I didn't need a study to tell me that. I figured it out in middle and high school when observing male vs. female gym teachers.
I sometimes take it as a compliment though. I figure if a woman is more critical, it sometimes means they expect more. That means they think women are capable of more than the male bosses might think.
But then women get more gossipy, and that's when I want to get into bitchslap mode. That's especially true in store settings. The men are normally just so much easier to get along with.
When I taught junior and senior high, I found the male students were much easier in the classroom. They listened more, were more cooperative and weren't as gossipy. Many of the females were better students, but generally weren't as pleasant.