7

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
  • 11,395
  • 3
  • 49
  • 109
  • 1
    Your question is closely related to [Why are p-values uniformly distributed under the null hypothesis](http://stats.stackexchange.com/questions/10613/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

0 Answers0