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# Variance homogeneity test

Explanations > Social ResearchAnalysis > Variance homogeneity test

## 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.

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