Post-Hoc Tests

Definition

Post-hoc tests, also known as a posteriori tests, are statistical procedures used in analysis of variance (ANOVA) to determine which specific groups or conditions differ from one another when the overall ANOVA result is significant. They allow for a more detailed examination of the differences between group means after an initial significant F-test.

5 Must Know Facts For Your Next Test

1. Post-hoc tests are conducted after a significant one-way ANOVA result to determine which specific group means differ from one another.
2. They help control the family-wise error rate when making multiple comparisons between groups.
3. Common post-hoc tests include Tukey's Honest Significant Difference (HSD), Bonferroni correction, and Dunnett's test.
4. Post-hoc tests vary in their sensitivity and ability to control the family-wise error rate, with more conservative tests like Bonferroni being less powerful but having stricter control.
5. The choice of post-hoc test depends on factors such as the number of groups, the research question, and the desired balance between Type I and Type II error control.

Review Questions

• Explain the purpose of conducting post-hoc tests following a significant one-way ANOVA result.
  • After a significant one-way ANOVA result indicates that at least one group mean differs from the others, post-hoc tests are used to determine which specific group means are significantly different from one another. This allows for a more detailed examination of the differences between the groups and helps control the family-wise error rate when making multiple comparisons.
• Describe how post-hoc tests differ in their sensitivity and ability to control the family-wise error rate.
  • Different post-hoc tests, such as Tukey's HSD, Bonferroni, and Dunnett's test, vary in their sensitivity and ability to control the family-wise error rate. More conservative tests like Bonferroni have stricter control over the family-wise error rate, but they are also less powerful and may be less likely to detect significant differences between groups. The choice of post-hoc test depends on the research question, the number of groups, and the desired balance between Type I and Type II error control.
• Evaluate the importance of considering the family-wise error rate when conducting post-hoc tests following a significant one-way ANOVA.
  • Controlling the family-wise error rate is crucial when conducting post-hoc tests following a significant one-way ANOVA. Making multiple comparisons between groups increases the risk of a Type I error, where a significant difference is detected when it does not actually exist. Post-hoc tests help mitigate this issue by adjusting the p-values to maintain an overall alpha level, ensuring that the probability of making one or more Type I errors across all comparisons is controlled. Failing to consider the family-wise error rate can lead to inflated Type I errors and incorrect conclusions about the differences between groups.

Related terms

One-Way ANOVA: A statistical test used to determine if there are any statistically significant differences between the means of three or more independent groups.

Multiple Comparisons:

The process of making several statistical comparisons simultaneously, which increases the risk of a Type I error (false positive).

Family-Wise Error Rate: The probability of making one or more Type I errors when performing multiple statistical tests.