The question you opened
Berkeley, 1973, and a bias that moved
In 1973 Berkeley admitted 44 percent of 8,442 male applicants and 35 percent of 4,321 women.
What happened to that gap when statisticians read it department by department?
It reversed: the department level figures leaned slightly toward women.
Women applied more often to departments that turned nearly everyone away. Splitting the pool by department flipped the direction of the gap.
Berkeley faced a discrimination complaint in 1973 on numbers that looked unanswerable. Of 8,442 men who applied to graduate study, 44 percent were admitted. Of 4,321 women, 35 percent were. The university asked its own statisticians to look, and Peter Bickel, Eugene Hammel, and William O'Connell published the result in Science in 1975. Department by department, the gap went the other way.
The department level figures leaned slightly toward women. The pooled figure reversed because admission rates differed enormously between departments, and the two groups applied to different ones. Departments in the physical sciences admitted a large share of applicants. Departments in the humanities admitted a small share and were heavily oversubscribed, and women applied to those in much larger numbers.
This is Simpson's paradox: a trend that holds inside every subgroup can vanish or invert once the subgroups are pooled, because pooling weights each subgroup by its size. The aggregate is an average of averages, and averages of averages are only trustworthy when the groups being averaged are the same size.
The authors were careful about what the result did and did not show. It showed that the department level data gave no evidence of bias in admission decisions. It did not show that the system was fair, since the choice of field is shaped long before an application form. That distinction is why the paper is still assigned.
The same shape appears in medicine, where a treatment can look worse overall while winning in both the mild and severe groups, and in sport, where a batter can lead in each of two seasons and trail across the pair. The defence is always the same: before believing a pooled rate, ask what the groups are and whether they are comparable in size.
Technique: Simpson's paradox
Source checked 2026-09-06