The LA Times, recently ran an article arguing that a study investigating the math skills of women and men undermined Summers’ claim that biological reasons may actually play a part in the explanation for the difference between men and women in professorial positions in math and science. Yet, it seems like it’s the pressed who missed the mark.
A number of recent studies have confirmed Larry Summers’ much debated remarks regarding the relative dearth of tenured female professors in the fields of Math, Physics, and other mathematically intensive subject areas. While media reports have argued that recent studies have undermined Summers’ argument, they are rather fast and loose with the findings. Essentially, what the studies have found is that average mathematical ability across the two genders is statistically even- which leads the mathematically maladroit press to assume that this means that Summers was wrong- that there is no difference between the genders in mathematical ability. However, when you’re talking about the relative prevalence of women in the ranks of phd professors the average mathematical ability is almost completely irrelevant. Men and women with average mathematical ability do not become professors in math or physics. Rather, it is the individuals that are three or four standard deviations from the mean that enter the world of high-level mathematics. Quoting Summers:
“…if one is talking about physicists at a top twenty-five research university, one is not talking about people who are two standard deviations above the mean…But it’s talking about people who are three and a half, four standard deviations above the mean in the one in 5,000, one in 10,000 class. Even small differences in the standard deviation will translate into very large differences in the available pool substantially out.”
Apparently, numerous studies have shown that the variance of ability among men is a lot higher than it is among women- that is, among a sample of men, there will be more mathematical geniuses and more mathematical morons than a comparable group of women. The group of women will be characterized by fewer idiots, but a correspondingly smaller number of math prodigies. The averages will be the same for both samples, but the distribution of ability in the two groups will differ significantly. Perhaps Summers did not deserve the amount of criticism he received.
Of course, while the raw number of mathematically skilled (by skilled I mean 99th percentile or higher) women may simply be smaller than the number of similarly skilled men, it does not necessarily follow that this explains the discrepancy between men and women in prestigious math positions. It is merely a contributing factor. The question of the extent of the sexism in higher education – and sexism in the guidance of intellectual pursuits for young boys and girls when they are in elementary school – remains unanswered.
I borrow heavily in this entry from a post at Marginal Revolution, but I wanted to put it in my own words and perhaps prompt some discussion.
For further reading, references here: