Post-hoc analysis

Definition

Post-hoc analysis refers to the statistical evaluation conducted after an experiment has been completed, particularly when initial findings suggest significant effects. It is often employed to explore the differences between groups when the overall test indicates that at least one group differs from the others. This type of analysis helps to identify specific relationships and can provide insights into the nature and extent of those effects, connecting closely with concepts like power analysis and effect size estimation.

5 Must Know Facts For Your Next Test

1. Post-hoc analyses are typically performed after finding a statistically significant result in an overall test like ANOVA, which indicates that not all group means are equal.
2. These analyses can include multiple comparison tests that help to pinpoint which specific groups differ from each other, thus revealing more detailed insights from the data.
3. While post-hoc tests can increase the understanding of data relationships, they also come with risks of Type I errors, so it's important to apply corrections for multiple comparisons.
4. Effect sizes calculated during post-hoc analyses provide additional context about the practical significance of differences found between groups, beyond just statistical significance.
5. The choice of post-hoc test can affect the results and interpretations; common options include Tukey's HSD, Bonferroni correction, and Scheffé's method, each with its own strengths and weaknesses.

Review Questions

• How does post-hoc analysis contribute to understanding group differences after an ANOVA test?
  • Post-hoc analysis plays a crucial role in understanding group differences by allowing researchers to identify which specific groups are different following an ANOVA test. When an ANOVA indicates significant results, it tells us that at least one group differs, but does not specify which ones. Post-hoc tests help clarify these differences by comparing each pair of groups directly, thus providing detailed insights into where significant variations exist.
• Discuss the importance of effect size in post-hoc analyses and how it influences research conclusions.
  • Effect size is essential in post-hoc analyses because it provides context about how meaningful or impactful the observed differences are between groups. While statistical significance alone may indicate that a difference exists, effect size quantifies that difference's magnitude. By incorporating effect size into post-hoc findings, researchers can make more informed conclusions about whether their results have practical significance in addition to statistical significance.
• Evaluate the potential risks associated with post-hoc analyses in research studies and propose strategies to mitigate these risks.
  • Post-hoc analyses carry potential risks such as increased Type I error rates due to multiple comparisons when testing many hypotheses simultaneously. This could lead researchers to falsely conclude that differences exist when they do not. To mitigate these risks, researchers should apply corrections for multiple comparisons, such as Bonferroni or Tukey's HSD methods, which help adjust the significance levels. Additionally, planning for post-hoc tests before data collection can enhance the robustness and reliability of conclusions drawn from the study.

Related terms

ANOVA:

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

Effect Size:

Effect size is a quantitative measure that describes the magnitude of a phenomenon or the strength of a relationship between variables, often used to understand the practical significance of study results.

Multiple Comparisons: Multiple comparisons refer to the statistical analysis of more than two groups, which increases the risk of Type I errors, prompting the need for adjustments like Tukey's HSD or Bonferroni correction.