## The math wars

If there is one figure who neatly divides feminism and economics, it is Larry Summers. The now ex-president of Harvard drew a great deal of criticism in 2005 after suggesting that women’s under-representation in science and engineering was due in part to differences in ability. Among most feminists, Summers’ name is synonymous with pseudoscientific sexism. But Summers is an economist, and many other economists seem to see him as something of an intellectual martyr.

This week, both sides of the debate have more or less claimed victory – and they are citing the same paper (gated), just published in Science. Compare Alex Tabarrok’s post at Marginal Revolution with Jessica Valenti’s post at Feministing. So how did this happen?

**What the study actually says**

The Feministing post, and most of the mainstream media’s coverage of the study, focus on its main finding: using 7 million students’ standardized tests scores from across the United States, Hyde et al have shown that the average girl is as good at math as the average boy. This holds for all ethnic groups, and for average students tackling difficult material as well as basic skills. This is an important finding, and I’m glad it’s getting some attention.

Most people who seriously argue that ability is at the root of men’s dominance in mathematical fields, however, are not talking about the average – they are talking about the variance. In layman’s terms, the variance measures how spread out data is, or how far most individuals are from the average. The Science study’s second finding is that the boys’ scores have a higher variance than the girls’ scores.

The studies’ authors note that the difference in variances is not very large, but as Tabarrok points out, it’s tough to discount when you focus on the very top of the distribution. In this study, if you look only at students in the 99th percentile of mathematical ability, white boys outnumber white girls two to one. (There is an imbalance among Asian and Pacific Islander children as well, though it is smaller, and there wasn’t enough data available for other ethnicities.)

In short, boys are more likely to be exceptionally bad at math, and more likely to be exceptionally good at math. Of course, we should ask what causes higher variance. It could be the product of nature *or* nurture.

**What it means for women in economics**

The Marginal Revolution comment thread has focused on this hypothetical:

If a particular specialty required mathematical skills at the 99th percentile, and the gender ratio is 2.0, we would expect 67% men in the occupation and 33% women. Yet today, for example, Ph.D. programs in engineering average only about 15% women.

First of all, I can’t believe that success in economics requires mathematical ability in the 99th percentile. Economics is not pure mathematics, and even if it was, getting through a Ph.D. program is more about perseverance than IQ. (And we know what hostile, sexist environments can do to perseverance.) I’d like to see some studies of mathematical ability among actual economics professors. I bet most wouldn’t be above the 90th percentile.

Second, notice that even in their example, undoubtedly more empirically challenging than economics, by this model the number of women in the profession should double. Fifteen per cent to 33 per cent is a significant gap. I’m reminded of debates over the wage gap, where 15 per cent becomes “insignificant” in some economists’ hands.

Third, let’s remember for a second that economics is a social science. Great economic theory draws on all sorts of skills, perspectives and experiences. To the extent that we want to answer questions about the real world, women’s perspectives are necessary.

“I’d like to see some studies of mathematical ability among actual economics professors. I bet most wouldn’t be above the 90th percentile.”

I’d take that bet. Think about the GRE. What percentile do most grad programs require you to be in. I know that in the top places, anything below 90th percentile would almost certainyl disqualify you. Now remember that the GRE percentiles are among people planning on going to graduate school, which is certainly less that .1 of the whole population, so the 90th percentile on the GRE could very likely be more like the 95+ percentile in the population.

PLW29 July 2008 at 9:23 pm

I find it so amusingly vain that so many academics often think that the upper 99th percentile is somehow relevant to them! It shows that somewhere in their minds they believe that the only reason someone wouldn’t go into academia is because they weren’t smart enough. Which is pretty funny, when you think about it.

If I had to guess, I would say that mathematically inclined economists are probably drawn from the upper 75th percentile of mathematical talent of the whole population. That is just an guess based on my experience being a mathematically inclined academic.

yolio30 July 2008 at 12:23 am

[…] science | Tags: feminism, math, science, women in math, women in science | by Stephen Malczin The Economic Woman writes up an excellent post bringing up some important points in the recent University of Wisconsin study about the vanishing […]

Following up on Girls=Boys @ Math « The Eclectic Hedonist30 July 2008 at 2:27 pm

“I would say that mathematically inclined economists are probably drawn from the upper 75th percentile of mathematical talent of the whole population. That is just an guess based on my experience being a mathematically inclined academic.”

Are you kidding me? The person sitting at the 75th percentile of the math aptitude distribution doesn’t even understand calculus. I think you have a very skewed idea of the math ability of the general population, maybe because you mix with a lot of mathematically inclined academics.

The average person who is considering economics graduate school gets just over a 700 in the GRE math, which puts her just above the 70th percentile of GRE takers. Those are actually admitted and matriculate average even higher than that, and those that actually complete a degree and work as economists, higher still. Now unless you want to argue that the average person who takes the GRE is just about as mathematically able as the average person who doesn’t, it’s absurd to argue that “the most mathematically inclined economists” are from the upper 75th percentile.

PLW30 July 2008 at 10:33 pm

After reading this I had two thoughts

(1) “In short, boys are more likely to be exceptionally bad at math, and more likely to be exceptionally good at math.”

My primitive understanding of evolutionary biology is that most of the evolutionary changes has taken place on the Y chromosome (thus men are more likely to get a chromosomal disease and it has shrunk over time). Because of this, for certain abilities (like maybe spatial abilities) we should expect more men to be at both tails of the distribution curve then women. On the other hand (a) we don’t know that math is such an ability and (b) a 2 to 1 ratio in the tale probably indicates some social factors (such as gender role expectations) as well.

(2) As a female who majored in math (going to grad school in the social sciences though) I would think that measuring the gender ration math majors and math Ph.D.s rather than economics or or engineering would be a better measure of women breaking the “math ceiling” but that’s just my math chauvinism coming through – I would expect a winnowing function where people good at math go to math and physics and then engineering and then the social sciences at the undergrad level.

Then there is a further winnowing function in math where only people extremely good at math go on to a math Ph.D. (and weirdly we knew who those guys were early in the program) while those who were merely good pursue other avenues of interest (I was good, thus I was a major, but not extremely good so no math PhD. OTOH I was always interested in the social sciences so I’m there now but not in economics because that subject didn’t really interest me).

EB31 July 2008 at 12:23 pm

I very much agree with:

“First of all, I can’t believe that success in economics requires mathematical ability in the 99th percentile…”

I suspect that most doctoral economics programs probably do not in general draw the 99th percentile of mathematical ability. I’m thinking most of those people actually enter math or physics related programs. Note, I’m saying in general. At top programs, certainly there is more emphasis on mathematical ability and certainly in terms of economic theory. If you’re going to be a theorist in econometrics, obviously you need a high degree of mathematical abillity.

But, most economics PHDs are not theorists. Most dissertations are done on labor related topics. Labor economics is not particularly mathematically intensive (again when compared to pure econometric theory).

Eric16 September 2008 at 12:14 am

Summers presided over a rapid and remarkable decrease in the number of women at Harvard. If he had been someone whose decisions and leadership was strictly theoretical, then his comments may have been less damaging. Instead, he was someone whose leadership coincided with a closing of doors for women. And, given an option to understand why this possibly could have happened, he basically blamed women for being inferior.

btw ………….

Science 30 May 2008:

Vol. 320. no. 5880, pp. 1164 – 1165

DOI: 10.1126/science.1154094

Analysis of PISA results suggests that the gender gap in math scores disappears in countries with a more gender-equal culture.

Jean18 November 2008 at 10:07 pm

[…] The math wars […]

Role models and the STEM gender gap « economic woman16 May 2009 at 12:53 pm