Probability to pass multiple studies [Power / Sample Size]

posted by Helmut Homepage – Vienna, Austria, 2021-02-19 12:02 (498 d 04:12 ago) – Posting: # 22214
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Dear all (and esp. our expert in probability zizou),

say, we have \(\small{n}\) studies, each powered at 90%. What is the probability (i.e., power) that all of them pass BE?

Let’s keep it simple: T/R-ratios and CVs are identical in studies \(\small{1\ldots n}\). Hence, \(\small{p_{\,1}=\ldots=p_{\,n}}\). If the outcomes of studies are independent, is \(\small{p_{\,\text{pass all}}=\prod_{i=1}^{i=n}p_{\,i}}\), e.g., for \(\small{p_{\,1}=\ldots=p_{\,6}=0.90\rightarrow 0.90^6\approx0.53}\)?
Or does each study stand on its own and we don’t have to care? :confused:

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