Academic programs presumably want people with high ability. The GRE bills itself as an ability test, and under our expanded definition of ability this is a reasonable claim. So let’s talk about what would happen if programs selected based solely on ability as measured by GREs.
This is, of course, not the whole story. Programs also use a lot of other things like grades, interviews, and publications. But these are all correlated with GRE scores, and anyway it’s nice to have a single number to work with. So for now let’s suppose colleges accept applicants based entirely on GRE scores and see what happens. The STEM subjects we’re looking at here are presumably most interested in GRE Quantitative, so once again we’ll focus on that.
Mathematics unsurprisingly has the highest required GRE Quantitative score. Suppose that the GRE score of the average Mathematics student – 162.0 – represents the average level that Mathematics departments are aiming for – ie you must be this smart to enter.
The average man gets 154.3 ± 8.6 on GRE Quantitative. The average woman gets 149.4 ± 8.1. So the threshold for Mathematics admission is 7.7 points ahead of the average male test-taker, or 0.9 male standard deviation units. This same threshold is 12.6 points ahead of the average female test-taker, or 1.55 female standard deviation units.
GRE scores are designed to follow a normal distribution, so we can plug all of this into our handy-dandy normal distribution calculator and find that 19% of men and 6% of women taking the GRE meet the score threshold to get into graduate level Mathematics. 191,394 men and 244,712 women took the GRE last year, so there will be about 36,400 men and 14,700 women who pass the score bar and qualify for graduate level mathematics. That means the pool of people who can do graduate Mathematics is 29% female. And when we look at the actual gender balance in graduate Mathematics, it’s also 29% female.
Vast rivers of ink have been spilled upon the question of why so few women are in graduate Mathematics programs. Are interviewers misogynist? Are graduate students denied work-life balance? Do stereotypes cause professors to “punish” women who don’t live up to their sexist expectations? Is there a culture of sexual harassment among mathematicians?
But if you assume that Mathematics departments are selecting applicants based on the thing they double-dog swear they are selecting applicants based on, there is literally nothing left to be explained.
I am sort of cheating here. The exact perfect prediction in Mathematics is a coincidence. And I can’t extend this methodology rigorously to any other subject because I would need a much more complicated model where people of a given score level are taken out of the pool as they choose the highest-score-requiring discipline, leaving fewer high-score people available for the low-score-requiring ones. Without this more complicated task, at best I can set a maximum expected gender imbalance, then eyeball whether the observed deviation from that maximum is more or less than expected. Doing such eyeballing, there are slightly fewer women in graduate Physics and Computer Science than expected and slightly more women in graduate Economics than expected.
But on the whole, the prediction is very good. That it is not perfect means there is still some room to talk about differences in stereotypes and work-life balance and so on creating moderate deviations from the predicted ratio in a few areas like computer science. But this is arguing over the scraps of variance left over, after differences in mathematical ability have devoured their share.
Scott Alexander, “Perceptions of Required Ability Act As A Proxy For Actual Required Ability In Explaining The Gender Gap”, Slate Star Codex, 2015-01-24.
August 14, 2016
QotD: Women in graduate math programs
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