What are Post-Hoc Tests for One-Way ANOVA?

📚 Quick Study Guide

• 🎯 Post-hoc tests are used after a One-Way ANOVA to determine which group means are significantly different from each other. They are only conducted if the ANOVA results are significant.
• 💡 Common post-hoc tests include: Tukey's HSD (Honestly Significant Difference), Bonferroni correction, Scheffé's method, and Dunnett's test.
• 🔢 Tukey's HSD controls the family-wise error rate, making it suitable for pairwise comparisons.
• 🧮 Bonferroni correction adjusts the significance level ($\alpha$) by dividing it by the number of comparisons.
• 🧪 Scheffé's method is the most conservative, providing strong control over the family-wise error rate.
• 📊 Dunnett's test is used when comparing multiple treatment groups to a single control group.
• 📝 The choice of post-hoc test depends on the specific research question and the characteristics of the data.

Practice Quiz

1. Which of the following is the primary purpose of conducting post-hoc tests after a One-Way ANOVA?
   1. A. To determine if the overall ANOVA is significant.
   2. B. To identify which specific group means are significantly different.
   3. C. To reduce the likelihood of Type I error.
   4. D. To increase the power of the ANOVA test.
2. Which post-hoc test is known for being conservative and providing strong control over the family-wise error rate?
   1. A. Tukey's HSD
   2. B. Bonferroni correction
   3. C. Scheffé's method
   4. D. Dunnett's test
3. When should post-hoc tests be conducted?
   1. A. Before running the ANOVA.
   2. B. Only if the ANOVA result is not significant.
   3. C. Only if the ANOVA result is significant.
   4. D. Always, regardless of the ANOVA result.
4. Which post-hoc test is particularly suitable when comparing several treatment groups to a single control group?
   1. A. Tukey's HSD
   2. B. Bonferroni correction
   3. C. Scheffé's method
   4. D. Dunnett's test
5. What is the main effect of applying Bonferroni correction?
   1. A. Increasing the significance level ($\alpha$).
   2. B. Decreasing the significance level ($\alpha$).
   3. C. Maintaining the significance level ($\alpha$).
   4. D. Ignoring the significance level ($\alpha$).
6. Which post-hoc test is generally considered a good balance between power and control of Type I error for pairwise comparisons?
   1. A. Tukey's HSD
   2. B. Bonferroni correction
   3. C. Scheffé's method
   4. D. Fisher's LSD
7. What does 'family-wise error rate' refer to in the context of post-hoc tests?
   1. A. The error rate for a single comparison.
   2. B. The probability of making at least one Type I error across multiple comparisons.
   3. C. The probability of making a Type II error.
   4. D. The error rate when comparing families.