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F Distribution Table for Statistical Analysis, Summaries of Mathematical Analysis

Hanoi University of Science & Technology (HUST)Mathematical Analysis

An f distribution table, a crucial tool in statistical analysis. It provides critical values for the f-distribution, enabling researchers to determine the significance of differences between variances or to perform hypothesis tests involving variances. The table is organized by degrees of freedom in the numerator and denominator, with different alpha levels (significance levels) for various statistical applications.

Typology: Summaries

2022/2023

Uploaded on 11/27/2024

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F Distribution Table
1
d.f.N. = degrees of freedom in numerator
d.f.D. = degrees of freedom in denominator
α = 0.005
d.f.N.
d.f.D.
1
2
3
4
5
6
7
8
9
10
12
15
20
24
30
40
60
120
∞
1
16211
20000
21615
22500
23056
23437
23715
23925
24091
24224
24426
24630
24836
24940
25044
25148
25253
25359
25465
2
198.5
199.0
199.2
199.2
199.3
199.3
199.4
199.4
199.4
199.4
199.4
199.4
199.4
199.5
199.5
199.5
199.5
199.5
199.5
3
55.55
49.80
47.47
46.19
45.39
44.84
44.43
44.13
43.88
43.69
43.39
43.08
42.78
42.62
42.47
42.31
42.15
41.99
41.83
4
31.33
26.28
24.26
23.15
22.46
21.97
21.62
21.35
21.14
20.97
20.70
20.44
20.17
20.03
19.89
19.75
19.61
19.47
19.32
5
22.78
18.31
16.53
15.56
14.94
14.51
14.20
13.96
13.77
13.62
13.38
13.15
12.90
12.78
12.66
12.53
12.40
12.27
12.14
6
18.63
14.54
12.92
12.03
11.46
11.07
10.79
10.57
10.39
10.25
10.03
9.81
9.59
9.47
9.36
9.24
9.12
9.00
8.88
7
16.24
12.40
10.88
10.05
9.52
9.16
8.89
8.68
8.51
8.38
8.18
7.97
7.75
7.65
7.53
7.42
7.31
7.19
7.08
8
14.69
11.04
9.60
8.81
8.30
7.95
7.69
7.50
7.34
7.21
7.01
6.81
6.61
6.50
6.40
6.29
6.18
6.06
5.95
9
13.61
10.11
8.72
7.96
7.47
7.13
6.88
6.69
6.54
6.42
6.23
6.03
5.83
5.73
5.62
5.52
5.41
5.30
5.19
10
12.83
9.43
8.08
7.34
6.87
6.54
6.30
6.12
5.97
5.85
5.66
5.47
5.27
5.17
5.07
4.97
4.86
4.75
4.64
11
12.23
8.91
7.60
6.88
6.42
6.10
5.86
5.68
5.54
5.42
5.24
5.05
4.86
4.76
4.65
4.55
4.44
4.34
4.23
12
11.75
8.51
7.23
6.52
6.07
5.76
5.52
5.35
5.20
5.09
4.91
4.72
4.53
4.43
4.33
4.23
4.12
4.01
3.90
13
11.37
8.19
6.93
6.23
5.79
5.48
5.25
5.08
4.94
4.82
4.64
4.46
4.27
4.17
4.07
3.97
3.87
3.76
3.65
14
11.06
7.92
6.68
6.00
5.56
5.26
5.03
4.86
4.72
4.60
4.43
4.25
4.06
3.96
3.86
3.76
3.66
3.55
3.44
15
10.80
7.70
6.48
5.80
5.37
5.07
4.85
4.67
4.54
4.42
4.25
4.07
3.88
3.79
3.69
3.58
3.48
3.37
3.26
16
10.58
7.51
6.30
5.64
5.21
4.91
4.69
4.52
4.38
4.27
4.10
3.92
3.73
3.64
3.54
3.44
3.33
3.22
3.11
17
10.38
7.35
6.16
5.50
5.07
4.78
4.56
4.39
4.25
4.14
3.97
3.79
3.61
3.51
3.41
3.31
3.21
3.10
2.98
18
10.22
7.21
6.03
5.37
4.96
4.66
4.44
4.28
4.14
4.03
3.86
3.68
3.50
3.40
3.30
3.20
3.10
2.99
2.87
19
10.07
7.09
5.92
5.27
4.85
4.56
4.34
4.18
4.04
3.93
3.76
3.59
3.40
3.31
3.21
3.11
3.00
2.89
2.78
20
9.94
6.99
5.82
5.17
4.76
4.47
4.26
4.09
3.96
3.85
3.68
3.50
3.32
3.22
3.12
3.02
2.92
2.81
2.69
21
