The key insight to recognize is that within the Bayesian framework hypothesis testing is parameter estimation. Your certainty in the outcome of the test is your posterior probability over the test-relevant parameters.
Once you realize this you can easily develop very sophisticated testing models (if necessary) that are also easy to understand and reason about. This dramatically simplifies.
If you're looking for a specific book recommendation Statistical Rethinking does a good job covering this at length and Bayesian Statistics the Fun Way is a more beginner friendly book that covers the basics of Bayesian hypothesis testing.
I might checkout Statistical Rethinking given how frequently it is being recommended!
Edit: Haha I just found the textbook and I’m remembering now that I actually worked through sections of it back when I was working through BDA several years back.
This book is very relevant to those fields. There is a common choice in statistics to either stratify or aggregate your dataset.
There is an example in his book discussing efficacy trials across seven hospitals. If you stratify the data, you lose a lot of confidence, if you aggregate the data, you end up just modeling the difference between hospitals.
Hierarchical modeling allows you to split your dataset under a single unified model. This is really powerful for extracting signal for noise because you can split your dataset according to potential confounding variables eg the hospital from which the data was collected.
I am writing this on my phone so apologies for the lack of links, but in short the approach in this book is extremely relevant of medical testing.
