 Bickel et al. (1975) present a classic example of Simpson’s Paradox involving a study of gender discrimination at Berkeley. The data revealed that men were more likely than women to be accepted to the university’s graduate programs, but the authors were unable to detect a bias towards men in any individual department. The authors use the paradox to explain why the higher university-wide acceptance rate for men does not show that any department discriminated against women. Specifically, women were more likely to apply to departments with lower acceptance rates. This leads to a probabilistic association between gender and the partitioning variable (department), which we have seen can lead to Simpson’s reversals.