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First I generate two one-sided p-values from independent samples using null hypothesis $H_0: \Delta\leq0$, so that $p_1$ and $p_2$ are generated. Next, I apply the inverse normal combination function $T=\sqrt{w_1}\Theta(1-p_1)+\sqrt{w_2}\Theta(1-p_2)$ with weights $w_1$ and $w_2$ which fulfil $w_1+w_2=1$.

What would the associated null hypothesis be? $H_0$:No effect in the overall population, or no effect in neither of the samples?

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The null hypothesis is that the $p_i$ all have a uniform distribution on the unit interval.

For more details and a discussion of the alternative hypotheses see Test for significant excess of significant p-values across multiple comparisons

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