9.83
6.89
5.73
5.09
4.68
4.39
4.18
4.01
3.88
3.77
3.60
3.43
3.24
3.15
3.05
2.95
2.84
2.73
2.61
22
9.73
6.81
5.65
5.02
4.61
4.32
4.11
3.94
3.81
3.70
3.54
3.36
3.18
3.08
2.98
2.88
2.77
2.66
2.55
23
9.63
6.73
5.58
4.95
4.54
4.26
4.05
3.88
3.75
3.64
3.47
3.30
3.12
3.02
2.92
2.82
2.71
2.60
2.48
24
9.55
6.66
5.52
4.89
4.49
4.20
3.99
3.83
3.69
3.59
3.42
3.25
3.06
2.97
2.87
2.77
2.66
2.55
2.43
25
9.48
6.60
5.46
4.84
4.43
4.15
3.94
3.78
3.63
3.54
3.37
3.20
3.01
2.92
2.82
2.72
2.61
2.50
2.38
26
9.41
6.54
5.41
4.79
4.38
4.10
3.89
3.73
3.60
3.49
3.33
3.15
2.97
2.87
2.77
2.67
2.56
2.45
2.33
27
9.34
6.49
5.36
4.74
4.34
4.06
3.85
3.69
3.56
3.45
3.28
3.11
2.93
2.83
2.73
2.63
2.52
2.41
2.25
28
9.28
6.44
5.32
4.70
4.30
4.02
3.81
3.65
3.52
3.41
3.25
3.07
2.89
2.79
2.69
2.59
2.48
2.37
2.29
29
9.23
6.40
5.28
4.66
4.26
3.98
3.77
3.61
3.48
3.38
3.21
3.04
2.86
2.76
2.66
2.56
2.45
2.33
2.24
30
9.18
6.35
5.24
4.62
4.23
3.95
3.74
3.58
3.45
3.34
3.18
3.01
2.82
2.73
2.63
2.52
2.42
2.30
2.18
40
8.83
6.07
4.98
4.37
3.99
3.71
3.51
3.35
3.22
3.12
2.95
2.78
2.60
2.50
2.40
2.30
2.18
2.06
1.93
60
8.49
5.79
4.73
4.14
3.76
3.49
3.29
3.13
3.01
2.90
2.74
2.57
2.39
2.29
2.19
2.08
1.96
1.83
1.69
120
8.18
5.54
4.50
3.92
3.55
3.28
3.09
2.93
2.81
2.71
2.54
2.37
2.19
2.09
1.98
1.87
1.75
1.61
1.43
∞
7.88
5.30
4.28
3.72
3.35
3.09
2.90
2.74
2.62
2.52
2.36
2.19
2.00
1.90
1.79
1.67
1.53
1.36
1.00
pf3
pf4
pf5

Partial preview of the text

Download F Distribution Table for Statistical Analysis and more Summaries Mathematical Analysis in PDF only on Docsity!

d.f.N. = degrees of freedom in numerator

d.f.N. d.f.D. 1 2 3 4 5 6 7 8 9 10 12 15 20 24 30 40 60 120 ∞

d.f.N.

d.f.N.

d.f.N.

 - α = 0. d.f.D. = degrees of freedom in denominator - 2 198.5 199.0 199.2 199.2 199.3 199.3 199.4 199.4 199.4 199.4 199.4 199.4 199.4 199.5 199.5 199.5 199.5 199.5 199. - 3 55.55 49.80 47.47 46.19 45.39 44.84 44.43 44.13 43.88 43.69 43.39 43.08 42.78 42.62 42.47 42.31 42.15 41.99 41. - 4 31.33 26.28 24.26 23.15 22.46 21.97 21.62 21.35 21.14 20.97 20.70 20.44 20.17 20.03 19.89 19.75 19.61 19.47 19. - 5 22.78 18.31 16.53 15.56 14.94 14.51 14.20 13.96 13.77 13.62 13.38 13.15 12.90 12.78 12.66 12.53 12.40 12.27 12. - 6 18.63 14.54 12.92 12.03 11.46 11.07 10.79 10.57 10.39 10.25 10.03 9.81 9.59 9.47 9.36 9.24 9.12 9.00 8. - 7 16.24 12.40 10.88 10.05 9.52 9.16 8.89 8.68 8.51 8.38 8.18 7.97 7.75 7.65 7.53 7.42 7.31 7.19 7. - 8 14.69 11.04 9.60 8.81 8.30 7.95 7.69 7.50 7.34 7.21 7.01 6.81 6 .61 6.50 6.40 6.29 6.18 6.06 5. - 9 13.61 10.11 8.72 7.96 7.47 7.13 6.88 6.69 6.54 6.42 6.23 6.03 5.83 5.73 5.62 5.52 5.41 5.30 5.
  • 10 12.83 9.43 8.08 7.34 6.87 6.54 6.30 6.12 5.97 5.85 5.66 5.47 5.27 5.17 5.07 4.97 4.86 4.75 4.
  • 11 12.23 8.91 7.60 6. 88 6.42 6.10 5.86 5.68 5.54 5.42 5.24 5.05 4.86 4.76 4.65 4.55 4.44 4.34 4.
  • 12 11.75 8.51 7.23 6.52 6.07 5.76 5.52 5.35 5.20 5.09 4.91 4.72 4.53 4.43 4.33 4.23 4.12 4.01 3.
  • 13 11.37 8.19 6.93 6.23 5.79 5.48 5.25 5.08 4.94 4.82 4.64 4.46 4.27 4.17 4.0 7 3.97 3.87 3.76 3.
