F distribution table with details PDF

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This pdf contains an F-distribution table with an amount of F statistic values...

Description

T-12

Tables •

Probability p

Table entry for p is the critical value F ∗ with probability p lying to its right.

F*

TABLE E F critical values

Degrees of freedom in the denominator

Degrees of freedom in the numerator p

1

2

1

.100 .050 .025 .010 .001

39.86 161.45 647.79 4052.2 405284

49.50 199.50 799.50 4999.5 500000

53.59 215.71 864.16 5403.4 540379

55.83 224.58 899.58 5624.6 562500

57.24 230.16 921.85 5763.6 576405

58.20 233.99 937.11 5859.0 585937

58.91 236.77 948.22 5928.4 592873

59.44 238.88 956.66 5981.1 598144

59.86 240.54 963.28 6022.5 602284

2

.100 .050 .025 .010 .001

8.53 18.51 38.51 98.50 998.50

9.00 19.00 39.00 99.00 999.00

9.16 19.16 39.17 99.17 999.17

9.24 19.25 39.25 99.25 999.25

9.29 19.30 39.30 99.30 999.30

9.33 19.33 39.33 99.33 999.33

9.35 19.35 39.36 99.36 999.36

9.37 19.37 39.37 99.37 999.37

9.38 19.38 39.39 99.39 999.39

3

.100 .050 .025 .010 .001

5.54 10.13 17.44 34.12 167.03

5.46 9.55 16.04 30.82 148.50

5.39 9.28 15.44 29.46 141.11

5.34 9.12 15.10 28.71 137.10

5.31 9.01 14.88 28.24 134.58

5.28 8.94 14.73 27.91 132.85

5.27 8.89 14.62 27.67 131.58

5.25 8.85 14.54 27.49 130.62

5.24 8.81 14.47 27.35 129.86

4

.100 .050 .025 .010 .001

4.54 7.71 12.22 21.20 74.14

4.32 6.94 10.65 18.00 61.25

4.19 6.59 9.98 16.69 56.18

4.11 6.39 9.60 15.98 53.44

4.05 6.26 9.36 15.52 51.71

4.01 6.16 9.20 15.21 50.53

3.98 6.09 9.07 14.98 49.66

3.95 6.04 8.98 14.80 49.00

3.94 6.00 8.90 14.66 48.47

5

.100 .050 .025 .010 .001

4.06 6.61 10.01 16.26 47.18

3.78 5.79 8.43 13.27 37.12

3.62 5.41 7.76 12.06 33.20

3.52 5.19 7.39 11.39 31.09

3.45 5.05 7.15 10.97 29.75

3.40 4.95 6.98 10.67 28.83

3.37 4.88 6.85 10.46 28.16

3.34 4.82 6.76 10.29 27.65

3.32 4.77 6.68 10.16 27.24

6

.100 .050 .025 .010 .001

3.78 5.99 8.81 13.75 35.51

3.46 5.14 7.26 10.92 27.00

3.29 4.76 6.60 9.78 23.70

3.18 4.53 6.23 9.15 21.92

3.11 4.39 5.99 8.75 20.80

3.05 4.28 5.82 8.47 20.03

3.01 4.21 5.70 8.26 19.46

2.98 4.15 5.60 8.10 19.03

2.96 4.10 5.52 7.98 18.69

7

.100 .050 .025 .010 .001

3.59 5.59 8.07 12.25 29.25

3.26 4.74 6.54 9.55 21.69

3.07 4.35 5.89 8.45 18.77

2.96 4.12 5.52 7.85 17.20

2.88 3.97 5.29 7.46 16.21

2.83 3.87 5.12 7.19 15.52

2.78 3.79 4.99 6.99 15.02

2.75 3.73 4.90 6.84 14.63

2.72 3.68 4.82 6.72 14.33

3

4

5

6

7

8

9

Tables

T-13 •

Probability p

Table entry for p is the critical value F ∗ with probability p lying to its right.

