How can men be admitted at a much higher rate overall — while women do as well or better in most departments?
UC Berkeley's 1973 graduate admissions numbers raised fears of a gender-discrimination lawsuit. The overall gap was real. So was the fact that it mostly wasn't there once you looked closer.
Pooled across the six largest departments — a 15-point gap, enough to look like a clear case of bias.
Now split the same data by department
Women were admitted at an equal or higher rate than men in four of these six departments (A, B, D, F).
Women applied to the hardest departments. That, not bias against them, made the overall numbers look unfair. Analyzed department by department, the original researchers found a small bias in favor of women. Men disproportionately applied to the easy departments (A and B admitted 62–82%), and women to the hard ones (C through F, some as low as 6–7%). Combine all six and that difference in where people applied masquerades as a difference in how they were evaluated.
An overall average can reverse the pattern inside every group when the groups are mixed in very different proportions. Before trusting any combined comparison — two schools' graduation rates, two players' batting averages — ask what happens when the same data is split into groups.
When a combined total shows a gap, what happens if you split it into groups?
Explore how the same aggregation trap shows up elsewhere
The effect has a name: Simpson's paradox. It needs two ingredients: groups with very different baseline rates (easy vs. hard departments), and a very different mix of people in each group (men applying mostly to easy ones, women to hard ones). Take away either ingredient and the reversal disappears.
It's a cousin of our Friendship Paradox exhibit: in both, how a population gets combined or sampled shapes the number you end up seeing.
Related exhibits
Sources: P.J. Bickel, E.A. Hammel, J.W. O'Connell, "Sex Bias in Graduate Admissions: Data from Berkeley," Science, 1975. Six-department table (departments A–F, admit rates and applicant counts) as reproduced in Freedman, Pisani & Purves, Statistics, and widely used as the standard classroom example of Simpson's paradox. University-wide 1973 figures across all departments were approximately 44% of men and 35% of women admitted. The six largest departments shown here (45%/30%) are the subset popularized by Freedman, Pisani & Purves; Bickel's team analyzed every department.