  • 14 11.06 7.92 6.68 6.00 5.56 5.26 5.03 4.86 4.72 4.60 4.43 4.25 4.06 3.96 3.86 3.76 3.66 3.55 3.
  • 15 10.80 7.70 6.48 5.80 5.37 5.07 4.85 4.67 4.54 4.42 4.25 4.07 3.88 3.79 3.69 3.58 3.48 3.37 3.
  • 16 10.58 7.51 6.30 5.64 5.21 4.91 4.69 4.52 4.38 4.27 4.10 3.92 3.73 3.64 3.54 3.44 3.33 3.22 3.
  • 17 10.38 7.35 6.16 5.50 5.07 4.78 4.56 4.39 4.25 4.14 3.97 3.79 3.61 3.51 3.41 3.31 3.21 3.10 2.
  • 18 10.22 7.21 6.03 5.37 4.96 4.66 4.44 4.28 4.14 4.03 3.86 3.68 3.50 3.40 3.30 3.20 3.10 2.99 2.
  • 19 10.07 7.09 5.92 5.27 4.85 4.56 4.34 4.18 4.04 3.93 3.76 3.59 3.40 3.31 3.21 3.11 3.00 2.89 2.
  • 20 9.94 6.99 5.82 5.17 4.76 4.47 4.26 4.09 3.96 3.85 3.68 3.50 3.32 3.22 3.12 3.02 2.92 2.81 2.
  • 21 9.83 6.89 5.73 5.09 4.68 4.39 4.18 4.01 3.8 8 3.77 3.60 3.43 3.24 3.15 3.05 2.95 2.84 2.73 2.
  • 22 9.73 6.81 5.65 5.02 4.61 4.32 4.11 3.94 3.81 3.70 3.54 3.36 3.18 3.08 2.98 2.88 2.77 2.66 2.
  • 23 9.63 6.73 5.58 4.95 4.54 4.26 4.05 3.88 3.75 3.64 3.47 3.30 3.12 3.02 2.92 2.82 2.71 2.60 2.
  • 24 9. 55 6.66 5.52 4.89 4.49 4.20 3.99 3.83 3.69 3.59 3.42 3.25 3.06 2.97 2.87 2.77 2.66 2.55 2.
  • 25 9.48 6.60 5.46 4.84 4.43 4.15 3.94 3.78 3.63 3.54 3.37 3.20 3.01 2.92 2.82 2.72 2.61 2.50 2.
  • 26 9.41 6.54 5.41 4.79 4.38 4.10 3.89 3.73 3.60 3.49 3.33 3.15 2.97 2.87 2.77 2.67 2.56 2.45 2.
  • 27 9.34 6.49 5.36 4.74 4.34 4.06 3.85 3.69 3.56 3.45 3.28 3.11 2.93 2.83 2.73 2.63 2.52 2.41 2.
  • 28 9.28 6.44 5.32 4.70 4.30 4.02 3.81 3.65 3.52 3.41 3.25 3.07 2.89 2.79 2.69 2.59 2.48 2.37 2.
  • 29 9.23 6.40 5.28 4.66 4.26 3.98 3.77 3.61 3.48 3.38 3.21 3.04 2.86 2.76 2.66 2.56 2.45 2.33 2.
  • 30 9.18 6.35 5.24 4.62 4.23 3.95 3.74 3.58 3.45 3.34 3.18 3.01 2.82 2.73 2.63 2.52 2.42 2.30 2.
  • 40 8.83 6.07 4.98 4.37 3.99 3.71 3.51 3.35 3.22 3.12 2.95 2.78 2.60 2.50 2.40 2. 30 2.18 2.06 1.
  • 60 8.49 5.79 4.73 4.14 3.76 3.49 3.29 3.13 3.01 2.90 2.74 2.57 2.39 2.29 2.19 2.08 1.96 1.83 1.
  • 120 8.18 5.54 4.50 3.92 3.55 3.28 3.09 2.93 2.81 2.71 2.54 2.37 2.19 2.09 1.98 1.87 1.75 1.61 1. - α = 0. - 1 4052 4999.5 d.f.D. 1 2 3 4 5 6 7 8 9 10 12 15 20 24 30 40 60 120 ∞ - 2 98.50 99.00 99. 17 99.25 99.30 99.33 99.36 99.37 99.39 99.40 99.42 99.43 99.45 99.46 99.47 99.47 99,48 99.49 99. - 3 34.12 30.82 29.46 28.71 28.24 27.91 27.67 27.49 27.35 27.23 27.05 26.87 26.69 26.60 26.50 26.41 26.32 26.22 26. - 4 21.20 18.00 16.69 15.98 15.52 15.21 1 4.98 14.80 14.66 14.55 14.37 14.20 14.02 13.93 13.84 13.75 13.65 13.56 13. - 5 16.26 13.27 12.06 11.39 10.97 10.67 10.46 10.29 10.16 10.05 9.89 9.72 9.55 9.47 9.38 9.29 9.20 9.11 9. - 6 13.75 10.92 9.78 9.15 8.75 8.47 8.26 8.10 7.98 7.87 7.72 7.56 7.40 7 .31 7.23 7.14 7.06 6.97 6. - 7 12.25 9.55 8.45 7.85 7.46 7.19 6.99 6.84 6.72 6.62 6.47 6.31 6.16 6.07 5.99 5.91 5.82 5.74 5. - 8 11.26 8.65 7.59 7.01 6.63 6.37 6.18 6.03 5.91 5.81 5.67 5.52 5.36 5.28 5.20 5.12 5.03 4.95 4. - 9 10.56 8.02 6.99 6.42 6.06 5.80 5.61 5.47 5.35 5.26 5.11 4.96 4.81 4.73 4.65 4.57 4.48 4.40 4.
