Eta squared (n^2) is an effect size that expresses what?

Eta squared (n^2) is an effect size that expresses what?

• A. The proportion of variability in the dependent variable explained by the independent variable
• B. The squared correlation between variables
• C. The difference between group means
• D. The probability value associated with a test

Answer: (A)

Eta squared expresses the proportion of variability in the dependent variable that is explained by the independent variable. In ANOVA, the total variance in the outcome is split into variance due to the factor and residual variance, and eta squared is the ratio SS_factor / SS_total. This makes it an effect size that tells you how large the impact of the factor is on the overall variability. It’s not the squared correlation between two variables (that would be a different context, like r^2 in regression). It’s also not simply the difference between group means (that would relate to mean differences, often described with d). And it doesn’t reflect statistical significance (that’s what a p-value indicates). If there are multiple factors, you might see partial eta squared, which also reflects the proportion of variance explained but controls for other factors.

Eta squared expresses the proportion of variability in the dependent variable that is explained by the independent variable. In ANOVA, the total variance in the outcome is split into variance due to the factor and residual variance, and eta squared is the ratio SS_factor / SS_total. This makes it an effect size that tells you how large the impact of the factor is on the overall variability.

It’s not the squared correlation between two variables (that would be a different context, like r^2 in regression). It’s also not simply the difference between group means (that would relate to mean differences, often described with d). And it doesn’t reflect statistical significance (that’s what a p-value indicates). If there are multiple factors, you might see partial eta squared, which also reflects the proportion of variance explained but controls for other factors.