# The Assumption of Homogeneity of Variance

Posted February 27, 2013

The assumption of homogeneity of variance is an assumption of the independent samples t-test and ANOVA stating that all comparison groups have the same variance.  The independent samples t-test and ANOVA utilize the t and F statistics respectively, which are generally robust to violations of the assumption as long as group sizes are equal.  Equal group sizes may be defined by the ratio of the largest to smallest group being less than 1.5.  If group sizes are vastly unequal and homogeneity of variance is violated, then the F statistic will be biased when large sample variances are associated with small group sizes.  When this occurs, the significance level will be underestimated, which can cause the null hypothesis to be falsely rejected.  On the other hand, the F statistic will be biased in the opposite direction if large variances are associated with large group sizes.  This would mean that the significance level will be overestimated.  This does not cause the same problems as falsely rejecting the null hypothesis, however, it can cause a decrease in the power of the test.  To test for homogeneity of variance, there are several statistical tests that can be used.  These tests include: Hartley’s Fmax, Cochran’s, Levene’s and Barlett’s test.  Several of these assessments have been found to be too sensitive to non-normality and are not frequently used.  Of these tests, the most common assessment for homogeneity of variance is Levene’s test.  The Levene’s test uses an F-test to test the null hypothesis that the variance is equal across groups.  A p value less than .05 indicates a violation of the assumption.  If a violation occurs, it is likely that conducting the non-parametric equivalent of the analysis is more appropriate.

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