The assumption of homogeneity of variance is an assumption
of the ANOVA that assumes that all groups have the same or similar
variance. The ANOVA utilizes the F statistic, which is robust to 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 is considered liberal when large
sample variances are associated with small group sizes. When this occurs, the alpha value is greater
than the level of significance. This
indicates that the null hypothesis is being falsely rejected. On the other hand, the F statistic is considered too conservative if large variances are
associated with large group sizes. This
would mean that the actual alpha value is less than the level of
significance. This does not cause the
same problems as falsely rejecting the null hypothesis, however, it can cause a
decrease in the power of the study.
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, a more
common assessment for homogeneity of variance is Levene’s test. The test statistic for Levene’s test is
calculated by diverging the data for each group from the group mean, and then comparing
the absolute values. Levene’s test is
presented with the F statistic, as an
ANOVA is conducted to compare the absolute values. 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.
