Simpson's paradox
Women were admitted less often overall. In four of the six biggest departments they were admitted more often. Both statements are true.
Try it
Switch between the whole university and the six departments.
Real counts for the six largest departments (A to F), Berkeley, 1973, from the UCBAdmissions dataset in R.
What is going on
Averages across groups are weighted by how many people are in each group. If one kind of person tends to apply to the hard-to-get-into places, their overall rate looks poor even when they are treated as well as, or better than, everyone else in each place.
The paradox is not a mistake in the arithmetic. It is a reminder that a combined number answers a different question from a split one, and which question you want depends on what you think is causing what.
How to spot it
- A headline compares two groups using one overall percentage.
- The groups differ in size or in what they are choosing between.
- Ask: what does each sub-group look like, and why would people sort themselves into them?
Berkeley graduate admissions, autumn 1973
Applicants to the University of California, Berkeley were examined for sex bias because 44% of men who applied were admitted against 35% of women. Bickel, Hammel and O’Connell showed in Science that the gap came from where people applied: women applied in greater numbers to departments with low admission rates for everyone.
The demo uses the six largest departments (A to F) from the dataset distributed with R as UCBAdmissions. The figures are real counts from that dataset; this is not the whole university, so the six-department totals differ from the 44% and 35% quoted in the paper.