The Paradox in the Admissions Office

In the autumn of 1973, about 44 per cent of men who applied to graduate school at Berkeley were admitted. For women, it was 35 per cent. With over twelve thousand applicants, a gap that size is not an accident.

So the university's own statisticians went looking for the guilty departments, the ones admitting men and turning away women. They broke the figures down, and this chart shows the six largest.

And here is the thing. In four of those six departments, women were admitted at a higher rate than men. In department A the gap was enormous, and it ran the other way: 82 per cent of women to 62 per cent of men.

The other two gaps were small. Nothing here looks like a bias against women. So how can every part of a picture lean one way, while the whole of it leans the other?

Because of where people applied. Each circle here is a department, placed by how easy it was to get into. Its size shows how many applied. Men flooded the departments that were easy to get into.

Women applied mostly to the departments that were hard to get into, where nearly everybody is turned away, whoever they are. The overall gap came from which door people knocked on, not from how they were treated when they got there.

This is Simpson's paradox: a trend in groups can vanish or reverse when the groups are combined. Which question is the right one depends on what caused what, and no spreadsheet will tell you that.