F*

TABLE E F critical values (continued) Degrees of freedom in the numerator 10

12

15

20

25

30

40

50

60

120

1000

60.19 241.88 968.63 6055.8 605621

60.71 243.91 976.71 6106.3 610668

61.22 245.95 984.87 6157.3 615764

61.74 248.01 993.10 6208.7 620908

62.05 249.26 998.08 6239.8 624017

62.26 250.10 1001.4 6260.6 626099

62.53 251.14 1005.6 6286.8 628712

62.69 251.77 1008.1 6302.5 630285

62.79 252.20 1009.8 6313.0 631337

63.06 253.25 1014.0 6339.4 633972

63.30 254.19 1017.7 6362.7 636301

9.39 19.40 39.40 99.40 999.40

9.41 19.41 39.41 99.42 999.42

9.42 19.43 39.43 99.43 999.43

9.44 19.45 39.45 99.45 999.45

9.45 19.46 39.46 99.46 999.46

9.46 19.46 39.46 99.47 999.47

9.47 19.47 39.47 99.47 999.47

9.47 19.48 39.48 99.48 999.48

9.47 19.48 39.48 99.48 999.48

9.48 19.49 39.49 99.49 999.49

9.49 19.49 39.50 99.50 999.50

5.23 8.79 14.42 27.23 129.25

5.22 8.74 14.34 27.05 128.32

5.20 8.70 14.25 26.87 127.37

5.18 8.66 14.17 26.69 126.42

5.17 8.63 14.12 26.58 125.84

5.17 8.62 14.08 26.50 125.45

5.16 8.59 14.04 26.41 124.96

5.15 8.58 14.01 26.35 124.66

5.15 8.57 13.99 26.32 124.47

5.14 8.55 13.95 26.22 123.97

5.13 8.53 13.91 26.14 123.53

3.92 5.96 8.84 14.55 48.05

3.90 5.91 8.75 14.37 47.41

3.87 5.86 8.66 14.20 46.76

3.84 5.80 8.56 14.02 46.10

3.83 5.77 8.50 13.91 45.70

3.82 5.75 8.46 13.84 45.43

3.80 5.72 8.41 13.75 45.09

3.80 5.70 8.38 13.69 44.88

3.79 5.69 8.36 13.65 44.75

3.78 5.66 8.31 13.56 44.40

3.76 5.63 8.26 13.47 44.09

3.30 4.74 6.62 10.05 26.92

3.27 4.68 6.52 9.89 26.42

3.24 4.62 6.43 9.72 25.91

3.21 4.56 6.33 9.55 25.39

3.19 4.52 6.27 9.45 25.08

3.17 4.50 6.23 9.38 24.87

3.16 4.46 6.18 9.29 24.60

3.15 4.44 6.14 9.24 24.44

3.14 4.43 6.12 9.20 24.33

3.12 4.40 6.07 9.11 24.06

3.11 4.37 6.02 9.03 23.82

2.94 4.06 5.46 7.87 18.41

2.90 4.00 5.37 7.72 17.99

2.87 3.94 5.27 7.56 17.56

2.84 3.87 5.17 7.40 17.12

2.81 3.83 5.11 7.30 16.85

2.80 3.81 5.07 7.23 16.67

2.78 3.77 5.01 7.14 16.44

2.77 3.75 4.98 7.09 16.31

2.76 3.74 4.96 7.06 16.21

2.74 3.70 4.90 6.97 15.98

2.72 3.67 4.86 6.89 15.77

2.70 3.64 4.76 6.62 14.08

2.67 3.57 4.67 6.47 13.71

2.63 3.51 4.57 6.31 13.32

2.59 3.44 4.47 6.16 12.93

2.57 3.40 4.40 6.06 12.69

2.56 3.38 4.36 5.99 12.53

2.54 3.34 4.31 5.91 12.33

2.52 3.32 4.28 5.86 12.20

2.51 3.30 4.25 5.82 12.12

2.49 3.27 4.20 5.74 11.91

2.47 3.23 4.15 5.66 11.72

(Continued)

T-14

Tables •

TABLE E F critical values (continued)

