The Mechanism
In the autumn of 1973, the University of California, Berkeley appeared to be discriminating against women in graduate admissions: across the university, 44% of male applicants were admitted versus only 35% of women — a gap far too large to be chance. The case became one of the most cited examples of statistical bias. Then statisticians Peter Bickel, Eugene Hammel, and J. William O'Connell broke the numbers down department by department, and the bias vanished — even reversed. In most departments women were admitted at the *same or a higher* rate than men. The aggregate gap came from where people applied: women disproportionately applied to the most competitive departments (humanities, with low admission rates), while men applied more often to less competitive ones (sciences and engineering, with high admission rates). A trend that holds inside every subgroup can flip when the subgroups are merged — a counterintuitive reversal now called Simpson's paradox (after Edward Simpson's 1951 paper, though Karl Pearson and Udny Yule had noted versions decades earlier). The unsettling lesson: the same true numbers can tell opposite stories depending on whether you zoom in or out, and the aggregate is not always the honest view.
Why It Matters
This case is remarkable because both summaries are true, yet they seem to disagree. Looking at all applicants together, Berkeley appeared to favor men. Looking department by department, the apparent bias mostly disappeared. The puzzle comes from mixing groups that have very different admission rates and very different numbers of applicants. It shows that an overall average can hide what is happening inside the parts, especially when the groups are unevenly sized. That reversal is one reason statisticians still use the Berkeley case to teach Simpson's paradox and to warn readers to check how data were collected and combined.
Wait — That's Not Quite Right
A common mistake is to assume that one overall percentage always gives the fairest picture. But when different groups have different baseline chances, the combined number can be misleading. At Berkeley, women were not admitted at lower rates in most departments; the overall gap came from applying more often to the hardest-to-enter departments. The right conclusion is not that the total number is fake, but that it answers a different question from the department-by-department numbers.
Vocabulary
- statistics
- admissions
- aggregate
- subgroup
- department
- bias
- Simpson's paradox
- distribution
- rate
- reversal
- applicant pool
Quick Quiz
5 questions · For classroom or kitchen table
The Experiment
Sort a Mini Admissions Puzzle
Write down 20 pretend applicants on slips of paper - 10 labeled 'A' and 10 labeled 'B'. Make two groups of pretend departments on another sheet: one 'hard' group with a low admit rate and one 'easier' group with a higher admit rate. Then decide that most A applicants applied to the hard group and most B applicants applied to the easier group. Record the admit rate for each group and then combine the totals. You will see how the overall numbers can look different from the numbers inside each group.
A parent or teacher can help make the rates simple, such as 2 out of 10 for hard and 8 out of 10 for easier. The point is not to copy Berkeley exactly, but to see how mixing groups can change the story. Afterward, talk about which question each total answers: 'How did each group do?' or 'What happened overall?'
paper, pencil, 20 small slips of paper or cards, adult supervision for setting up the example
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