PhilGoetz comments on The Universal Medical Journal Article Error - Less Wrong
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That's not how it works. You measure the magnitude of an effect, then do a statistical test of the hypothesis that all of the children have a response, which gives a cutoff that the effect magnitude must reach to accept that hypothesis with 95% confidence. If only 10% of the children have such a response, you won't reach that cutoff. If 10% have a positive response and 10% have a negative response, you will detect nothing, no matter how big your sample is.