Degrees of freedom in the denominator

Degrees of freedom in the numerator p

1

2

3

8

.100 .050 .025 .010 .001

3.46 5.32 7.57 11.26 25.41

3.11 4.46 6.06 8.65 18.49

2.92 4.07 5.42 7.59 15.83

2.81 3.84 5.05 7.01 14.39

2.73 3.69 4.82 6.63 13.48

2.67 3.58 4.65 6.37 12.86

2.62 3.50 4.53 6.18 12.40

2.59 3.44 4.43 6.03 12.05

2.56 3.39 4.36 5.91 11.77

9

.100 .050 .025 .010 .001

3.36 5.12 7.21 10.56 22.86

3.01 4.26 5.71 8.02 16.39

2.81 3.86 5.08 6.99 13.90

2.69 3.63 4.72 6.42 12.56

2.61 3.48 4.48 6.06 11.71

2.55 3.37 4.32 5.80 11.13

2.51 3.29 4.20 5.61 10.70

2.47 3.23 4.10 5.47 10.37

2.44 3.18 4.03 5.35 10.11

10

.100 .050 .025 .010 .001

3.29 4.96 6.94 10.04 21.04

2.92 4.10 5.46 7.56 14.91

2.73 3.71 4.83 6.55 12.55

2.61 3.48 4.47 5.99 11.28

2.52 3.33 4.24 5.64 10.48

2.46 3.22 4.07 5.39 9.93

2.41 3.14 3.95 5.20 9.52

2.38 3.07 3.85 5.06 9.20

2.35 3.02 3.78 4.94 8.96

11

.100 .050 .025 .010 .001

3.23 4.84 6.72 9.65 19.69

2.86 3.98 5.26 7.21 13.81

2.66 3.59 4.63 6.22 11.56

2.54 3.36 4.28 5.67 10.35

2.45 3.20 4.04 5.32 9.58

2.39 3.09 3.88 5.07 9.05

2.34 3.01 3.76 4.89 8.66

2.30 2.95 3.66 4.74 8.35

2.27 2.90 3.59 4.63 8.12

12

.100 .050 .025 .010 .001

3.18 4.75 6.55 9.33 18.64

2.81 3.89 5.10 6.93 12.97

2.61 3.49 4.47 5.95 10.80

2.48 3.26 4.12 5.41 9.63

2.39 3.11 3.89 5.06 8.89

2.33 3.00 3.73 4.82 8.38

2.28 2.91 3.61 4.64 8.00

2.24 2.85 3.51 4.50 7.71

2.21 2.80 3.44 4.39 7.48

13

.100 .050 .025 .010 .001

3.14 4.67 6.41 9.07 17.82

2.76 3.81 4.97 6.70 12.31

2.56 3.41 4.35 5.74 10.21

2.43 3.18 4.00 5.21 9.07

2.35 3.03 3.77 4.86 8.35

2.28 2.92 3.60 4.62 7.86

2.23 2.83 3.48 4.44 7.49

2.20 2.77 3.39 4.30 7.21

2.16 2.71 3.31 4.19 6.98

14

.100 .050 .025 .010 .001

3.10 4.60 6.30 8.86 17.14

2.73 3.74 4.86 6.51 11.78

2.52 3.34 4.24 5.56 9.73

2.39 3.11 3.89 5.04 8.62

2.31 2.96 3.66 4.69 7.92

2.24 2.85 3.50 4.46 7.44

2.19 2.76 3.38 4.28 7.08

2.15 2.70 3.29 4.14 6.80

