Post hoc analysis

Definition

Post hoc analysis refers to the set of procedures conducted after an initial analysis, specifically when significant results are found, to explore differences between group means. This process is crucial for understanding which specific groups differ from one another in a dataset, especially after applying non-parametric tests like the Kruskal-Wallis test, which assesses differences among multiple independent groups without assuming a normal distribution.

5 Must Know Facts For Your Next Test

1. Post hoc analysis is performed after finding a significant result in a non-parametric test like the Kruskal-Wallis test to determine where those differences lie among the groups.
2. Common post hoc tests include Dunn's test and the Mann-Whitney U test, which help identify specific group pairs that show significant differences.
3. In conducting post hoc analysis, adjustments such as the Bonferroni correction are often applied to control for Type I errors resulting from multiple comparisons.
4. Post hoc analysis does not establish causation but rather identifies patterns or trends among group differences following initial statistical testing.
5. It is essential to have a clearly defined hypothesis before conducting post hoc analysis to avoid data mining and ensure valid conclusions.

Review Questions

• What is the purpose of conducting post hoc analysis after performing a Kruskal-Wallis test?
  • The purpose of conducting post hoc analysis after a Kruskal-Wallis test is to identify which specific groups differ from each other when the overall test indicates significant differences among multiple independent groups. Since the Kruskal-Wallis test can only tell us that at least one group median is different, post hoc analysis helps break down those differences and pinpoint the specific pairs of groups that are statistically different.
• How does the Bonferroni correction play a role in post hoc analysis?
  • The Bonferroni correction is important in post hoc analysis as it adjusts for the increased risk of Type I errors that occurs when multiple comparisons are made. When conducting several tests simultaneously, the likelihood of incorrectly rejecting the null hypothesis rises. By applying the Bonferroni correction, researchers can set a more stringent significance level, thus helping ensure that any significant findings are more likely to be true positives rather than false positives.
• Evaluate the implications of using post hoc analysis without a predefined hypothesis in research studies.
  • Using post hoc analysis without a predefined hypothesis can lead to issues such as data mining, where researchers may unintentionally find patterns that do not hold up under rigorous scrutiny. This practice can result in misleading conclusions and undermine the validity of the study's findings. By not having a clear hypothesis, researchers risk chasing random correlations rather than meaningful relationships, ultimately affecting the reliability of their results and interpretations in future research.

Related terms

Kruskal-Wallis test: A non-parametric statistical test used to determine if there are statistically significant differences between the medians of three or more independent groups.

ANOVA: Analysis of Variance (ANOVA) is a statistical method used to test differences between two or more group means by comparing the variance within groups to the variance between groups.

Bonferroni correction: A statistical adjustment made to account for multiple comparisons in hypothesis testing, reducing the chances of obtaining false-positive results.