You didn't cite any papers in this thread. Maybe you were replying to someone else?

But there are at least 3 generations of poorly trained physicians. (statistically illiterate, see eg (Odette Wegwarth 2013))

Yes, 2 sigma is NOT much evidence, but we are stuck in a paradigm where medicine generally thinks it is enough. And it verges on scientism!

Ok 5 sigma for Physics, I mistated. But I am not advocating for that in medicine, 3 sigma would be sufficient.

But I would note that Shewhart and then Deming, were pretty explicit that their approach was not probabilistic. It was empirically based on the best place to minimize (but not eliminate) Type I and Type II errors.

I will keep an open mind about "degree of surprise" (Shackle, I presume) and further contemplate. Is starting with Derbyshire (1977), a good place?