Examples of the Paradox
One classic example of Simpson’s Paradox is from a 1975 study of sex bias in graduate admissions at the University of California, Berkeley. When considering the overall figures, there was a significant difference between the percentage of male versus female applicants admitted (44% out of 8,442 men were admitted, vs. 35% out of 4,321 women). However, when considering individual departments, the data showed a statistically significant bias in favor of women (6 out of the 85 departments were significantly biased against men, while only 4 were significantly biased against women). How can this be? It seems counterintuitive that this result is even possible. Perhaps a graph will help:- Image source: Wikipedia