Posted February 27, 2013

*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.

*F _{max}, *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