2.12 2.65 3.21 4.03 6.58

15

.100 .050 .025 .010 .001

3.07 4.54 6.20 8.68 16.59

2.70 3.68 4.77 6.36 11.34

2.49 3.29 4.15 5.42 9.34

2.36 3.06 3.80 4.89 8.25

2.27 2.90 3.58 4.56 7.57

2.21 2.79 3.41 4.32 7.09

2.16 2.71 3.29 4.14 6.74

2.12 2.64 3.20 4.00 6.47

2.09 2.59 3.12 3.89 6.26

16

.100 .050 .025 .010 .001

3.05 4.49 6.12 8.53 16.12

2.67 3.63 4.69 6.23 10.97

2.46 3.24 4.08 5.29 9.01

2.33 3.01 3.73 4.77 7.94

2.24 2.85 3.50 4.44 7.27

2.18 2.74 3.34 4.20 6.80

2.13 2.66 3.22 4.03 6.46

2.09 2.59 3.12 3.89 6.19

2.06 2.54 3.05 3.78 5.98

17

.100 .050 .025 .010 .001

3.03 4.45 6.04 8.40 15.72

2.64 3.59 4.62 6.11 10.66

2.44 3.20 4.01 5.19 8.73

2.31 2.96 3.66 4.67 7.68

2.22 2.81 3.44 4.34 7.02

2.15 2.70 3.28 4.10 6.56

2.10 2.61 3.16 3.93 6.22

2.06 2.55 3.06 3.79 5.96

2.03 2.49 2.98 3.68 5.75

4

5

6

7

8

9

Tables

T-15 •

TABLE E F critical values (continued) Degrees of freedom in the numerator 10

12

15

20

25

2.54 3.35 4.30 5.81 11.54

2.50 3.28 4.20 5.67 11.19

2.46 3.22 4.10 5.52 10.84

2.42 3.15 4.00 5.36 10.48

2.40 3.11 3.94 5.26 10.26

2.42 3.14 3.96 5.26 9.89

2.38 3.07 3.87 5.11 9.57

2.34 3.01 3.77 4.96 9.24

2.30 2.94 3.67 4.81 8.90

2.32 2.98 3.72 4.85 8.75

2.28 2.91 3.62 4.71 8.45

2.24 2.85 3.52 4.56 8.13

2.25 2.85 3.53 4.54 7.92

2.21 2.79 3.43 4.40 7.63

2.19 2.75 3.37 4.30 7.29

30

40

50

60

120

1000

2.38 3.08 3.89 5.20 10.11

2.36 3.04 3.84 5.12 9.92

2.35 3.02 3.81 5.07 9.80

2.34 3.01 3.78 5.03 9.73

2.32 2.97 3.73 4.95 9.53

2.30 2.93 3.68 4.87 9.36

2.27 2.89 3.60 4.71 8.69

2.25 2.86 3.56 4.65 8.55

2.23 2.83 3.51 4.57 8.37

2.22 2.80 3.47 4.52 8.26

2.21 2.79 3.45 4.48 8.19

2.18 2.75 3.39 4.40 8.00

2.16 2.71 3.34 4.32 7.84

2.20 2.77 3.42 4.41 7.80

2.17 2.73 3.35 4.31 7.60

2.16 2.70 3.31 4.25 7.47

2.13 2.66 3.26 4.17 7.30

2.12 2.64 3.22 4.12 7.19

2.11 2.62 3.20 4.08 7.12

2.08 2.58 3.14 4.00 6.94

2.06 2.54 3.09 3.92 6.78

2.17 2.72 3.33 4.25 7.32

2.12 2.65 3.23 4.10 7.01

