Study done by Grammarly with over three thousand participants
While not exactly a broad spectrum study that can be used as a source for a greater study, this is a somewhat interesting look at how close male and female writers are in what they do with the main characters of their stories.
Grammarly is a site where you can insert whole paragraphs and have them checked over grammatically. I use them myself for my longer stories, and love the results. Check them out of you're a writer, even if you are only one for school. Never a bad thing to double check your work.