Question

In the realm of quantitative measure research, there are those researchers who believe some small violations of the homogeneity of variance assumption may have little practical effect on the analysis due to the robust nature of parametric tests. However, other researchers believe any violation of the homogeneity of variance assumption can result in tarnished or unbelievable results regardless of the robust nature of parametric tests. Discuss the viability or falsity of both viewpoints and how you would approach one view point versus the other.

Answer 1

The assumption of Homogeneity of Variance is an assumption of the Independent Samples t -test and ANOVA. As per the assumption, all comparison groups have the same variance. For equal group sizes, t statistic and F statistic which are used respectively by Independent Samples t - test and ANOVA are robust to violations of this assumption. If the group sizes are unequal and the homogeneity of variances is violate, then F statistic will be biased when large sample variances are associated with small group sizes.. In that case,the significance level is underestimated. This will cause the null hypothesis to be rejected falsely. F test will be biased in the opposite direction if large variances are associated with large group sizes. Then the significance level is overestimated. It causes decrease in the power of the test.