Test Your Knowledge: Eta-Squared and Partial Eta-Squared Quiz

📚 Quick Study Guide

• 📐 Eta-Squared ($\eta^2$): Measures the proportion of variance in the dependent variable that is explained by the independent variable. It's calculated as $$\eta^2 = \frac{SS_{between}}{SS_{total}}$$, where $SS_{between}$ is the sum of squares between groups and $SS_{total}$ is the total sum of squares.
• 📊 Partial Eta-Squared ($\eta_p^2$): Measures the proportion of variance in the dependent variable that is explained by the independent variable, while controlling for other independent variables. It's calculated as $$\eta_p^2 = \frac{SS_{effect}}{SS_{effect} + SS_{error}}$$, where $SS_{effect}$ is the sum of squares for the effect and $SS_{error}$ is the sum of squares for error.
• 💡 Interpretation: Both eta-squared and partial eta-squared range from 0 to 1, with higher values indicating a larger proportion of variance explained.
• 🧪 Context: Eta-squared is used in simpler ANOVA designs, while partial eta-squared is typically used in more complex ANOVA designs like factorial ANOVAs or repeated measures ANOVAs.
• ✍️ Key Difference: Partial eta-squared focuses on the variance explained by an effect relative to the variance unexplained by that effect, whereas eta-squared looks at the variance explained relative to the *total* variance.

Practice Quiz

1. Which of the following formulas represents Eta-Squared?

   1. A. $$\eta^2 = \frac{SS_{effect}}{SS_{error}}$$
   2. B. $$\eta^2 = \frac{SS_{between}}{SS_{total}}$$
   3. C. $$\eta^2 = \frac{SS_{within}}{SS_{total}}$$
   4. D. $$\eta^2 = \frac{SS_{effect}}{SS_{total}}$$

2. What does Eta-Squared measure?

   1. A. The effect size while controlling for other variables.
   2. B. The proportion of variance in the independent variable explained by the dependent variable.
   3. C. The proportion of variance in the dependent variable explained by the independent variable.
   4. D. The correlation between two variables.

3. Which formula represents Partial Eta-Squared?

   1. A. $$\eta_p^2 = \frac{SS_{between}}{SS_{total}}$$
   2. B. $$\eta_p^2 = \frac{SS_{effect}}{SS_{total}}$$
   3. C. $$\eta_p^2 = \frac{SS_{effect}}{SS_{effect} + SS_{error}}$$
   4. D. $$\eta_p^2 = \frac{SS_{error}}{SS_{effect} + SS_{error}}$$

4. In what type of ANOVA is Partial Eta-Squared most commonly used?

   1. A. Simple one-way ANOVA.
   2. B. Repeated measures ANOVA.
   3. C. Simple linear regression.
   4. D. Chi-squared test.

5. What is the range of values for both Eta-Squared and Partial Eta-Squared?

   1. A. -1 to +1
   2. B. 0 to infinity
   3. C. 0 to 1
   4. D. -infinity to +infinity

6. What does a higher value of Partial Eta-Squared indicate?

   1. A. A smaller effect size.
   2. B. A larger effect size.
   3. C. No effect.
   4. D. A negative effect.

7. How does Partial Eta-Squared differ from Eta-Squared?

   1. A. Partial Eta-Squared does not measure effect size.
   2. B. Partial Eta-Squared controls for other independent variables.
   3. C. Eta-Squared controls for other independent variables.
   4. D. They are the same thing.