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Decius comments on The Universal Medical Journal Article Error - Less Wrong
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It's not a rule of thumb; it's used as the primary factor in making policy decisions incorrectly. In this specific example, the regulatory agency made the statement "There is no evidence that artificial colorings are linked to hyperactivity" based on the data that artificial colorings are linked to hyperactivity with p~.13
There are many other cases in medical where 0.05p<.5 is used as evidence against p.