    • 10 10.04 7.56 6.55 5.99 5.64 5.39 5.20 5.06 4.94 4.85 4.71 4.56 4.41 4.33 4.25 4.17 4.08 4.00 3.
    • 11 9.65 7.21 6.22 5.67 5.32 5.07 4.89 4.74 4.63 4.54 4.40 4.25 4.10 4.02 3.94 3.86 3. 78 3.69 3.
    • 12 9.33 6.93 5.95 5.41 5.06 4.82 4.64 4.50 4.39 4.30 4.16 4.01 3.86 3.78 3.70 3.62 3.54 3.45 3.
    • 13 9.07 6.70 5.74 5.21 4.86 4.62 4.44 4.30 4.19 4.10 3.96 3.82 3.66 3.59 3.51 3.43 3.34 3.25 3.
    • 14 8.86 6.51 5.56 5.04 4.69 4.46 4.28 4.14 4 .03 3.94 3.80 3.66 3.51 3.43 3.35 3.27 3.18 3.09 3.
    • 15 8.68 6.36 5.42 4.89 4.56 4.32 4.14 4.00 3.89 3.80 3.67 3.52 3.37 3.29 3.21 3.13 3.05 2.96 2.
    • 16 8.53 6.23 5.29 4.77 4.44 4.20 4.03 3.89 3.78 3.69 3.55 3.41 3.26 3.18 3.10 3.02 2.93 2.84 2.
    • 17 8.40 6.11 5.18 4.67 4.34 4.10 3.93 3.79 3.68 3.59 3.46 3.31 3.16 3.08 3.00 2.92 2.83 2.75 2.
    • 18 8.29 6.01 5.09 4.58 4.25 4.01 3.84 3.71 3.60 3.51 3.37 3.23 3.08 3.00 2.92 2.84 2.75 2.66 2.
    • 19 8.18 5.93 5.01 4.50 4.17 3.94 3.77 3.63 3.52 3.43 3.30 3.1 5 3.00 2.92 2.84 2.76 2.67 2.58 2.
    • 20 8.10 5.85 4.94 4.43 4.10 3.87 3.70 3.56 3.46 3.37 3.23 3.09 2.94 2.86 2.78 2.69 2.61 2.52 2.
    • 21 8.02 5.78 4.87 4.37 4.04 3.81 3.64 3.51 3.40 3.31 3.17 3.03 2.88 2.80 2.72 2.64 2.55 2.46 2.
    • 22 7.95 5.72 4.82 4. 31 3.99 3.76 3.59 3.45 3.35 3.26 3.12 2.98 2.83 2.75 2.67 2.58 2.50 2.40 2.
    • 23 7.88 5.66 4.76 4.26 3.94 3.71 3.54 3.41 3.30 3.21 3.07 2.93 2.78 2.70 2.62 2.54 2.45 2.35 2.
    • 24 7.82 5.61 4.72 4.22 3.90 3.67 3.50 3.36 3.26 3.17 3.03 2.89 2.74 2.66 2.58 2.49 2.40 2.31 2.
    • 25 7.77 5.57 4.68 4.18 3.85 3.63 3.46 3.32 3.22 3.13 2.99 2.85 2.70 2.62 2.54 2.45 2.36 2.27 2.
    • 26 7.72 5.53 4.64 4.14 3.82 3.59 3.42 3.29 3.18 3.09 2.96 2.81 2.66 2.58 2.50 2.42 2.33 2.23 2.
    • 27 7.68 5.49 4.60 4.11 3.78 3.56 3.39 3.26 3.15 3.06 2.93 2.78 2.63 2.55 2.47 2.38 2.29 2.20 2.
    • 28 7.64 5.45 4.57 4.07 3.75 3.53 3.36 3.23 3.12 3.03 2.90 2.75 2.60 2.52 2.44 2.35 2.26 2.17 2.
    • 29 7.60 5.42 4.54 4.04 3.73 3.50 3.33 3.20 3.09 3.00 2.87 2.73 2.57 2.49 2.41 2.33 2.23 2.14 2.
    • 30 7.56 5.39 4.51 4.02 3.70 3.47 3.30 3.17 3.07 2.98 2.84 2.70 2.55 2.47 2.39 2.30 2.21 2.11 2.
    • 40 7.31 5.18 4.31 3.83 3.51 3.29 3.12 2.99 2.89 2.80 2.66 2.52 2.37 2.29 2.20 2.11 2.02 1.92 1.
    • 60 7.08 4.98 4.13 3.65 3.34 3.12 2.95 2.82 2.72 2.63 2 .50 2.35 2.20 2.12 2.03 1.94 1.84 1.73 1.
