An electronic text makes the following assertion:
When the null hypothesis, H0, is true, all p-values between 0 and 1 are
equally likely. In other words, the p-value has a rectangular distribution
between 0 and 1.
Is that so? I would have thought that if the null is true then, the test
statistic is [asymtotically] normally distiributed about its mean, and
p=values near to .5 would be more probable than extreme p-values.
Can anyone provide a proof of the assertion or a counterexample?
Best
Diana
Professor Diana Kornbrot
School of Psychology
University of Hertfordshire
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