In 1973, Berkeley appeared to admit men at a higher rate than women, hinting at bias. But when admissions were broken down department by department, most departments showed no bias against women, and several slightly favoured them. The reversal was real, not a mistake. Women had applied in larger numbers to the most competitive departments, where everyone’s odds were low. The aggregate hid the structure.
This is Simpson’s paradox: a relationship that holds within every subgroup can vanish or flip when the subgroups are pooled. A treatment can help both mild and severe patients yet look worse overall, simply because it was given more often to the sicker ones. The lurking variable, whether department, severity or the way cases were sorted, quietly steers the total.
The pattern is a warning about aggregation: a single number summarising a mixed population can point in a direction that is true of no one inside it. The fix is to ask what was combined, and why.
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