  • 120 6.85 4.79 3.95 3.48 3.17 2.96 2.79 2.66 2.56 2.47 2.34 2.19 2.03 1.95 1.86 1.76 1.66 1.53 1. - α = 0. - 1 647.8 799.5 864.2 899.6 921.8 937.1 948.2 956.7 963.3 968.6 976.7 984.9 993.1 997.2 d.f.D. 1 2 3 4 5 6 7 8 9 10 12 15 20 24 30 40 60 120 ∞ - 2 38.51 39.00 39.17 39.25 39.30 39.33 39.36 39.37 39.39 39.40 39.41 39.43 39.45 39.46 39.46 39.47 39.48 39.49 39. - 3 17.44 16.04 15.44 15.10 14.88 14.73 14.62 14.54 14.47 14.42 14.34 14.25 14.17 14.12 14.08 14.04 13.99 13.95 13. - 4 12.22 10.65 9.98 9.60 9.36 9.20 9.07 8.98 8.90 8.84 8.75 8.66 8.56 8.51 8.46 8.41 8.36 8.31 8. - 5 10.01 8.43 7.76 7.39 7.15 6.98 6.85 6.76 6.68 6.62 6.52 6.43 6.33 6.28 6.23 6.18 6.12 6.07 6. - 6 8.81 7.26 6.60 6.23 5.99 5.82 5.70 5.60 5.52 5.46 5.37 5.27 5.17 5.12 5.07 5.01 4.96 4.90 4. - 7 8.07 6.54 5.89 5.52 5.29 5.12 4.99 4.90 4.82 4.76 4.6 7 4.57 4.47 4.42 4.36 4.31 4.25 4.20 4. - 8 7.57 6.06 5.42 5.05 4.82 4.65 4.53 4.43 4.36 4.30 4.20 4.10 4.00 3.95 3.89 3.84 3.78 3.73 3. - 9 7.21 5.71 5.08 4.72 4.48 4.32 4.20 4.10 4.03 3.96 3.87 3.77 3.67 3.61 3.56 3.51 3.45 3.39 3.
    • 10 6.94 5.46 4.83 4.47 4.24 4.07 3.95 3.85 3.78 3.72 3.62 3.52 3.42 3.37 3.31 3.26 3.20 3.14 3.
    • 11 6.72 5.26 4.63 4.28 4.04 3.88 3.76 3.66 3.59 3.53 3.43 3.33 3.23 3.17 3.12 3.06 3.00 2.94 2.
    • 12 6.55 5.10 4.47 4.12 3.89 3.73 3.61 3.51 3.44 3.37 3.28 3.18 3.07 3.02 2. 96 2.91 2.85 2.79 2.
    • 13 6.41 4.97 4.35 4.00 3.77 3.60 3.48 3.39 3.31 3.25 3.15 3.05 2.95 2.89 2.84 2.78 2.72 2.66 2.
    • 14 6.30 4.86 4.24 3.89 3.66 3.50 3.38 3.29 3.21 3.15 3.05 2.95 2.84 2.79 2.73 2.67 2.61 2.55 2.
    • 15 6.20 4.77 4.15 3.80 3.58 3.41 3 .29 3.20 3.12 3.06 2.96 2.86 2.76 2.70 2.64 2.59 2.52 2.46 2.
    • 16 6.12 4.69 4.08 3.73 3.50 3.34 3.22 3.12 3.05 2.99 2.89 2.79 2.68 2.63 2.57 2.51 2.45 2.38 2.
    • 17 6.04 4.62 4.01 3.66 3.44 3.28 3.16 3.06 2.98 2.92 2.82 2.72 2.62 2.56 2.50 2.44 2.38 2.32 2.
    • 18 5.98 4.56 3.95 3.61 3.38 3.22 3.10 3.01 2.93 2.87 2.77 2.67 2.56 2.50 2.44 2.38 2.32 2.26 2.
    • 19 5.92 4.51 3.90 3.56 3.33 3.17 3.05 2.96 2.88 2.82 2.72 2.62 2.51 2.45 2.39 2.33 2.27 2.20 2.
    • 20 5.87 4.46 3.86 3.51 3.29 3.13 3.01 2.91 2.84 2.7 7 2.68 2.57 2.46 2.41 2.35 2.29 2.22 2.16 2.
    • 21 5.83 4.42 3.82 3.48 3.25 3.09 2.97 2.87 2.80 2.73 2.64 2.53 2.42 2.37 2.31 2.25 2.18 2.11 2.
    • 22 5.79 4.38 3.78 3.44 3.22 3.05 2.93 2.84 2.76 2.70 2.60 2.50 2.39 2.33 2.27 2.21 2.14 2.08 2.
    • 23 5.75 4. 35 3.75 3.41 3.18 3.02 2.90 2.81 2.73 2.67 2.57 2.47 2.36 2.30 2.24 2.18 2.11 2.04 1.
    • 24 5.72 4.32 3.72 3.38 3.15 2.99 2.87 2.78 2.70 2.64 2.54 2.44 2.33 2.27 2.21 2.15 2.08 2.01 1.
