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