Problems of Post Hoc Analysis

“Misuse of statistical testing often involves post hoc analyses of data already collected, making it seem as though statistically significant results provide evidence against the null hypothesis, when in fact they may have a high probability of being false positives…. A study from the late-1980s gives a striking example of how such post hoc analysis can be misleading. The International Study of Infarct Survival was a large-scale, international, randomized trial that examined the potential benefit of aspirin for patients who had had a heart attack. After data collection and analysis were complete, the publishing journal asked the researchers to do additional analysis to see if certain subgroups of patients benefited more or less from aspirin. Richard Peto, one of the researchers, refused to do so because of the risk of finding invalid but seemingly significant associations. In the end, Peto relented and performed the analysis, but with a twist: he also included a post hoc analysis that divided the patients into the twelve astrological signs, and found that Geminis and Libras did not benefit from aspirin, while Capricorns benefited the most (Peto, 2011). This obviously spurious relationship illustrates the dangers of analyzing data with hypotheses and subgroups that were not prespecified (p.97).”

—Mayo, quoting
National Academies of Science “Consensus Study” Reproducibility and Replicability in Science 2019 in “National Academies of Science: Please Correct Your Definitions of P-values.” Statsblogs. September 30, 2019.

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