My first post. Thank you. Am public facing so opinions are my own.

Three preamble points and a question.

1. I see Fisher’s as an exact analogue of Chi Squared, at least in my use cases, where Fisher’s helps me assess the likelihood of certain contingency tables under the assumption of equality.

2. On recent reading I am to understand that tests based on a U-statistic (unbiased estimator) as laid out by Hoeffding are not exact. I have enjoyed Hoeffding’s paper in that as far as it takes my limited abilities and knowledge. Then I liked Mann and Whitney’s paper where they lay out their U test. Plotting out probabilities versus U in real life (scattering) visualises inexact mapping. It’s noticeable for for small sets.

3. I very much like Fisher’s exact. I like his clear reasoning - and the fact that his exact test was once impracticable due to bang numbers, but since then has become computationally feasible given personal computers.

Question: I have some ideas that have led me close to an exact test that does Mann Whitney U’s job. Is this already achieved? Are my opening points coherent enough to support the ambition? Which academic centres might know or care about this?

Thank you again.