Fisher criterion (F-criterion, φ*-criterion, the least significant difference) is a parametric criterion and it is used to compare variances of two variational series.
Consider two populations that include respectively m and n random values X and Y, and have normal distribution. Let us test if the variances of these samples are equal. Test statistics:
where is the sample variance.
If the statistics is greater than the critical value, the variances are not equal. Otherwise sample variances are equal.
The tables of the F criterion critical values for the significance level of 0.05:
f2\f1 | 1 | 2 | 3 | 4 | 5 | 6 |
1 | 161.45 | 199.50 | 215.71 | 224.58 | 230.16 | 233.99 |
2 | 18.51 | 19.00 | 19.16 | 19.25 | 19.30 | 19.33 |
3 | 10.13 | 9.55 | 9.28 | 9.12 | 9.01 | 8.94 |
4 | 7.71 | 6.94 | 6.59 | 6.39 | 6.26 | 6.16 |
5 | 6.61 | 5.79 | 5.41 | 5.19 | 5.05 | 4.95 |
6 | 5.99 | 5.14 | 4.76 | 4.53 | 4.39 | 4.28 |
7 | 5.59 | 4.74 | 4.35 | 4.12 | 3.97 | 3.87 |
8 | 5.32 | 4.46 | 4.07 | 3.84 | 3.69 | 3.58 |
9 | 5.12 | 4.26 | 3.86 | 3.63 | 3.48 | 3.37 |
10 | 4.96 | 4.10 | 3.71 | 3.48 | 3.33 | 3.22 |
11 | 4.84 | 3.98 | 3.59 | 3.36 | 3.20 | 3.09 |
12 | 4.75 | 3.89 | 3.49 | 3.26 | 3.11 | 3.00 |
13 | 4.67 | 3.81 | 3.41 | 3.18 | 3.03 | 2.92 |
14 | 4.60 | 3.74 | 3.34 | 3.11 | 2.96 | 2.85 |
15 | 4.54 | 3.68 | 3.29 | 3.06 | 2.90 | 2.79 |
16 | 4.49 | 3.63 | 3.24 | 3.01 | 2.85 | 2.74 |
17 | 4.45 | 3.59 | 3.20 | 2.96 | 2.81 | 2.70 |
18 | 4.41 | 3.55 | 3.16 | 2.93 | 2.77 | 2.66 |
19 | 4.38 | 3.52 | 3.13 | 2.90 | 2.74 | 2.63 |
20 | 4.35 | 3.49 | 3.10 | 2.87 | 2.71 | 2.60 |
f2\f1 | 7 | 8 | 9 | 10 | 15 |
1 | 236.77 | 238.88 | 240.54 | 241.88 | 245.95 |
2 | 19.35 | 19.37 | 19.38 | 19.40 | 19.43 |
3 | 8.89 | 8.85 | 8.81 | 8.79 | 8.70 |
4 | 6.09 | 6.04 | 6.00 | 5.96 | 5.86 |
5 | 4.88 | 4.82 | 4.77 | 4.74 | 4.62 |
6 | 4.21 | 4.15 | 4.10 | 4.06 | 3.94 |
7 | 3.79 | 3.73 | 3.68 | 3.64 | 3.51 |
8 | 3.50 | 3.44 | 3.39 | 3.35 | 3.22 |
9 | 3.29 | 3.23 | 3.18 | 3.14 | 3.01 |
10 | 3.14 | 3.07 | 3.02 | 2.98 | 2.85 |
11 | 3.01 | 2.95 | 2.90 | 2.85 | 2.72 |
12 | 2.91 | 2.85 | 2.80 | 2.75 | 2.62 |
13 | 2.83 | 2.77 | 2.71 | 2.67 | 2.53 |
14 | 2.76 | 2.70 | 2.65 | 2.60 | 2.46 |
15 | 2.71 | 2.64 | 2.59 | 2.54 | 2.40 |
16 | 2.66 | 2.59 | 2.54 | 2.49 | 2.35 |
17 | 2.61 | 2.55 | 2.49 | 2.45 | 2.31 |
18 | 2.58 | 2.51 | 2.46 | 2.41 | 2.27 |
19 | 2.54 | 2.48 | 2.42 | 2.38 | 2.23 |
20 | 2.51 | 2.45 | 2.39 | 2.35 | 2.20 |
See also: