Post-Hoc Analysis

Definition

Post-hoc analysis refers to the statistical techniques used to explore relationships or make comparisons between groups after an initial hypothesis test has been conducted. It is often employed to gain deeper insights into the results of a study when significant findings are obtained.

5 Must Know Facts For Your Next Test

1. Post-hoc analyses are conducted after the initial hypothesis test to explore unexpected findings or to investigate specific comparisons not included in the original research questions.
2. These analyses can help identify which groups or variables are driving the significant effect found in the overall test, but they increase the risk of making a Type I error.
3. Post-hoc tests are often used in the context of the Chi-Square Test of Independence and the Chi-Square Test for Homogeneity to determine which specific cells or groups are contributing to the significant result.
4. Adjustments, such as the Bonferroni correction, are commonly applied to post-hoc tests to control the familywise error rate and maintain the desired overall significance level.
5. The choice of post-hoc test depends on the specific research question, the number of groups being compared, and the goal of the analysis (e.g., pairwise comparisons, identifying the source of significance).

Review Questions

• Explain the purpose of conducting post-hoc analyses in the context of the Chi-Square Test of Independence.
  • The Chi-Square Test of Independence is used to determine if there is a significant relationship between two categorical variables. If the overall test is significant, post-hoc analyses can be performed to identify which specific cells or groups are contributing to the significant result. This helps researchers gain a more detailed understanding of the nature of the relationship between the variables and pinpoint the sources of the significant effect.
• Describe how post-hoc analyses can be used in the Chi-Square Test for Homogeneity and discuss the importance of adjusting the significance level.
  • The Chi-Square Test for Homogeneity is used to determine if the distribution of a categorical variable is the same across multiple groups or populations. If the overall test is significant, post-hoc analyses can be conducted to identify which specific groups or categories are driving the significant difference. However, performing multiple comparisons increases the risk of making a Type I error (false positive). To control the familywise error rate, researchers often apply statistical adjustments, such as the Bonferroni correction, to the significance level used for the post-hoc tests.
• Evaluate the role of planned comparisons versus post-hoc analyses in hypothesis testing and discuss the trade-offs between the two approaches.
  • Planned comparisons, which are specified before data collection based on a priori hypotheses, are generally considered more robust and reliable than post-hoc analyses. Planned comparisons have greater statistical power and a lower risk of making Type I errors, as the researcher has already accounted for the number of comparisons being made. In contrast, post-hoc analyses are more exploratory in nature and can be useful for generating new hypotheses or uncovering unexpected findings. However, post-hoc tests increase the risk of false positives and require adjustments to the significance level to maintain the desired overall error rate. The choice between planned comparisons and post-hoc analyses depends on the research goals, the complexity of the study, and the need to balance the trade-offs between statistical power, Type I error control, and the depth of insight gained from the analysis.

Related terms

Planned Comparisons: Planned comparisons are statistical tests that are specified before the data is collected, based on a priori hypotheses about the relationships between groups or variables.

Familywise Error Rate: The familywise error rate is the probability of making one or more false discoveries when performing multiple statistical tests simultaneously.

Bonferroni Correction:

A method used to control the familywise error rate by adjusting the significance level for each individual test to maintain an overall desired alpha level.