Recent PhD placement data: women more likely than men to secure permanent positions within two years of the PhD

The data and various charts are here.  What I can't tell from this data is what is "held constant" when the authors say that women are more likely than men to get permanent posts all else equal.  For example, does this analysis "hold constant" the quality of the PhD program from which the graduates come?  I'm not sure.  If more women are graduating from strong programs, proportionally, than men, then the result wouldn't be surprising.   Comments are open for anyone who can clarify what's going on here.