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Variance homogeneity test
Explanations > Social Research > Analysis > Variance homogeneity test
Description | Example | Discussion | See also
Description
Homogeneity of variance occurs where variance across multiple samples, possibly in different conditions, is similar.
To test for the homogeneity of a set of variances:
- Divide the largest by the smallest to give an F-ratio.
- Select the cell in the table below to represent your experiment
- (note: degrees of freedom = number of samples - 1)
- If the F-ratio is less than the value in the selected cell, then it is safe to assume that variances are homogeneous.
| Degrees of freedom |
Number of groups / treatments |
||||||||||
| 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
| 2 | 39.0 | 87.5 | 142 | 202 | 266 | 333 | 403 | 475 | 550 | 626 | 704 |
| 3 | 15.4 | 27.8 | 39.2 | 50.7 | 62.0 | 72.9 | 83.5 | 93.9 | 104 | 114 | 124 |
| 4 | 9.6 | 15.5 | 20.6 | 25.2 | 29.5 | 33.6 | 37.5 | 41.1 | 44.6 | 48.0 | 51.4 |
| 5 | 7.2 | 10.8 | 13.7 | 16.3 | 18.7 | 20.8 | 22.9 | 24.7 | 26.5 | 28.2 | 29.9 |
| 6 | 5.82 | 8.38 | 10.4 | 12.1 | 13.7 | 15.0 | 16.3 | 17.5 | 18.6 | 19.7 | 20.7 |
| 7 | 4.99 | 6.94 | 8.44 | 9.70 | 10.8 | 11.8 | 12.7 | 13.5 | 14.3 | 15.1 | 15.8 |
| 8 | 4.43 | 6.00 | 7.18 | 8.12 | 9.03 | 9.78 | 10.5 | 11.1 | 11.7 | 12.2 | 12.7 |
| 9 | 4.03 | 5.34 | 6.31 | 7.11 | 7.80 | 8.41 | 8.95 | 9.45 | 9.91 | 10.3 | 10.7 |
| 10 | 3.72 | 4.85 | 5.67 | 6.34 | 6.92 | 7.42 | 7.87 | 8.28 | 8.66 | 9.01 | 9.34 |
| 12 | 3.28 | 4.16 | 4.75 | 5.30 | 5.72 | 6.09 | 6.42 | 6.72 | 7.00 | 7.25 | 7.43 |
| 15 | 2.86 | 3.54 | 4.01 | 4.37 | 4.68 | 4.95 | 5.19 | 5.40 | 5.59 | 5.77 | 5.95 |
| 20 | 2.46 | 2.95 | 3.29 | 3.54 | 3.76 | 3.94 | 4.10 | 4.24 | 4.37 | 4.49 | 4.59 |
| 30 | 2.07 | 2.40 | 2.61 | 2.78 | 2.91 | 3.02 | 3.12 | 3.21 | 3.29 | 3.36 | 3.39 |
| 60 | 1.67 | 1.85 | 1.96 | 2.04 | 2.11 | 2.17 | 2.22 | 2.26 | 2.30 | 2.33 | 2.36 |
| very large | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
Example
Variances from a set of three samples are 3.44, 8.82 and 5.42. 8.82 / 3.44 = 2.56. Each group receives four treatments, and 2.56 is less than the value in the cell (142), so it is easily safe to assume homogeneity of variances.
Discussion
Homogeneity of variances are a basic assumption of a number of statistical tests, including t-test and ANOVA.
Homogeneity can also be tested using Levene's test or Mauchly's test.
See also
t-test, ANOVA, Parametric vs. non-parametric tests
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