In this paper we provide a formal yet simple and straightforward proof of the asymptotic χ<Superscript>2</Superscript> distribution for Cochran test statistic. Then, we show that the general form of this type of test statistics is invariant for the choice of weights. This fact is important since in practice many such...</superscript>

Researchers have shown that the optimally weighted z-test, where the weights are the standardized expected difference in means, is more powerful than other methods when combining p-values from independent studies. However, in practice the effect for each independent study is usually unknown,...