Random sampling versus random allocation/randomization- implications for p-value interpretation

I agree that this is a good way to understand frequentist inference, but I think it doesn’t do justice to the Bayesian perspective that places conditioning on what is known as fundamental.

It is easy to generate useless procedures with frequency guarantees. Sensible use of frequentist methods rely on the likelihood principle in the background. For example:

https://projecteuclid.org/journals/annals-of-statistics/volume-22/issue-4/A-Unified-Conditional-Frequentist-and-Bayesian-Test-for-Fixed-and/10.1214/aos/1176325757.full

https://projecteuclid.org/journals/statistical-science/volume-18/issue-1/Could-Fisher-Jeffreys-and-Neyman-Have-Agreed-on-Testing/10.1214/ss/1056397485.full

I don’t know if it is possible, but I wish there was a course that took the perspective of Herman Chernoff – develop an initial Bayesian decision theoretic perspective, then develop frequentist procedures guided by those constraints.