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John_Maxwell_IV comments on Too good to be true - Less Wrong
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This seems like a big leap. 95% confidence means at least 95% confidence, right? So if I reject the "vaccines cause autism" hypothesis with p = 0.001, that makes me 95% confident and I publish?
There's a 5% chance of having at least 95% confidence if there's no correlation.
If there's no correlation, p is a random number between zero and one. p = 0.001 would show that vaccines do cause autism. p = 0.999 would show that they prevent it.