In the autumn of 1973, the University of California, Berkeley, looked like it had a problem. Across its graduate school, about 44 per cent of the men who applied were admitted, against only about 35 per cent of the women. The gap was large and hard to blame on chance. It looked like plain discrimination.
Then statisticians broke the numbers down department by department, and the story turned inside out. Within the individual departments, women were admitted at roughly the same rate as men, and in several departments slightly more often. The university-wide gap that looked so damning simply dissolved once you stopped lumping everyone together.
This is Simpson’s paradox: a trend that shows up clearly in combined data can weaken, vanish or completely reverse when the data is split into its natural groups. It is not a rounding error or a statistical sleight of hand. It is a genuine feature of how averages behave, and it catches trained researchers as easily as anyone.
At Berkeley the explanation lay in where people applied. Women were applying in larger numbers to the most competitive departments, the ones that rejected most applicants of either sex. Men were applying more often to departments that admitted a comfortable majority. Each department was treating its applicants even-handedly, but because women were crowding through the hard doors and men through the easy ones, the overall figures made it look as though the university favoured men. The 1975 analysis by Peter Bickel and his colleagues, published in the journal Science, found no evidence of bias against women in the admissions process itself.
The unsettling part is how ordinary this is. Any time a rate is averaged across groups of very different sizes, the aggregate can point one way while every subgroup points the other. Medical trials, hiring records, sports statistics and exam results all hide versions of it. A single headline percentage can be perfectly accurate and still tell you the opposite of what is really happening underneath, which is why a careful statistician always asks to see the data split apart.