2.10 2.60 3.16 4.01 6.81

2.08 2.57 3.12 3.94 6.68

2.05 2.53 3.06 3.86 6.52

2.04 2.51 3.03 3.81 6.42

2.03 2.49 3.00 3.78 6.35

2.00 2.45 2.94 3.69 6.18

1.98 2.41 2.89 3.61 6.02

2.15 2.69 3.28 4.16 7.00

2.10 2.62 3.18 4.01 6.71

2.06 2.54 3.07 3.86 6.40

2.03 2.50 3.01 3.76 6.22

2.01 2.47 2.96 3.70 6.09

1.99 2.43 2.91 3.62 5.93

1.97 2.40 2.87 3.57 5.83

1.96 2.38 2.85 3.54 5.76

1.93 2.34 2.79 3.45 5.59

1.91 2.30 2.73 3.37 5.44

2.14 2.67 3.25 4.10 6.80

2.10 2.60 3.15 3.96 6.52

2.05 2.53 3.05 3.82 6.23

2.01 2.46 2.95 3.66 5.93

1.98 2.41 2.88 3.57 5.75

1.96 2.38 2.84 3.51 5.63

1.93 2.34 2.78 3.43 5.47

1.92 2.31 2.74 3.38 5.37

1.90 2.30 2.72 3.34 5.30

1.88 2.25 2.66 3.25 5.14

1.85 2.21 2.60 3.18 4.99

2.10 2.60 3.15 3.94 6.40

2.05 2.53 3.05 3.80 6.13

2.01 2.46 2.95 3.66 5.85

1.96 2.39 2.84 3.51 5.56

1.93 2.34 2.78 3.41 5.38

1.91 2.31 2.73 3.35 5.25

1.89 2.27 2.67 3.27 5.10

1.87 2.24 2.64 3.22 5.00

1.86 2.22 2.61 3.18 4.94

1.83 2.18 2.55 3.09 4.77

1.80 2.14 2.50 3.02 4.62

2.06 2.54 3.06 3.80 6.08

2.02 2.48 2.96 3.67 5.81

1.97 2.40 2.86 3.52 5.54

1.92 2.33 2.76 3.37 5.25

1.89 2.28 2.69 3.28 5.07

1.87 2.25 2.64 3.21 4.95

1.85 2.20 2.59 3.13 4.80

1.83 2.18 2.55 3.08 4.70

1.82 2.16 2.52 3.05 4.64

1.79 2.11 2.46 2.96 4.47

1.76 2.07 2.40 2.88 4.33

2.03 2.49 2.99 3.69 5.81

1.99 2.42 2.89 3.55 5.55

1.94 2.35 2.79 3.41 5.27

1.89 2.28 2.68 3.26 4.99

1.86 2.23 2.61 3.16 4.82

1.84 2.19 2.57 3.10 4.70

1.81 2.15 2.51 3.02 4.54

1.79 2.12 2.47 2.97 4.45

1.78 2.11 2.45 2.93 4.39

1.75 2.06 2.38 2.84 4.23

1.72 2.02 2.32 2.76 4.08

2.00 2.45 2.92 3.59 5.58

1.96 2.38 2.82 3.46 5.32

1.91 2.31 2.72 3.31 5.05

1.86 2.23 2.62 3.16 4.78

1.83 2.18 2.55 3.07 4.60

1.81 2.15 2.50 3.00 4.48

1.78 2.10 2.44 2.92 4.33

1.76 2.08 2.41 2.87 4.24

1.75 2.06 2.38 2.83 4.18

1.72 2.01 2.32 2.75 4.02

1.69 1.97 2.26 2.66 3.87

(Continued)

T-16

Tables •

TABLE E F critical values (continued)

