Let us assume that the p-values p k are known for testing H 0k versus H Ak , k = 1, …, n, in n independent studies on some common issue, and our aim is to achieve a decision on the overall question H 0 ∗: all the H0k are true versus H A ∗ : some of the HAk are true. As there are many different ways in which H 0 ∗ can be false, selecting an appropriate test is in general unfeasible. On the other hand, combining the available p k ’s so that T(p 1, …, p n ) is the observed value of a random variable whose sampling distribution under H 0 ∗ is known is a simple issue, since under H 0 ∗, p is the observed value of a random sample P = (P 1, …P n ) from a Uniform(0, 1) population. In fact, several different sensible combined testing procedures are often used.
A rational combined procedure should of course be monotone, in the sense that if one set of p-values p = (p 1, …, p n ) leads to rejection of the overall null hypothesis H 0 ∗, any set of componentwise smaller p-values p′ = p′...
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Pestana, D. (2011). P-Values, Combining of. In: Lovric, M. (eds) International Encyclopedia of Statistical Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04898-2_646
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