I've seen this called Simpson's paradox in my Statistics book. The example given there was of 2 hospitals. Hospital A specializes in serious cases, and B is an all-around hospital. A takes in 1000 patients a year, 900 of which are serious. B takes in 1000 a year, 200 of which are serious. 210 patients die every year in A, 200 of which are serious. 200 die a year in B, 100 of which are serious. So less people die overall in B, but a smaller proportion of serious patients AND non-serious patients die in A (22% vs 50% and 10% vs 13%). This is because the 2 events are not mutually exclusive; A is better but takes in many more serious patients because they are better.