Simpson's Paradox

A prominent university was accused of gender discrimination in its graduate admission policies. The difference seemed to be too large to be due just to chance. Here are the numbers: Gender Applicants % Admitted Men 8,442 44% Women 4,321 35% But an examination of the admissions of individual departments revealed no such bias. Instead, there was a small bias in favor of admitting women. Here are the numbers for the main departments: Department Men Women Applicants % Admitted Applicants % Admitted A 825 62% 108 82% B 560 63% 25 68% C 325 37% 593 34% D 417 33% 375 35% E 191 28% 393 24% F 272 6% 341 7% This occured because women were applying to competitive departments with a low rate of admissions, while men were applying to less competitive departments with high rates of admissions.