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Posterior probability of the null hypothesis being true, given a significant effect

## 3 comments:

The assumed prior mean Pr(H0)=.92 puts a very strong prior on the alternative hypothesis being false. How does this change under the (probably wider-spread) assumption in many experiments that the alternative hypothesis has a higher prior probability? I guess things should change in this case, right?

The assumed prior mean Pr(H0)=.92 puts a very strong prior the alternative hypothesis being false. How does this change under the (probably wide-spread) assumption in many experiments that the alternative hypothesis has a higher prior probability?

So I updated my post to incorporate a low prior probability of the null; the outcome depends on the details, see updated post. But if the null is already thought to be false before doing the statistical test, why are we doing a null hypothesis test?

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