All-male physics departments are not necessarily more biased than other departments

I learned via my former student Brent Follin about a study performed by the American Institute of Physics on the distribution of women on the faculty of US physics departments. Inside Higher Ed has a summary.

The specific question they were looking at is whether physics departments whose faculty are 100% male are discriminating against women. From Inside Higher Ed:

More than one-third of physics departments in the United States lack a single female faculty member. That figure has been cited by some as evidence of discrimination. With women making up just 13 percent of the faculty members (assistant through full professors) in physics, could there be another explanation?

The authors, being physicists, answer this with a simulation. They show that, given that the overall percentage of physics faculty members is so low, the number of all-male departments is not surprising. To be specific, if you start with a pool of candidates that’s 13% female, and distribute them at random among physics departments (many of which have a pretty small number of faculty members), you’d get a distribution pretty similar to the actual one. In fact, you’d actually get more all-male departments under the random-distribution scenario.

Bizarrely, the original study says

Our results suggest that there is no bias against hiring women in the system as a whole.

This sentence strikes me as nearly the exact opposite of an accurate description. Here are two things that I think they could say:

1. Our results do not show evidence either for or against the hypothesis of bias against hiring women in the system as a whole, because the study was not designed to answer this question.
2. Our results show no evidence that all-male departments are more biased against hiring women than other departments.

Maybe it’s obvious what I mean here, but let me blather on a bit anyway.

The results show that, given the low percentage of women in the overall pool of people hired, you’d expect about as many all-male departments as there actually are (or even more). It doesn’t say anything about why the pool has so few women in the first place. That could be due to bias, or it could be due to other reasons: women might self-select out of careers in academic physics before they get to the faculty level, for instance, or women might be intrinsically less qualified than men (the latter is the “Larry Summers hypothesis,” which I emphatically do not endorse but which is a logical possibility [UPDATE: Phillip Helbig points out correctly that this is a mischaracterization of Summers. See his comment below.]). Since the study, by design, has nothing to say about why the pool skews so heavily male, it’s ridiculous to suggest that it supports any conclusion about whether there is bias in the “system as a whole.”

Here’s what the study does suggest: whatever factors are causing the overall pool to be heavily male, those factors are more or less evenly distributed across departments. If, for instance, some departments were heavily biased while others were strongly egalitarian, you’d expect women to be clustered in some departments and absent from others. The study shows that that’s not the case. If anything, the gender distribution is less clustered than you’d get by chance.

Despite my complaints, that’s an interesting fact to know. If you believe (as I do) that we could and should be doing better at getting women into physics and related fields, it makes a difference whether the problem lies in a few “bad apple” departments or is more evenly distributed. This data set suggests that it’s evenly distributed.