Post hoc analysis

Not to be confused with Post hoc theorizing.

In a scientific study, post hoc analysis (from Latin post hoc, "after this") consists of statistical analyses that were specified after the data were seen.^[1][2] They are usually used to uncover specific differences between three or more group means when an analysis of variance (ANOVA) test is significant.^[3] This typically creates a multiple testing problem because each potential analysis is effectively a statistical test. Multiple testing procedures are sometimes used to compensate, but that is often difficult or impossible to do precisely. Post hoc analysis that is conducted and interpreted without adequate consideration of this problem is sometimes called data dredging by critics because the statistical associations that it finds are often spurious.^[4]

Post hoc analyses are not inherently bad or good;^{[5]: 12–13} rather, the main requirement for their ethical use is simply that their results not be mispresented as the original hypothesis.^{[5]: 12–13} Modern editions of scientific manuals have clarified this point; for example, APA style now specifies that "hypotheses should now be stated in three groupings: preplanned–primary, preplanned–secondary, and exploratory (post hoc). Exploratory hypotheses are allowable, and there should be no pressure to disguise them as if they were preplanned."^{[5]: 12–13}

Common post hoc tests

Some common post hoc tests include:^[6][7]

• Holm-Bonferroni Procedure
• Newman-Keuls
• Rodger’s Method
• Scheffé’s Method
• Tukey’s Test (see also: Studentized Range Distribution)

However, with the exception of Scheffès Method, these tests should be specified "a priori" despite being called "post-hoc" in conventional usage. For example, a difference between means could be significant with the Holm-Bonferroni method but not with the Turkey Test and vice versa. It would be poor practice for a data analyst to choose which of these tests to report based on which gave the desired result.

Causes

Sometimes the temptation to engage in post hoc analysis is motivated by a desire to produce positive results or see a project as successful. In the case of pharmaceutical research, there may be significant financial consequences to a failed trial.^{[citation needed]}

See also

• HARKing
• Testing hypotheses suggested by the data
• Nemenyi test
• Outcome switching

References

1. "What is the significance and use of post-hoc analysis studies?". www.cwauthors.com. Retrieved 2022-12-09.
2. "11.8: Post Hoc Tests". Statistics LibreTexts. 2019-11-12. Retrieved 2022-12-09.
3. "SAGE Research Methods - The SAGE Encyclopedia of Communication Research Methods". methods.sagepub.com. Retrieved 2022-12-09.
4. Zhang, Yiran; Hedo, Rita; Rivera, Anna; Rull, Rudolph; Richardson, Sabrina; Tu, Xin M. (2019-08-01). "Post hoc power analysis: is it an informative and meaningful analysis?". General Psychiatry. 32 (4): e100069. doi:10.1136/gpsych-2019-100069. ISSN 2517-729X. PMC 6738696.
5. American Psychological Association (2020). Publication Manual of the American Psychological Association: the Official Guide to APA Style (7th ed.). Washington, DC: American Psychological Association. ISBN 978-1433832178.
6. "Post Hoc Definition and Types of Tests". Statistics How To. Retrieved 2022-12-09.
7. Pamplona, Fabricio (2022-07-28). "Post Hoc Analysis: Process and types of tests". Mind the Graph Blog. Retrieved 2022-12-09.