What does eta-squared represent in ANOVA?

• A. The mean square error of the residuals.
• B. The proportion of total variance in the dependent variable explained by an independent variable.
• C. The correlation between groups.
• D. The p-value of the F statistic.

Answer: (B)

Eta-squared is a measure of effect size in ANOVA that tells you how much of the total variance in the dependent variable is explained by a given independent variable. It is calculated as the sum of squares for the effect divided by the total sum of squares (SS_effect / SS_total). This makes it a straightforward way to express the practical importance of an effect: a higher eta-squared means the factor accounts for a larger portion of the variability in the outcome. For example, if the total variance is 100 and the factor explains 25 of that variance, eta-squared is 0.25, meaning 25% of the variance is due to that factor. In contrast, the mean square error of residuals is a measure of unexplained variance used in the F statistic, the correlation between groups isn’t a standard ANOVA summary of variance explained, and the p-value of the F statistic addresses statistical significance rather than how much variance is explained.