Simpson's Paradox and Statistical Urban Legends: Gender Bias at Berkeley the refsmmat report · a blog at refsmmat.com

Introductory statistics textbooks usually point out Simpson’s paradox, an interesting phenomenon that’s usually illustrated with a story from the University of California, Berkeley. The story goes something like this:

In 1973, UC Berkeley was sued for gender bias, because their graduate school admission figures showed obvious bias against women:

Applicants Admitted Men 8442 44% Women 4321 35%

Men were much more successful in admissions than women, leading Berkeley to be “one of the first universities to be sued for sexual discrimination”. (The difference is statistically significant with p ≈ 10-26!) The lawsuit failed, however, when statisticians examined each department separately. Graduate departments have independent admissions systems, so it makes sense to check them separately—and when you do, there appears to be a bias in favor of women.

How does this happen? The simple explanation is that women tended to apply to the departments that are the hardest to get into, and men tended to apply to departments that were easier to get into. (Humanities departments tended to have less research funding to support graduate students, while science and engineer departments were awash with money.) So women were rejected more than men. Presumably, the bias wasn’t at Berkeley but earlier in women’s education, when other biases led them to different fields of study than men.

Now, this example has been analyzed to death in many places: on Wikipedia, in various blogs, in many textbooks (including my own book), and pretty much everywhere else. I’m not going to present a new analysis of the data or of Simpson’s paradox.

I just want to point out something simpler: There never was a lawsuit!

The real Berkeley story A Wall Street Journal interview with Peter Bickel, one of the statisticians involved in the original study, makes clear that Berkeley was never sued—it was merely afraid of being sued: Simpson’s Paradox has fooled many. In the fall of 1973, for instance, the University of California, Berkeley’s graduate division admitted about 44% of male applicants and 35% of female applicants. That raised eyebrows among school officials, who feared bias and asked Peter Bickel, now a professor emeritus of statistics at Berkeley, to analyze the data. “The associate dean of the graduate school thought that the university might be sued,” Mr. Bickel says. When Mr. Bickel and his colleagues scrutinized the data, they found little evidence of gender bias. Instead, they discovered that more women had applied to departments that admitted a small percentage of applicants, like English, than to departments that admitted a large percentage of applicants, like mechanical engineering. The core paradox matches the usual story, but no lawsuit was involved. I’ve done some digging and I haven’t been able to find the original source of the mythical lawsuit—perhaps an early textbook or journal article author misheard the original story, wrote about a lawsuit, and authors ever since have copied the story unchanged.