    • 25 5.69 4.29 3.69 3.35 3.13 2.97 2.85 2.75 2.68 2.61 2.51 2.41 2.30 2.24 2.18 2.12 2.05 1.98 1.
    • 26 5.66 4.27 3.67 3.33 3.10 2.94 2.82 2.73 2.65 2.59 2.49 2.39 2.28 2.22 2.16 2.09 2.03 1.95 1.
    • 27 5.63 4.24 3.65 3.31 3.08 2.92 2.80 2.71 2.63 2.57 2.47 2.36 2.25 2.19 2.13 2.07 2.00 1.93 1.
    • 28 5.61 4.22 3.63 3.29 3.06 2.90 2.78 2.69 2.61 2.55 2.45 2.34 2.23 2.17 2.11 2.05 1.98 1.91 1.
    • 29 5.59 4.20 3.61 3.27 3.04 2.88 2.76 2.67 2.59 2.53 2.43 2.32 2.21 2.15 2.09 2.03 1.96 1.89 1.
    • 30 5.57 4.18 3.69 3.25 3.03 2.87 2.75 2.65 2.57 2.51 2.41 2.31 2.20 2.14 2.07 2.01 1. 94 1.87 1.
    • 40 5.42 4.05 3.46 3.13 2.90 2.74 2.62 2.53 2.45 2.39 2.29 2.18 2.07 2.01 1.94 1.88 1.80 1.72 1.
    • 60 5.29 3.93 3.34 3.01 2.79 2.63 2.51 2.41 2.33 2.27 2.17 2.06 1.94 1.88 1.82 1.74 1.67 1.58 1.
  • 120 5.15 3.80 3.23 2.89 2.67 2.52 2.39 2.30 2.22 2.16 2.05 1.94 1.82 1.76 1.69 1.61 1.53 1.43 1. - α = 0. - 1 161.4 199.5 215.7 224.6 230.2 234.0 236.8 238.9 240.5 241.9 243.9 245.9 248.0 249.1 250.1 251.1 252.2 253.3 254. d.f.D. 1 2 3 4 5 6 7 8 9 10 12 15 20 24 30 40 60 120 ∞ - 2 18.51 19.00 19.16 19.25 19.30 19.33 19.35 19.37 19.38 19.40 19.41 19.43 19.45 19.45 19.46 19.47 19.48 19.49 19. - 3 10.13 9.55 9.28 9.12 9.01 8.94 8.89 8.85 8.81 8.79 8.74 8.70 8.66 8.64 8.62 8.59 8.57 8.55 8. - 4 7.71 6.94 6.59 6.39 6.26 6.16 6.09 6.04 6.00 5.96 5.91 5.86 5.80 5.77 5.75 5.72 5.69 5.66 5. - 5 6.61 5.79 5.41 5.19 5.05 4.95 4.88 4.82 4.77 4.74 4.68 4.62 4.56 4.53 4.50 4.46 4.43 4.40 4. - 6 5 .99 5.14 4.76 4.53 4.39 4.28 4.21 4.15 4.10 4.06 4.00 3.94 3.87 3.84 3.81 3.77 3.74 3.70 3. - 7 5.59 4.74 4.35 4.12 3.97 3.87 3.79 3.73 3.68 3.64 3.57 3.51 3.44 3.41 3.38 3.34 3.30 3.27 3. - 8 5.32 4.46 4.07 3.84 3.69 3.58 3.50 3.44 3.39 3.35 3.28 3.22 3 .15 3.12 3.08 3.04 3.01 2.97 2. - 9 5.12 4.26 3.86 3.63 3.48 3.37 3.29 3.23 3.18 3.14 3.07 3.01 2.94 2.90 2.86 2.83 2.79 2.75 2.
    • 10 4.96 4.10 3.71 3.48 3.33 3.22 3.14 3.07 3.02 2.98 2.91 2.85 2.77 2.74 2.70 2.66 2.62 2.58 2.
    • 11 4.84 3.98 3.59 3.36 3 .20 3.09 3.01 2.95 2.90 2.85 2.79 2.72 2.65 2.61 2.57 2.53 2.49 2.45 2.
    • 12 4.75 3.89 3.49 3.26 3.11 3.00 2.91 2.85 2.80 2.75 2.69 2.62 2.54 2.51 2.47 2.43 2.38 2.34 2.
    • 13 4.67 3.81 3.41 3.18 3.03 2.92 2.83 2.77 2.71 2.67 2.60 2.53 2.46 2.42 2.38 2.34 2.30 2.25 2.
    • 14 4.60 3.74 3.34 3.11 2.96 2.85 2.76 2.70 2.65 2.60 2.53 2.46 2.39 2.35 2.31 2.27 2.22 2.18 2.
    • 15 4.54 3.68 3.29 3.06 2.90 2.79 2.71 2.64 2.59 2.54 2.48 2.40 2.33 2.29 2.25 2.20 2.16 2.11 2.
    • 16 4.49 3.63 3.24 3.01 2.85 2.74 2.66 2.5 9 2.54 2.49 2.42 2.35 2.28 2.24 2.19 2.15 2.11 2.06 2.
