For 2x2 contingency tables, my understanding is that Boschloo and Barnard both have uniformly more power than Fisher's exact test (even if all marginals are fixed??). But I am still confused about the difference between these tests.
In the end which one should be used in which case?
This answer indicates that Boschloo might be better but slower. But I cannot find any reference in the literature.
We are adding Barnard (done) and Boschloo (here) in SciPy and we are unsure about how to document the difference and give practical recommandations on these methods.
