What is the effect size in ANOVA (eta-squared)?

• A. Eta-squared represents the proportion of total variance explained by an effect.
• B. It reflects the p-value of the F-test.
• C. It is the degrees of freedom for between-group variance.
• D. It is the mean squared error.

Answer: (C)

Eta-squared expresses how much of the total variability in the dependent variable is explained by the effect in an ANOVA. It’s calculated as the sum of squares for the effect divided by the total sum of squares: eta-squared = SS_effect / SS_total. The value ranges from 0 to 1, with larger values indicating that the factor accounts for a bigger share of the total variance. This is a measure of effect size, not a significance test, so it complements the F-test and its p-value by showing how substantial the effect is in practical terms. For example, if SS_effect is 20 and SS_total is 100, eta-squared would be 0.20, meaning 20% of the total variance is explained by the factor. Note that there’s also a related statistic called partial eta-squared, which uses a slightly different denominator (SS_effect + SS_error) and can produce larger values in the same data depending on the design.