    • 17 4.45 3.59 3.20 2.96 2.81 2.70 2.61 2.55 2.49 2.45 2.38 2.31 2.23 2.19 2.15 2.10 2.06 2.01 1.
    • 18 4.41 3.55 3.16 2.93 2.77 2.66 2.58 2.51 2.46 2.41 2.34 2.27 2.19 2.15 2.11 2.06 2.02 1.97 1.
    • 19 4.38 3.52 3.13 2.90 2.74 2.63 2.54 2.48 2.42 2.38 2.31 2.23 2.16 2.11 2.07 2.03 1.98 1.93 1.
    • 20 4.35 3.49 3.10 2.87 2.71 2.60 2.51 2.45 2.39 2.35 2.28 2.20 2.12 2.08 2.04 1.99 1.95 1.90 1.
    • 21 4.32 3.47 3.07 2.84 2.68 2.57 2.49 2.42 2.37 2.32 2.25 2.18 2.10 2.05 2.01 1.96 1.92 1.87 1.
    • 22 4.30 3.44 3.05 2.82 2.66 2.55 2.46 2.40 2.34 2.30 2.23 2.15 2.07 2.03 1.98 1.94 1.89 1.84 1.
    • 23 4.28 3.42 3.03 2.80 2.64 2.53 2.44 2.37 2.32 2.27 2.20 2.13 2.05 2.01 1.96 1.91 1.86 1.81 1.
    • 24 4.26 3.40 3.01 2.78 2.62 2.51 2.42 2.36 2.30 2.25 2.18 2.11 2.03 1.98 1.94 1.89 1.84 1.79 1.
    • 25 4.24 3.39 2.99 2.76 2.60 2.49 2.40 2.34 2.28 2.24 2.16 2.09 2.01 1.96 1.92 1.87 1.82 1.77 1.
    • 26 4.23 3.37 2.98 2.74 2.59 2.47 2.39 2.32 2.27 2.22 2.15 2.07 1.99 1.95 1. 90 1.85 1.80 1.75 1.
    • 27 4.21 3.35 2.96 2.73 2.57 2.46 2.37 2.31 2.25 2.20 2.13 2.06 1.97 1.93 1.88 1.84 1.79 1.73 1.
    • 28 4.20 3.34 2.95 2.71 2.56 2.45 2.36 2.29 2.24 2.19 2.12 2.04 1.96 1.91 1.87 1.82 1.77 1.71 1.
    • 29 4.18 3.33 2.93 2.70 2.55 2.43 2 .35 2.28 2.22 2.18 2.10 2.03 1.94 1.90 1.85 1.81 1.75 1.70 1.
    • 30 4.17 3.32 2.92 2.69 2.53 2.42 2.33 2.27 2.21 2.16 2.09 2.01 1.93 1.89 1.84 1.79 1.74 1.68 1.
    • 40 4.08 3.23 2.84 2.61 2.45 2.34 2.25 2.18 2.12 2.08 2.00 1.92 1.84 1.79 1.74 1.69 1.64 1.58 1.
    • 60 4.00 3.15 2.76 2.52 2.37 2.25 2.17 2.10 2.04 1.99 1.92 1.84 1.75 1.70 1.65 1.59 1.53 1.47 1.
  • 120 3.92 3.07 2.68 2.45 2.29 2.17 2.09 2.02 1.96 1.91 1.83 1.75 1.66 1.61 1.55 1.50 1.43 1.35 1. - α = 0. - 1 39.86 49.50 53.59 55.83 57.24 58.20 58.91 59.44 59.86 60.19 60.71 61.22 61.74 62.00 62.26 62.53 62.79 63.06 63. d.f.D. 1 2 3 4 5 6 7 8 9 10 12 15 20 24 30 40 60 120 ∞ - 2 8.53 9. 00 9.16 9.24 9.29 9.33 9.35 9.37 9.38 9.39 9.41 9.42 9.44 9.45 9.46 9.47 9.47 9.48 9. - 3 5.54 5.46 5.39 5.34 5.31 5.28 5.27 5.25 5.24 5.23 5.22 5.20 5.18 5.18 5.17 5.16 5.15 5.14 5. - 4 4.54 4.32 4.19 4.11 4.05 4.01 3.98 3.95 3.94 3.92 3.90 3.87 3.84 3. 83 3.82 3.80 3.79 3.78 3. - 5 4.06 3.78 3.62 3.52 3.45 3.40 3.37 3.34 3.32 3.30 3.27 3.24 3.21 3.19 3.17 3.16 3.14 3.12 3. - 6 3.78 3.46 3.29 3.18 3.11 3.05 3.01 2.98 2.96 2.94 2.90 2.87 2.84 2.82 2.80 2.78 2.76 2.74 2. - 7 3.59 3.26 3.07 2.96 2.88 2.83 2.78 2.75 2.72 2.70 2.67 2.63 2.59 2.58 2.56 2.54 2.51 2.49 2. - 8 3.46 3.11 2.92 2.81 2.73 2.67 2.62 2.59 2.56 2.54 2.50 2.46 2.42 2.40 2.38 2.36 2.34 2.32 2. - 9 3.36 3.01 2.81 2.69 2.61 2.55 2.51 2.47 2.44 2.42 2.38 2.34 2.30 2.28 2.25 2.23 2.21 2.18 2.
