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On this page it says

...if HA holds, the p-values have a distribution for which values near 0 are more likely than values near 1. However the p-values may have a distribution that is not rectangular if H0 holds. The more general result for a test with a composite null hypothesis is that p-values are no more likely to be near 0 than to be near 1 when H0 holds -- the distribution may favour values near 1.

Should I take this to mean that if I simulate or maybe bootstrap a distribution of p-values, I can make some kind of informal inference about H0 based on the skew of that distribution? If so, where can I read more about this technique? If not, why not?

shadowtalker
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    Your question is closely related to Why are p-values uniformly distributed under the null hypothesis but that applies for point null hypotheses. (As is discussed in the comments to the main question and top answer there.) Perhaps this question should be retitled to something like "Distribution of p-values under a composite null hypothesis", which seems to capture the spirit of the linked page. – Silverfish Jan 10 '15 at 10:57
  • @Silverfish thanks for the suggestion, i agree and changed the title. I'd completely forgotten I asked this question until someone randomly up voted it. – shadowtalker Jan 10 '15 at 13:55

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