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I know that the mathematically, p values should be uniformly distributed under the null hypothesis. However, what is this null hypothesis (in this context)?

Can someone give me an example please ?

user1769197
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    Take a look at this paper by Murdoch et al (2008) [p values are random variables](http://xa.yimg.com/kq/groups/16412409/1018781877/name/Pvalues.pdf‎) in *The American Statistician*. (Link is to a self-archived version of paper.) – Gavin Simpson Sep 10 '13 at 04:07
  • The typical *p*-value (e.g., from a *t*-test) is the probability of the observed data (or something more extreme) if the null hypothesis is true. The null hypothesis is typically (e.g., in case of a *t*-test) the hypothesis that in the population, the parameter is some fixed value. Very often, the null hypothesis is that the parameter is zero. So the typical *p*-value you'll find is the probability of the observed data if the parameter in the population was 0. – jona Sep 10 '13 at 04:07
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    It's simply (in the continuous case) that the p-value is the Probability Integral Transform (or its complement) applied to the relevant test statistic (e.g. |t| for a two-tailed t-test) under the null; it's uniform for exactly the same reason that $U=F_X(X)$ is. – Glen_b Sep 10 '13 at 04:19

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