Statistical Tables

F Distribution



The F distributions are skewed to the right.

The F distributions are a family of distributions with two paramenters, 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

12345678910111215
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


Phil Ender, 26Jan98