Probability to pass multiple studies [Power / Sample Size]

posted by ElMaestro  – Denmark, 2021-02-19 13:57 (710 d 17:51 ago) – Posting: # 22215
Views: 2,090

Hi Helmut,

❝ 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:

Yes to 0.53.
The risk is up to you or your client. I think there is no general awareness, but my real worry is the type I error, as I have indicated elsewhere.
"Have to care" really involves the fine print. I think in the absence of further info it is difficult to tell if you should care and/or from which perspective care is necessary.

Related issue, the one that worries me more:
You test one formulation, it fails on the 90% CI, you develop a new formulation, it passes on the 90% CI. What is the type I error? Well, strictly speaking that would be inflated. But noone seems to give a damn.:-D

Pass or fail!

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