76

2.60

2.49

2.34

2.24

26

4.23

3.37

2.98

2.74

2.59

2.47

2.32

2.22

27

4.21

3.35

2.96

2.73

2.57

2.46

2.31

2.20

28

4.20

3.34

2.95

2.71

2.56

2.45

2.29

2.19

29

4.18

3.33

2.93

2.70

2.55

2.43

2.28

2.18

30

4.17

3.32

2.92

2.69

2.53

2.42

2.27

2.16

40

4.08

3.23

2.84

2.61

2.45

2.34

2.18

2.08

df1 df2

(Continued)

Appendix G: F Distribution Table  ❖  29

Table G.1  Distribution of F (p = .05) (Continued) 1

2

3

4

5

6

8

10

 60

4.00

3.15

2.76

2.53

2.37

2.25

2.10

1.99

 80

3.96

3.11

2.72

2.48

2.33

2.21

2.05

1.95

120

3.92

3.07

2.68

2.45

2.29

2.17

2.02

1.91



3.84

3.00

2.60

2.37

2.21

2.10

1.94

1.83



df1 df2

Table G.1 Distribution of F (p = 0.05), Continued df1

12

15

20

30

40

60

120

243.9

245.9

248.0

250.1

251.1

252.2

253.3

df2 1

254.3

2

19.41

19.43

19.45

19.46

19.47

19.48

19.49

19.50

3

8.74

8.70

8.66

8.62

8.59

8.57

8.55

8.53

4

5.91

5.86

5.80

5.75

5.72

5.69

5.66

5.63

5

4.68

4.62

4.56

4.50

4.46

4.43

4.40

4.36

6

4.00

3.94

3.87

3.81

3.77

3.74

3.70

3.67

7

3.57

3.51

3.44

3.38

3.34

3.30

3.27

3.23

8

3.28

3.22

3.15

3.08

3.04

3.01

2.97

2.93

9

3.07

3.01

2.94

2.86

2.83

2.79

2.75

2.71

10

2.91

2.85

2.77

2.70

2.66

2.62

2.58

2.54

11

2.79

2.72

2.65

2.57

2.53

2.49

2.45

2.40

12

2.69

2.62

2.54

2.47

2.43

2.38

2.34

2.30

13

2.60

2.53

2.46

2.38

2.34

2.30

2.25

2.21

14

2.53

2.46

2.39

2.31

2.27

2.22

2.18

2.13

15

2.48

2.40

2.33

2.25

2.20

2.16

2.11

2.07

16

2.42

2.35

2.28

2.19

2.15

2.11

2.06

2.01

17

2.38

2.31

2.23

2.15

2.10

2.06

2.01

1.96

18

2.34

2.27

2.19

2.11

2.06

2.02

1.97

1.92 (Continued)

30   ❖  STATISTICS FOR CRIMINAL JUSTICE AND CRIMINOLOGY

Table G.1  Distribution of F (p = .05) (Continued) 12

15

20

30

40

60

120



19

2.31

2.23

2.16

2.07

2.03

1.98

1.93

1.88

20

2.28

2.20

2.12

2.04

1.99

1.95

1.90

1.84

21

2.25

2.18

2.10

2.01

1.96

1.92

1.87

1.81

22

2.23

2.15

2.07

1.98

1.94

1.89

1.84

1.78

23

2.20

2.13

2.05

1.96

1.91

1.86

1.81

1.76

24

2.18

2.11

2.03

1.94

1.89

1.84

1.79

1.73

25

2.16

2.09

2.01

1.92

1.87

1.82

1.77

1.71

26

2.15

2.07

1.99

1.90

1.85

1.80

1.75

1.69

27

2.13

2.06

1.97

1.88

1.84

1.79

1.73

1.67

28

2.12

2.04

1.96

1.87

1.82

1.77

1.71

1.65

29

2.10

2.03

1.94

1.85

1.81

1.75

1.70

1.64

30

2.09

2.01

1.93

1.84

1.79

1.74

1.68

1.62

40

2.00

1.92

1.84

1.74

1.69

1.64

1.58

1.51

60

1.92

1.84

1.75

1.65

1.59

1.53

1.47

1.39

80

1.88

1.80

1.70

1.60

1.54

1.49

1.41

1.32

120

1.83

1.75

1.66

1.55

1.50

1.43

1.35

1.25



1.75

1.67

1.57

1.46

1.39

1.32

1.22

1.00

df1 df2

Table G.2 Distribution of F (p = 0.01) 1

2

3

4

5

6

8

10

1

4052

4999.5

5403

5625

5764

5859

5982

6056

2

98.50

99.00

99.17

99.25

99.30

99.33

99.37

99.40

3

34.12

30.82

29.46

28.71

28.24

27.91

27.49

27.23

df1 df2

(Continued)