    • 10 3.29 2.92 2.73 2.61 2.52 2.46 2.41 2.38 2.35 2.32 2.28 2.24 2.20 2.18 2.16 2.13 2.11 2.08 2.
    • 11 3.23 2.86 2.66 2.54 2.45 2.39 2.34 2.30 2.27 2.25 2.21 2.17 2.12 2.10 2.08 2.05 2.03 2.00 1.
    • 12 3.18 2.81 2.61 2.48 2.39 2.33 2.28 2.24 2.21 2.1 9 2.15 2.10 2.06 2.04 2.01 1.99 1.96 1.93 1.
    • 13 3.14 2.76 2.56 2.43 2.35 2.28 2.23 2.20 2.16 2.14 2.10 2.05 2.01 1.98 1.96 1.93 1.90 1.88 1.
    • 14 3.10 2.73 2.52 2.39 2.31 2.24 2.19 2.15 2.12 2.10 2.05 2.01 1.96 1.94 1.91 1.89 1.86 1.83 1.
    • 15 3.07 2. 70 2.49 2.36 2.27 2.21 2.16 2.12 2.09 2.06 2.02 1.97 1.92 1.90 1.87 1.85 1.82 1.79 1.
    • 16 3.05 2.67 2.46 2.33 2.24 2.18 2.13 2.09 2.06 2.03 1.99 1.94 1.89 1.87 1.84 1.81 1.78 1.75 1.
    • 17 3.03 2.64 2.44 2.31 2.22 2.15 2.10 2.06 2.03 2.00 1.96 1.91 1.86 1.84 1.81 1.78 1.75 1.72 1.
    • 18 3.01 2.62 2.42 2.29 2.20 2.13 2.08 2.04 2.00 1.98 1.93 1.89 1.84 1.81 1.78 1.75 1.72 1.69 1.
    • 19 2.99 2.61 2.40 2.27 2.18 2.11 2.06 2.02 1.98 1.96 1.91 1.86 1.81 1.79 1.76 1.73 1.70 1.67 1.
    • 20 2.97 2.59 2.38 2.25 2.16 2.09 2.04 2.00 1.96 1.94 1.89 1.84 1.79 1.77 1.74 1.71 1.68 1.64 1.
    • 21 2.96 2.57 2.36 2.23 2.14 2.08 2.02 1.98 1.95 1.92 1.87 1.83 1.78 1.75 1.72 1.69 1.66 1.62 1.
    • 22 2.95 2.56 2.35 2.22 2.13 2.06 2.01 1.97 1.93 1.90 1.86 1.81 1.76 1.73 1.70 1.67 1. 64 1.60 1.
    • 23 2.94 2.55 2.34 2.21 2.11 2.05 1.99 1.95 1.92 1.89 1.84 1.80 1.74 1.72 1.69 1.66 1.62 1.59 1.
    • 24 2.93 2.54 2.33 2.19 2.10 2.04 1.98 1.94 1.91 1.88 1.83 1.78 1.73 1.70 1.67 1.64 1.61 1.57 1.
    • 25 2.92 2.53 2.32 2.18 2.09 2.02 1.97 1.93 1 .89 1.87 1.82 1.77 1.72 1.69 1.66 1.63 1.59 1.56 1.
    • 26 2.91 2.52 2.31 2.17 2.08 2.01 1.96 1.92 1.88 1.86 1.81 1.76 1.71 1.68 1.65 1.61 1.58 1.54 1.
    • 27 2.90 2.51 2.30 2.17 2.07 2.00 1.95 1.91 1.87 1.85 1.80 1.75 1.70 1.67 1.64 1.60 1.57 1.53 1.
    • 28 2.89 2.50 2.29 2.16 2.06 2.00 1.94 1.90 1.87 1.84 1.79 1.74 1.69 1.66 1.63 1.59 1.56 1.52 1.
    • 29 2.89 2.50 2.28 2.15 2.06 1.99 1.93 1.89 1.86 1.83 1.78 1.73 1.68 1.65 1.62 1.58 1.55 1.51 1.
    • 30 2.88 2.49 2.28 2.14 2.05 1.98 1.93 1.88 1.85 1.82 1.77 1.7 2 1.67 1.64 1.61 1.57 1.54 1.50 1.
    • 40 2.84 2.44 2.23 2.09 2.00 1.93 1.87 1.83 1.79 1.76 1.71 1.66 1.61 1.57 1.54 1.51 1.47 1.42 1.
    • 60 2.79 2.39 2.18 2.04 1.95 1.87 1.82 1.77 1.74 1.71 1.66 1.60 1.54 1.51 1.48 1.44 1.40 1.35 1.
  • 120 2.75 2.35 2.13 1 .99 1.90 1.82 1.77 1.72 1.68 1.65 1.60 1.55 1.48 1.45 1.41 1.37 1.32 1.26 1.
    • ∞ 2.71 2.30 2.08 1.94 1.85 1.77 1.72 1.67 1.63 1.60 1.55 1.49 1.42 1.38 1.34 1.30 1.24 1.17 1.