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In frequentist hypothesis testing, the $p$-value is the probability of a result as extreme (or more) than the observed result, under the assumption that the null hypothesis is true.

13 votes
1 answer
4k views

If the distribution of test statistic is bimodal, does p-value mean anything?

P-value is defined the probability of obtaining a test-statistic at least as extreme as what is observed, assuming null-hypothesis is true. In other words, $$P( X \ge t | H_0 )$$ But what if the test …
Alby's user avatar
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60 votes
3 answers
29k views

When combining p-values, why not just averaging?

I recently learned about Fisher's method to combine p-values. This is based on the fact that p-value under the null follows a uniform distribution, and that $$-2\sum_{i=1}^n{\log X_i} \sim \chi^2(2n), …
Alby's user avatar
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