The Great Statistical Schism
What is probability? This sounds like a discussion question for a philosophy class, one of those questions that’s fun to think about but that doesn’t have many practical consequences. Surprisingly, this is not the case. As it turns out, different answers to this question lead to completely different views of how to do statistics and data analysis in practice. In the early 20th century, this led to a split in the field of statistics, with intense debates taking place about whose methods and ways of thinking were better. Unfortunately, the wrong side won the debate and their ideas still dominate mainstream statistics, a situation which has exacerbated the reproducibility crises affecting science today [1].
Here’s a common, standard statistical inference problem. An old drug successfully treats 70% of patients. To test a new drug, researchers give it to 100 patients, 83 of whom recover. Based on this evidence, how certain should we be that the new drug is worse than, identical to, or better than the old one?
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