> There are only a handful of fields where women dominate.

I was curious if I could find some figures, so I did a quick Google search. While I can't vouch for the data used in this article, it seems your statement is incorrect, and quite strongly so

https://www.bostonglobe.com/metro/2017/03/06/chart-the-perce...

It draws data from the U.S. Department of Labor

Not entirely scientific, but the male majority roles took 18 "page ups" to scroll through versus 16 for the female majority roles.

A better approach would be to get the full counts of the positions, but that requires more work than the results are probably worth.