Marginal Revolution on the Male/Female Math Gap

Alex Tabarrok over at Marginal Revolution has an interesting post on media coverage of the recent Science paper that argued against gender differences in math test scores.

Tabarrok says that the media misreported the story and Larry Summers is still right.

Harvard Barbarian

I think it's hilarious that gender is one of the last categories to which people still apply Social Darwinist ideas with a completely straight face. All this hubbub about women lacking some innate ability to do math as well as men at the highest levels just recalls all of the stupid things people used to say decades ago about women's innate skills or foibles-- like how women were supposedly innately worse drivers, or conversely naturally gifted at cooking. So stupid. Yet people love to believe in these sorts of "natural" differences, because it's the easy way out!


For the record, the 2007 CPS shows that a higher proportion of women than men aged 25-34 in the U.S. have doctoral degrees. This would imply that, at least for younger cohorts, a. women outnumber men in disciplines other then math and science, and/or b. women are getting their degrees from lower quality universities. (For details, see here.) Clearly b is not a favorable outcome, but I doubt that that explains the majority of the difference. Why, then, is no one concerned by the fact that perhaps men are culturally discriminated against in the humanities? Equal opportunity is a two-way street...


the above comment RE: "Math tests don't measure math ability" - this is one of the biggest myths perpetuated by parents, some teachers, and of course kids. "Test don't measure X, therefore we should discount any tests". So now everyone gets a smiley face on their homework instead of a grade - because as we just proved grades are meaningless.

Test DO measure something, and very often measure something quite meaningful. Math tests measure ability to solve math problems. And they measure it pretty well. If you can't solve math problems, this probably doesn't bode well for your math abilities.

If you don't like math tests, look for gender makeup of participants in math or physics olympiads and various national competitions, similar to Putnam exams. Contrary to what some of the other posters claim, majorities of national teams are made up of male students, including countries such as Russia, Japan, India etc.
Interestingly enough, some muslim countries such as Iran or Turkey have typically higher percentage of female participants, but still far below 50%.



For me, the real story is why economic neo-liberals always seem so interested in any data that reinforce socially conservative agendas.

Sci Ed

Math test scores by their very nature do not measure innate ability. Therefore, whatever the results of the tests they do not address Summers' issue.

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Robert Berry

If men and women have equal average math ability, and the ratio of their std. dev is 1.16, then not only would there be more male math geniuses, more males who can't compute 2+2, but average scores for males would also be higher on any reasonable exam designed to test math ability (say, for instance, it scores linearly between -3 and 1 female in math ability). The average score for females on such an exam is 72.9%, while the average for males would be 77.5%.

Our exams likely favor populations with larger variance in ability.


Tabarrok's analysis is insightful, whether you agree with his conclusions or not, he clearly demonstrates that there were flaws in the media coverage. I wish there were more like it. Too many reporters have amazingly poor math skills. Understanding this sort of study requires some pretty exacting mathematical reasoning.

Sort of tangential to this topic, I participated in an experiment recently in which math teachers were asked to choose the most correct explanation for a number of different proofs. The explanations were given in groups of three for each proof ("pick the correct explanation from these three)", and were word for word the same no matter who was giving each explanation. And the math teachers were quite a bit more likely to think that men are correct than women when giving an identical explanation.


I have to agree with Harvard Barbarian.

The big problem with this sort of interesting science is that idiots [who aren't even among the elite male mathematicians] simply cannot avoid using it to advance political aims, generalizing minor abstractions into justifications for snatching a bigger piece for themselves.


lolphysics said "1. The gender ratio varies by ethnicity. Whether that's a nature or nurture thing is not discussed."

the asian american component maybe misleading b/c the 99th percentile is in relation to the entire population. if u look at the 99th percentile of only asian americans, u may see a different outcome.

PISA data shows that the M/F ratio of highest scorers in east asian nations is not 1:1 and in fact favors males.

George Shen

I think the new study can't prove or disprove Dr. Summers' hypothesis. Tabarrok is wrong to conclude that Summers is right. But he is right about the fact that many reports on the new study are wrong.

