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.
I'm sure it's not impossible. Consider the extreme case:
| Dept | Male Applications | Males Accepted | Female Applications | Females Accepted |
|---|---|---|---|---|
| A | 100 | 80% | 10 | 100% |
| B | 10 | 10% | 100 | 20% |
Female accepted in total: 30/110 ~ 27%. Males in total 81/110 ~ 74%.
Ars Technica are holding a competition for people to make a science video up to 3 minutes long "to explain a scientific concept in terms that a high school science class would not only understand, but actually be interested in watching". Prizes in three categories: biology, physics, and mathematics. Deadline is December 25. More details here.
Anyone want to have a go at Bayes' theorem? Cognitive bias? Defeating death? Invisible purple dragons?