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I have a simple query regarding the construction of a confidence interval for a p-value. How do I construct such a confidence interval? Like we construct a C.I. for t-value ($\bar{X} \pm t \times(s/ \sqrt{n})$), can such kind of intervals be created for p-value?

I think (not completely sure) such C.I. for p-value is called replication interval. I tried googling but couldn't find anything relevant.

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One constructs a confidence interval for a parameter of interest whose true value is unknown (the parameter is related to properties of the population). 95% of 95% confidence intervals contain the true value for the parameter.

A p-value, on the other hand, is an outcome of a random variable (its value depends on the sample). It makes no sense to speak of a confidence interval for a p-value, since it does not represent a parameter of unknown value. There is no such thing as the true p-value for a population.

Perhaps your question is asking about the distribution of p-values. For the non-discrete case, the p-value distribution is uniform [0-1], if the null hypothesis is correct.

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