Post hoc tests

Definition

Post hoc tests are statistical analyses conducted after an initial analysis, like ANOVA, to determine which specific groups differ from each other when the overall test shows significant differences. These tests help clarify where the differences lie between group means and control for the risk of Type I errors that can occur when making multiple comparisons. They are crucial in providing deeper insights into data following two-way ANOVA, factorial ANOVA, and other complex analyses.

5 Must Know Facts For Your Next Test

1. Post hoc tests are only performed when the overall ANOVA indicates significant differences among group means.
2. There are various types of post hoc tests available, including Tukey's HSD, Scheffé's method, and Bonferroni correction, each with its own strengths and weaknesses.
3. These tests help researchers understand specific group differences rather than just whether any differences exist at all.
4. Post hoc tests can increase the risk of Type I errors if not properly adjusted for, which is why using corrections like Bonferroni is important.
5. In factorial designs, post hoc tests can provide insights into interactions between factors, revealing more complex relationships in the data.

Review Questions

• How do post hoc tests enhance the understanding of results obtained from ANOVA analyses?
  • Post hoc tests enhance understanding by identifying which specific groups differ after an ANOVA shows significant results. While ANOVA indicates that at least one group mean is different, post hoc tests provide detailed comparisons among all group pairs. This helps clarify the nature of the differences and provides essential insights for interpreting the data.
• What is the impact of using different types of post hoc tests on the findings of an analysis involving factorial ANOVA?
  • Using different post hoc tests can lead to varying conclusions about group differences in a factorial ANOVA context. For instance, Tukey's HSD might identify different significant pairs than Scheffé's method due to their differing methodologies and assumptions. Thus, selecting an appropriate post hoc test is crucial to ensure accurate interpretation of interactions between factors and maintain control over Type I error rates.
• Evaluate how the choice of post hoc test influences the results and conclusions drawn from ANCOVA regarding covariates.
  • The choice of post hoc test in ANCOVA can significantly influence the interpretation of how covariates affect dependent variables. Different post hoc tests have unique power levels and error rates; for example, using Bonferroni may be more conservative compared to Tukey’s HSD. Consequently, depending on the selected test, one might either uncover significant differences affected by covariates or miss them entirely, leading to potentially erroneous conclusions about the relationships being studied.

Related terms

Type I Error: The incorrect rejection of a true null hypothesis, which can occur when conducting multiple comparisons without proper controls.

Tukey's HSD: A specific type of post hoc test used to compare all possible pairs of means while controlling for Type I error.

Bonferroni Correction: A method used to adjust the significance level when conducting multiple comparisons to reduce the chance of a Type I error.