Don't fully understand "we know ahead of time that just about all null hypotheses of interest are false". Did you mean true?
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I don’t think so. When you hypothesis test a regression your null is that the coefficient are zero, but if you thought that they were zero why would you run a regression? Hypothesis testing in practice is about showing that there may be an effect because you believe one exists.
End of conversation
New conversation -
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Sure, if we can separate the chance from the causal associations. Can't do it with just stats.
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