From xkcd. Understanding this would especially help in the DC Circuit, where the judges seem to think that the FDA can't ban claims that "X might help with prostate health" when there's one well-conducted study supporting the claim and fifteen not supporting it. That whole p > 0.05 thing means that every once in a while you get a solid, well-conducted study that is nonetheless finding a relationship that does not in fact exist, and those other fifteen provide not just counterbalancing evidence but reason to think the one study is wrong. And the "disclosures" the DC Circuit has approved communicate nothing like that truth to consumers, instead going for the "teach the controversy" approach xkcd mocks for its fundamental error of statistical understanding.
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