What is homogeneity of variances and how is it tested?

• A. The concept refers to equality of means across groups and is tested with Levene's test.
• B. Homogeneity of variances means equal variances across groups; tested with Levene's test.
• C. It refers to equality of variances across groups and is commonly tested with Levene's test.
• D. It relates to normality of distributions and is tested with Shapiro-Wilk.

Answer: (C)

Homogeneity of variances means that the variability of scores is roughly the same across all groups you’re comparing. This assumption matters because many analyses, like ANOVA and pooled-variance t-tests, rely on similar spreads in each group to produce accurate results.

Levene's test is the standard way to check this. It looks at how spread out the scores are within each group by measuring the absolute deviations from each group’s center (mean or median) and then tests whether those deviations differ between groups. If the test is not significant, you don’t have evidence that variances differ across groups, so the assumption holds. If it is significant, the variances aren’t equal, suggesting the analysis may be biased unless you adjust (for example, use a robust method or a different model).

So, homogeneity of variances is about equal variances across groups and is commonly tested with Levene's test. Normality is a separate concern (Shapiro-Wilk tests that), not about variances themselves.