It is often observed in practice, like in the famous Berkeley sex bias case of 1973 when the university as a whole was found to be biased toward admitting men, while every individual department was found to be biased toward admitting women.
This seems impossible, and checking the data (posted on wikipedia) that isn’t what happened.
[edit] Hm, I appear to not have been thinking clearly. See comment below.
This seems impossible, and checking the data (posted on wikipedia) that isn’t what happened.
That is not exactly what happened, as 2 departments exhibited a small bias towards men, but it is not impossible, and the reason is that more women applied to the more competitive departments, and so their total acceptance rate represented the departments with low overall acceptance rate more than the men’s total acceptance rate.
This seems impossible, and checking the data (posted on wikipedia) that isn’t what happened.
[edit] Hm, I appear to not have been thinking clearly. See comment below.
That is not exactly what happened, as 2 departments exhibited a small bias towards men, but it is not impossible, and the reason is that more women applied to the more competitive departments, and so their total acceptance rate represented the departments with low overall acceptance rate more than the men’s total acceptance rate.
I’m sure it’s not impossible. Consider the extreme case:
Female accepted in total: 30⁄110 ~ 27%. Males in total 81⁄110 ~ 74%.