## Probability to pass multiple studies [Power / Sample Size]

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? 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. Pass or fail!
ElMaestro  Ing. Helmut Schütz 