Appendix G: F Distribution Table  ❖  31

Table G.2  Distribution of F (p = 0.01)  (Continued) 1

2

3

4

5

6

8

10

4

21.20

18.00

16.69

15.98

15.52

15.21

14.80

14.55

5

16.26

13.27

12.06

11.39

10.97

10.67

10.29

10.05

6

13.75

10.92

9.78

9.15

8.75

8.47

8.10

7.87

7

12.25

9.55

8.45

7.85

7.46

7.19

6.84

6.62

8

11.26

8.65

7.59

7.01

6.63

6.37

6.03

5.81

9

10.56

8.02

6.99

6.42

6.06

5.80

5.47

5.26

10

10.04

7.56

6.55

5.99

5.64

5.39

5.06

4.85

11

9.65

7.21

6.22

5.67

5.32

5.07

4.74

4.54

12

9.33

6.93

5.95

5.41

5.06

4.82

4.50

4.30

13

9.07

6.70

5.74

5.21

4.86

4.62

4.30

4.10

14

8.86

6.51

5.56

5.04

4.69

4.46

4.14

3.94

15

8.68

6.36

5.42

4.89

4.56

4.32

4.00

3.80

16

8.53

6.23

5.29

4.77

4.44

4.20

3.89

3.69

17

8.40

6.11

5.18

4.67

4.34

4.10

3.79

3.59

18

8.29

6.01

5.09

4.58

4.25

4.01

3.71

3.51

19

8.18

5.93

5.01

4.50

4.17

3.94

3.63

3.43

20

8.10

5.85

4.94

4.43

4.10

3.87

3.56

3.37

21

8.02

5.78

4.87

4.37

4.04

3.81

3.51

3.31

22

7.95

5.72

4.82

4.31

3.99

3.76

3.45

3.26

23

7.88

5.66

4.76

4.26

3.94

3.71

3.41

3.21

24

7.82

5.61

4.72

4.22

3.90

3.67

3.36

3.17

25

7.77

5.57

4.68

4.18

3.85

3.63

3.32

3.13

26

7.72

5.53

4.64

4.14

3.82

3.59

3.29

3.09

27

7.68

5.49

4.60

4.11

3.78

3.56

3.26

3.06

df1 df2

(Continued)

32   ❖  STATISTICS FOR CRIMINAL JUSTICE AND CRIMINOLOGY

Table G.2  Distribution of F (p = 0.01)  (Continued) 1

2

3

4

5

6

8

10

 28

7.64

5.45

4.57

4.07

3.75

3.53

3.23

3.03

 29

7.60

5.42

4.54

4.04

3.73

3.50

3.20

3.00

 30

7.56

5.39

4.51

4.02

3.70

3.47

3.17

2.98

 40

7.31

5.18

4.31

3.83

3.51

3.29

2.99

2.80

 60

7.08

4.98

4.13

3.65

3.34

3.12

2.82

2.63

 80

6.96

4.88

4.04

3.56

3.25

3.04

2.74

2.55

120

6.85

4.79

3.95

3.48

3.17

2.96

2.66

2.47



6.63

4.61

3.78

3.32

3.02

2.80

2.51

2.32

df1 df2

Table G.2 Distribution of F (p = 0.01), Continued df1

12

15

20

30

40

60

120



6106

6157

6209

6261

6287

6313

6339

6366

df2 1 2

99.42

99.43

99.45

99.47

99.47

99.48

99.49

99.50

3

27.05

26.87

26.69

26.50

26.41

26.32

26.22

26.13

4

14.37

14.20

14.02

13.84

13.75

13.65

13.56

13.46

5

9.89

9.72

9.55

9.38

9.29

9.20

9.11

9.02

6

7.72

7.56

7.40

7.23

7.14

7.06

6.97

6.88

7

6.47

6.31

6.16

5.99

5.91

5.82

5.74

5.65

8

5.67

5.52

5.36

5.20

5.12

5.03

4.95

4.86

9

5.11

4.96

4.81

4.65

4.57

4.48

4.40

4.31

10

4.71

4.56

4.41

4.25

4.17

4.08

4.00

3.91

11

4.40

4.25

4.10

3.94

3.86

3.78

3.69

3.60

12

4.16

4.01

3.86

3.70

3.62

3.54

3.45

3.36

13

3.96

3.82

3.66

3.51

3.43

3.34

3.25

3.17

(Continued)

Appendix G: F Distribution Table  ❖  33

Table G.2  Distribution of F (p = 0.01)  (Continued) df1

12

15

20

30

40

60

120



df2 14

3.80

3.66

3.51

3.35

3.27

3.18

3.09

3.00

15

3.67

3.52

3.37

3.21

3.13

3.05

2.96

2.87

16

3.55

3.41

3.26

3.10

3.02

2.93

2.84

2.75

17

3.46

3.31

3.16

3.00

2.92

2.83

2.75

2.65

18

3.37

3.23

3.08

2.92

2.84

2.75

2.66

2.57

19

3.30

3.15

3.00

2.84

2.76

2.67

2.58

2.49

20

3.23

3.09

2.94

2.78

2.69

2.61

2.52

2.42

21

3.17

3.03

2.88

2.72

2.64

2.55

2.46

2.36

22

3.12

2.98

2.83

2.67

2.58

2.50

2.40

2.31

23

3.07

2.93

2.78

2.62

2.54

2.45

2.35

2.26

24

3.03

2.89

2.74

2.58

2.49

2.40

2.31

2.21

25

2.99

2.85

2.70

2.54

2.45

2.36

2.27

2.17

26

2.96

2.81

2.66

2.50

2.42

2.33

2.23

2.13

27

2.93

2.78

2.63

2.47

2.38

2.29

2.20

2.10

28

2.90

2.75

2.60

2.44

2.35

2.26

2.17

2.06

29

2.87

2.73

2.57

2.41

2.33

2.23

2.14

2.03

30

2.84

2.70

2.55

2.39

2.30

2.21

2.11

2.01

40

2.66

2.52

2.37

2.20

2.11

2.02

1.92

1.80

60

2.50

2.35

2.20

2.03

1.94

1.84

1.73

1.60

80

2.41

2.28

2.11

1.94

1.84

1.75

1.63

1.49

120

2.34

2.19

2.03

1.86

1.76

1.66

1.53

1.38



2.18

2.04

1.88

1.70

1.59

1.47

1.32

1.00

Source: Adapted from Table V of R. A. Fisher and F. Yates. Statistical Tables for Biological, Agricultural and Medical Research, 1948 edition. Reprinted by permission of Addison Wesley Longman Ltd.