Post-hoc test

Definition

A post-hoc test is a statistical procedure used after an analysis of variance (ANOVA) to identify which specific group means are different when the overall ANOVA indicates significant differences among groups. This type of test helps researchers to pinpoint exactly where those differences lie, making it a crucial step in interpreting ANOVA results and understanding the relationships between different groups.

5 Must Know Facts For Your Next Test

1. Post-hoc tests are only conducted after finding a significant result from an ANOVA, as they provide insights into where those differences exist.
2. Common post-hoc tests include Tukey's HSD, Bonferroni correction, and Scheffé's method, each with its own strengths and appropriate contexts for use.
3. These tests help to control for the increased risk of Type I errors that arises from making multiple comparisons between group means.
4. Post-hoc tests assume that the ANOVA has already met its assumptions, such as normality and homogeneity of variance, making them valid for use.
5. Results from post-hoc tests can aid in decision-making and further research by indicating which specific groups differ, thereby guiding subsequent analyses or interventions.

Review Questions

• How do post-hoc tests enhance the interpretation of results obtained from an ANOVA?
  • Post-hoc tests enhance interpretation by specifying which group means are significantly different after an ANOVA indicates overall differences. While ANOVA tells us there are differences among groups, it does not specify where those differences lie. Post-hoc tests provide detailed comparisons that help researchers understand the specific relationships between individual groups, leading to more meaningful conclusions.
• Compare and contrast Tukey's HSD with the Bonferroni correction as post-hoc testing methods. When might one be preferred over the other?
  • Tukey's HSD is best used when comparing all possible pairs of group means because it controls for Type I error while maintaining good power. In contrast, the Bonferroni correction is more conservative and adjusts p-values based on the number of comparisons, which can lead to a higher chance of Type II errors. Researchers might prefer Tukey's HSD when they want to maximize power and have equal sample sizes, while the Bonferroni correction could be chosen when the number of comparisons is small or when one wants to be particularly cautious about Type I errors.
• Evaluate how failing to conduct post-hoc tests after finding significant results in an ANOVA might impact research findings and conclusions.
  • Neglecting to perform post-hoc tests after finding significant results in an ANOVA could lead to incomplete or misleading conclusions. Without these tests, researchers would miss out on identifying specific group differences, which limits the understanding of how and why groups differ. This lack of detail can hinder further research directions and practical applications, as decisions based on vague overall results might not accurately reflect the nuanced dynamics present in the data.

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.

Tukey's HSD: Tukey's Honestly Significant Difference (HSD) is a specific type of post-hoc test that compares all possible pairs of means while controlling for Type I error.

Bonferroni correction: The Bonferroni correction is a statistical adjustment made to p-values when multiple comparisons are performed, helping to reduce the chances of Type I errors in post-hoc tests.