Post hoc tests

Definition

Post hoc tests are statistical procedures used after an analysis of variance (ANOVA) to determine which specific group means are significantly different from each other. These tests are essential when the overall ANOVA indicates significant differences, allowing researchers to explore these differences in a more detailed way. They help identify where the differences lie among multiple groups, which is crucial in factorial designs where interactions and main effects can complicate results.

5 Must Know Facts For Your Next Test

1. Post hoc tests are conducted only after a significant ANOVA result, as they assess specific group differences without inflating the error rate.
2. Common post hoc tests include Tukey's HSD, Bonferroni correction, and Scheffé's test, each with different strengths and assumptions regarding data distribution.
3. These tests control for Type I error rates by adjusting the significance threshold when multiple comparisons are made.
4. In factorial designs, post hoc tests can reveal important interaction effects that may not be evident in main effects alone.
5. The choice of post hoc test can depend on the number of groups being compared and the specific hypotheses being tested, making it vital to choose appropriately.

Review Questions

• What role do post hoc tests play in interpreting the results of an ANOVA, particularly in relation to factorial designs?
  • Post hoc tests are crucial for interpreting ANOVA results because they allow researchers to identify which specific group means differ from each other after finding a significant overall effect. In factorial designs, where multiple factors interact, post hoc tests help clarify how these interactions manifest between specific group combinations. This additional analysis provides deeper insights into the data that simple main effects might overlook.
• Compare and contrast different post hoc tests and their appropriateness in various scenarios within factorial designs.
  • Different post hoc tests like Tukey's HSD and Bonferroni correction cater to various research needs. Tukey's HSD is preferred when equal sample sizes exist across groups and focuses on controlling Type I errors. In contrast, Bonferroni correction is more conservative and works well with small sample sizes but can reduce power if too many comparisons are made. Understanding these nuances allows researchers to choose the most effective test based on their study's structure.
• Evaluate how the choice of post hoc test can influence the interpretation of results in factorial designs and suggest best practices for researchers.
  • Choosing the right post hoc test can significantly affect result interpretations in factorial designs by either revealing significant differences or masking them. For instance, using a more conservative test might lead to overlooking meaningful interactions due to higher thresholds for significance. Researchers should ensure that their choice aligns with their data characteristics and research questions while considering the balance between Type I error control and statistical power. Best practices include performing preliminary analyses to understand group variances and distributions before selecting the appropriate post hoc approach.

Related terms

ANOVA:

ANOVA, or Analysis of Variance, is a statistical method used to compare the means of three or more groups to determine if at least one group mean is significantly different from the others.

Factorial Design: Factorial design is an experimental setup that investigates the effects of two or more independent variables simultaneously, allowing for the examination of interactions between these variables.

Type I Error:

A Type I error occurs when a null hypothesis is incorrectly rejected, meaning a false positive result is reported, suggesting that a difference exists when there actually is none.