Test questions on Greenhouse-Geisser and Huynh-Feldt corrections

📚 Quick Study Guide

• 📊 Sphericity Assumption: Mauchly's test checks if the variances of the differences between all possible pairs of related groups are equal. Violation requires correction.
• 🧪 Greenhouse-Geisser (G-G) Correction: More conservative. Use when sphericity is severely violated. It adjusts the degrees of freedom by multiplying them by $\hat{\epsilon}$, where $0 < \hat{\epsilon} \leq 1$.
• 📈 Huynh-Feldt (H-F) Correction: Less conservative. Use when sphericity is only mildly violated. It also adjusts the degrees of freedom by multiplying them by $\hat{\epsilon}$, but $\hat{\epsilon}$ tends to be larger than G-G's.
• 💡 Epsilon Values: If $\hat{\epsilon} > .75$, use Huynh-Feldt; otherwise, use Greenhouse-Geisser.
• 📝 Degrees of Freedom Adjustment: Both corrections adjust the $F$-statistic's degrees of freedom to avoid Type I errors when sphericity is violated. The adjusted p-value is then compared to your alpha level.
• 🧮 Formula Overview: The adjusted degrees of freedom are calculated as $df_{adjusted} = df * \hat{\epsilon}$, where $df$ are the original degrees of freedom, and $\hat{\epsilon}$ is either the Greenhouse-Geisser or Huynh-Feldt epsilon.

🧠 Practice Quiz

1. Which of the following assumptions is tested by Mauchly's test of sphericity?
   1. A. Homogeneity of variance
   2. B. Homogeneity of covariance
   3. C. Equality of variances of the differences between levels
   4. D. Independence of observations
2. If Mauchly's test is significant, what does this indicate?
   1. A. The assumption of sphericity is met.
   2. B. The assumption of sphericity is violated.
   3. C. A between-subjects ANOVA should be used.
   4. D. The sample size is too small.
3. What is the primary purpose of Greenhouse-Geisser and Huynh-Feldt corrections?
   1. A. To increase statistical power.
   2. B. To correct for violations of sphericity.
   3. C. To reduce Type II errors.
   4. D. To simplify ANOVA calculations.
4. Under what condition is the Huynh-Feldt correction generally preferred over the Greenhouse-Geisser correction?
   1. A. When sphericity is severely violated.
   2. B. When sphericity is mildly violated.
   3. C. When the sample size is small.
   4. D. When the data is non-normal.
5. What value does the Greenhouse-Geisser epsilon ($\hat{\epsilon}$) typically fall between?
   1. A. -1 and 0
   2. B. 0 and 1
   3. C. 1 and 2
   4. D. Any real number
6. If $\hat{\epsilon}$ (epsilon) is estimated to be 0.8, which correction is generally recommended?
   1. A. Greenhouse-Geisser
   2. B. Huynh-Feldt
   3. C. No correction needed
   4. D. Bonferroni correction
7. How do Greenhouse-Geisser and Huynh-Feldt corrections affect the degrees of freedom?
   1. A. They increase the degrees of freedom.
   2. B. They decrease the degrees of freedom.
   3. C. They leave the degrees of freedom unchanged.
   4. D. They only affect the F-statistic, not the degrees of freedom.