Post-hoc analysis

Post-hoc analysis refers to the statistical analyses that are planned after the data has been observed, which means they are not specified before the experiment or study is conducted. This type of analysis is often used in research, particularly in the fields of medicine, psychology, and social sciences. The term "post-hoc" is derived from Latin, meaning "after this".

Overview

In scientific studies, particularly those involving experimental designs, it is crucial to distinguish between analyses planned before data collection (a priori) and those planned after the data are seen (post-hoc). Post-hoc analyses are typically used to explore patterns in the data that were not anticipated or to answer new questions that arise from the initial results. However, these analyses carry a higher risk of Type I errors (false positives), as they are more likely to capitalize on chance findings.

Purpose and Use

The primary purpose of post-hoc analysis is to explore additional hypotheses and to generate new leads that could be pursued in future research. It is particularly useful in large datasets, such as those derived from clinical trials or extensive surveys, where the volume of data can reveal unexpected associations.

However, findings from post-hoc analyses should be interpreted with caution. Since these analyses are not controlled for multiple comparisons, the likelihood of finding a statistically significant result by chance increases. Therefore, results from post-hoc analyses are generally considered to be exploratory and hypothesis-generating rather than confirmatory.

Common Methods

Some common statistical methods used in post-hoc analysis include:

• Tukey's range test
• Bonferroni correction
• Scheffé's method

These methods help to control the family-wise error rate and reduce the likelihood of Type I errors when multiple pairwise comparisons are made post-hoc.

Criticism and Considerations

Post-hoc analysis is often criticized for its potential to lead to misleading conclusions. Critics argue that because these analyses are performed after examining the data, they are inherently biased by the data itself. This can lead to "data dredging" or "p-hacking," where researchers intentionally or unintentionally manipulate the data until they find something of interest.

To mitigate these issues, it is essential for researchers to transparently report that the analyses were post-hoc and to discuss the exploratory nature of the findings. Additionally, replication in further studies is crucial to validate any significant results obtained from post-hoc analyses.

Conclusion

While post-hoc analysis can be a powerful tool for discovering new insights in data, it must be used judiciously and with full disclosure of its exploratory nature. Results derived from such analyses should be viewed as preliminary until they are confirmed by subsequent research.