Statistics
Simpson's paradox
Described by Karl Pearson, George Udny Yule and others around 1900; named after Edward Simpson's 1951 paper; the Berkeley case is from Bickel, Hammel and O'Connell (1975).
In autumn 1973, 8,442 men and 4,321 women applied for graduate study at the University of California, Berkeley. About 44 percent of the men were admitted and about 35 percent of the women. The gap was large enough that the university expected to be sued, and it asked its own statisticians to look at the data.
Admissions at Berkeley were not decided centrally. Each department read its own applications and chose its own students. Suppose you go through the departments one at a time and compare the admission rate for women with the rate for men in each. What do you expect to find across the departments?