Degrees of freedom in the denominator

Degrees of freedom in the numerator p

1

2

3

4

5

18

.100 .050 .025 .010 .001

3.01 4.41 5.98 8.29 15.38

2.62 3.55 4.56 6.01 10.39

2.42 3.16 3.95 5.09 8.49

2.29 2.93 3.61 4.58 7.46

2.20 2.77 3.38 4.25 6.81

2.13 2.66 3.22 4.01 6.35

2.08 2.58 3.10 3.84 6.02

2.04 2.51 3.01 3.71 5.76

2.00 2.46 2.93 3.60 5.56

19

.100 .050 .025 .010 .001

2.99 4.38 5.92 8.18 15.08

2.61 3.52 4.51 5.93 10.16

2.40 3.13 3.90 5.01 8.28

2.27 2.90 3.56 4.50 7.27

2.18 2.74 3.33 4.17 6.62

2.11 2.63 3.17 3.94 6.18

2.06 2.54 3.05 3.77 5.85

2.02 2.48 2.96 3.63 5.59

1.98 2.42 2.88 3.52 5.39

20

.100 .050 .025 .010 .001

2.97 4.35 5.87 8.10 14.82

2.59 3.49 4.46 5.85 9.95

2.38 3.10 3.86 4.94 8.10

2.25 2.87 3.51 4.43 7.10

2.16 2.71 3.29 4.10 6.46

2.09 2.60 3.13 3.87 6.02

2.04 2.51 3.01 3.70 5.69

2.00 2.45 2.91 3.56 5.44

1.96 2.39 2.84 3.46 5.24

21

.100 .050 .025 .010 .001

2.96 4.32 5.83 8.02 14.59

2.57 3.47 4.42 5.78 9.77

2.36 3.07 3.82 4.87 7.94

2.23 2.84 3.48 4.37 6.95

2.14 2.68 3.25 4.04 6.32

2.08 2.57 3.09 3.81 5.88

2.02 2.49 2.97 3.64 5.56

1.98 2.42 2.87 3.51 5.31

1.95 2.37 2.80 3.40 5.11

22

.100 .050 .025 .010 .001

2.95 4.30 5.79 7.95 14.38

2.56 3.44 4.38 5.72 9.61

2.35 3.05 3.78 4.82 7.80

2.22 2.82 3.44 4.31 6.81

2.13 2.66 3.22 3.99 6.19

2.06 2.55 3.05 3.76 5.76

2.01 2.46 2.93 3.59 5.44

1.97 2.40 2.84 3.45 5.19

1.93 2.34 2.76 3.35 4.99

23

.100 .050 .025 .010 .001

2.94 4.28 5.75 7.88 14.20

2.55 3.42 4.35 5.66 9.47

2.34 3.03 3.75 4.76 7.67

2.21 2.80 3.41 4.26 6.70

2.11 2.64 3.18 3.94 6.08

2.05 2.53 3.02 3.71 5.65

1.99 2.44 2.90 3.54 5.33

1.95 2.37 2.81 3.41 5.09

1.92 2.32 2.73 3.30 4.89

24

.100 .050 .025 .010 .001

2.93 4.26 5.72 7.82 14.03

2.54 3.40 4.32 5.61 9.34

2.33 3.01 3.72 4.72 7.55

2.19 2.78 3.38 4.22 6.59

2.10 2.62 3.15 3.90 5.98

2.04 2.51 2.99 3.67 5.55

1.98 2.42 2.87 3.50 5.23

1.94 2.36 2.78 3.36 4.99

1.91 2.30 2.70 3.26 4.80

25

.100 .050 .025 .010 .001

2.92 4.24 5.69 7.77 13.88

2.53 3.39 4.29 5.57 9.22

2.32 2.99 3.69 4.68 7.45

2.18 2.76 3.35 4.18 6.49

2.09 2.60 3.13 3.85 5.89

2.02 2.49 2.97 3.63 5.46

1.97 2.40 2.85 3.46 5.15

1.93 2.34 2.75 3.32 4.91

1.89 2.28 2.68 3.22 4.71

26

.100 .050 .025 .010 .001

2.91 4.23 5.66 7.72 13.74

2.52 3.37 4.27 5.53 9.12

2.31 2.98 3.67 4.64 7.36

2.17 2.74 3.33 4.14 6.41

2.08 2.59 3.10 3.82 5.80

2.01 2.47 2.94 3.59 5.38

1.96 2.39 2.82 3.42 5.07

1.92 2.32 2.73 3.29 4.83

1.88 2.27 2.65 3.18 4.64

27

.100 .050 .025 .010 .001

2.90 4.21 5.63 7.68 13.61

2.51 3.35 4.24 5.49 9.02

2.30 2.96 3.65 4.60 7.27

2.17 2.73 3.31 4.11 6.33

2.07 2.57 3.08 3.78 5.73

2.00 2.46 2.92 3.56 5.31

1.95 2.37 2.80 3.39 5.00

1.91 2.31 2.71 3.26 4.76

1.87 2.25 2.63 3.15 4.57

6

7

8

9

Tables

T-17 •

TABLE E F critical values (continued) Degrees of freedom in the numerator 10

12

15

20

25

30

40

50

60

120...