It’s a minefield. At the moment, most public research is generated by folk with ulterior motives using deliberately skewed assumptions and comparisons. The ones that aren’t lack sufficient data to show meaningful conclusions.

Joanna Harper is doing work in this space, but she’s in the latter category.

Some of the other comments have mentioned Joanna Harper, who is trying, but lacks enough data to make meaningful conclusions.

I recently did a presentation on the political side of this, and one thing to note was that with 1 or 2 exceptions, not a single state legislator could identify an instance of a trans woman dominating her field (because the anti trans movement is astroturf and designed to prey on people’s fear).

If you would like my sources for the presentation, DM me. I only had a couple on this subject, but some of the auxiliary sources might help too.