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In fall 1973, the University of California, Berkeley received 12,763 graduate applications — 8,442 from men and 4,321 from women. The aggregate numbers looked damning: 44% of male applicants were admitted versus only 35% of female applicants. The gap was statistically significant. A gender discrimination lawsuit seemed inevitable. Statistician Peter Bickel was asked to investigate. He pulled admission records for all 85 departments and began the tedious work of disaggregating the data. What he found stunned everyone. In 4 of the 6 largest departments, women were admitted at rates equal to or higher than men. Department A admitted 82% of women versus 62% of men. Department B: 68% women versus 63% men. The bias, if anything, ran slightly in favor of women. The mystery had a structural exp...
Popular framing: Berkeley discriminated against women in admissions; the 44% vs 35% gap proved it.
Structural analysis: Simpson's Paradox: aggregating across departments mixed two effects — admission rate per department and gender-distribution of applications across departments — producing a top-line signal opposite to the departmental reality. Self-selection of applicants into more vs. less competitive fields (shaped by decades of socialization upstream) acted as a confounding variable that the aggregate number couldn't see; the 9-point gap was noise generated by base-rate differences between departmental admission rates. The same dataset tells opposite stories depending on the slice, and only the disaggregated slice carries the real signal.
The popular frame forces a binary — discrimination or no discrimination — that the structural reality cannot satisfy. By focusing on whether Berkeley discriminated, discourse missed the more tractable and consequential question: what social machinery routes women to low-acceptance fields, and what levers exist to intervene before the application stage? Simpson's Paradox is not just a statistical curiosity; it is a signature of any system where a hidden variable (department choice) is correlated with both the treatment (gender) and the outcome (admission rate).
