Post-Hoc Tests

Definition

Post-hoc tests are statistical procedures used in analysis of variance (ANOVA) to identify which specific groups or conditions differ from each other when the overall ANOVA test indicates a significant difference. They are performed after the initial ANOVA to determine the nature and location of those differences.

5 Must Know Facts For Your Next Test

1. Post-hoc tests are necessary because the overall ANOVA test only indicates that at least one pair of means is significantly different, but does not specify which pairs differ.
2. Post-hoc tests adjust for the increased risk of Type I errors that occurs when making multiple comparisons, controlling the familywise error rate.
3. Common post-hoc tests include Tukey's Honest Significant Difference (HSD), Bonferroni correction, and Dunnett's test.
4. The choice of post-hoc test depends on factors such as the number of groups, the need to control for the familywise error rate, and the specific research question.
5. Post-hoc tests provide important information about the nature and location of significant differences detected by the initial one-way ANOVA.

Review Questions

• Explain the purpose of conducting post-hoc tests following a significant one-way ANOVA result.
  • The purpose of post-hoc tests in the context of a one-way ANOVA is to determine which specific groups or conditions differ from each other after the initial ANOVA test has indicated that at least one pair of means is significantly different. Post-hoc tests allow researchers to identify the nature and location of these differences, which is important for understanding the underlying relationships between the groups or conditions being studied.
• Describe how post-hoc tests address the issue of multiple comparisons in one-way ANOVA.
  • When conducting multiple pairwise comparisons following a significant one-way ANOVA, the risk of making a Type I error (false positive) increases. Post-hoc tests, such as Tukey's HSD or Bonferroni correction, address this issue by adjusting the significance level to control the familywise error rate. This ensures that the overall probability of making one or more Type I errors across all the comparisons is maintained at the desired level, typically 0.05 or 5%.
• Evaluate the role of post-hoc tests in interpreting the results of a one-way ANOVA and informing future research directions.
  • Post-hoc tests play a crucial role in interpreting the results of a one-way ANOVA by providing detailed information about the specific differences between groups or conditions. This information can inform future research directions by helping researchers understand the nature of the significant effects observed, identify the most relevant comparisons to focus on, and design more targeted studies to further explore the underlying relationships. The insights gained from post-hoc tests can lead to more nuanced and meaningful interpretations of the data, ultimately advancing the understanding of the phenomenon under investigation.

Related terms

One-Way ANOVA:

A statistical test used to determine if there are any 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 making a Type I error.

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