I can't read the full report because it is not free. But evidently, too many reports on the report are plain wrong. It seems to me that one conclusion we can draw already is that many journalists don't have a reasonable math/logical thinking skill from the way they interpret data. If the tests are standard math exams like the ones in SAT, GMAT,& GRE, I would suggest we all stop debating because it is not a good indicator for math talent. It's merely a normative test. Having a full score 800 in those tests doesn't mean you are a math genius, but it certainly will put you in the 99th percentile. In fact, I would argue that students with 780 or 790 (because of careless mistakes) potentially could have more math talent than the ones with 800. I had very decent math skill in high school and got into the Olympiad Math competition at national level in China (after winning the competition at municipal & provincial level) but I only got 780 in my GRE math portion while most of my fellow classmates who don't possess better math skill than I got 800, which really made me angry. This kind of BS test only makes the mediocre students who can ace easy questions happy. But it certainly doesn't test one's aptitude for math.

So the result from this kind test is almost meaningless. It doesn't prove or disprove Prof. Summers' point on male/female ratio disparity at the level of four standard deviations above the mean.



@ KP

Judith's point may be interesting, but by no means does that mean that it is correct. She gives no proof that what she states is actually the case. She might well have said that women on Venus INVENTED math.

In fact, the US seems quite well represented on a list of birthplaces of notable female mathematicians. So, contrary to Judith's belief, she may not have it so bad after all.


judith makes an interesting point, but doesn't back up her facts. Next she say that in japan, all the fastest sprinters are women. show me the data.



As I recall it, Summers mused only that a variance gap could be one contrbuting factor to explain an achievement gap. He suggested that other explanations, aside from straight cultural bias, should be evaluated as potential explanatory factors and cited the variance gap as an example; not that there is no cultural bias, but that it's possible it's not the only thing at work.

I'd disagree that these findings directly contradict his comments -- finding a variance gap would be the first step to showing that it contributed to an achievement gap.


Judith makes an interesting point. I would like this study (or a similar one) to be done in other cultures. But I find it very easy to believe that the incredibly smart men are balanced out by incredible stupid ones. I wonder if this would support an argument that women are generalists and men are specialists?


I don't understand why some people are so offended by this research. It may show that there (probably) are more extremely smart men than extremely smart women, but it also suggests that most women are smarter than most men. Shouldn't the gender warriors be happy with that?


@ lolphysics

Are you sure you read the article carefully? 99th percentile is roughly 2.25 SD, where, as the study notes, the gender variance is 2.0. But as is further explained, as the standard deviation goes up, so too should the gender variance number. Thus, by 4 SD (the group that Summers was referring to), the gender ratio is actually a little over 3:1. So on "innate ability" alone one should expect fewer than 25% females. Other factors (like whether anyone would even want to be a math genius) could also be considered, and it is probably worth looking at what the margin of error in that 15% is when you are dealing with the top .1% of the math population.

Thus, the point of Summers' comments (that the huge gender disparity might not be a nefarious cultural bias) IS vindicated by the facts of the article, when you really look at it.



I also haven't read the Science article, but your point about the tests insensitivity to 4+ standard deviations was the point as all those 4+ standard deviations above the norm would have had perfect scores. So the difference between male and female performance at very high levels could be even greater than the test would have measured. It seems odd to suggest the smaller pool of top females would contain more math rock stars than a larger sample of males.

I tend to agree with your point on "innate" math ability though. Even if we accept differences in some innate abilities, there is no reason to believe those differences correspond to what it takes to be a great mathematician or that there even is one thing, other than an interest in math, that creates a good mathematician.

Basically, it doesn't matter what is in your skull, it matters if you can do the math.


Unsurprisingly, in different cultural environments these gender ratios do not hold. For example, in Russia and much of Eastern Europe the most prestigious math posts are held by women. In India, and Japan, many of the top math performers are women. Maybe it's something in the water?

Or just maybe, it's something cultural.


What Summers said has always been true in the factual sense but it is not true in the political sense. There are always things which can be said and things which can't. The political point, apart from whatever faculty antipathy there was toward him personally, was that he was provocative about the wrong subject at the wrong time.


"It's a reflection of the bias in our culture, not of the inherent abilities of boys and girls."

that's incorrect. tabarrok only says that the standard deviation between males and females differs. he doesn't say the cause of the SD difference is culture.