Summers Vindicated; Feminists Spinning

From Jeff Fecke, the new guy at Alas, a bit of feminist triumphalism regarding a study finding no significant difference in math performance between boys and girls:

So, people, do you remember Larry Summers? Poor, poor Larry Summers, who was attacked mercilessly by those humorless feminists, just because he said women weren’t as good as men at math? He’s been held up by the gender essentialist set as a martyr to the cause of political correctness, convicted in what professional concern-troll William Saletan called a “pseudo-feminist show trial” for daring to give voice to the truth: that women are simply inferior to men when it comes to math. Though they do, I’m told, excel at baking.

This was all very horrible for poor Larry, except for the fact that he was absolutely, categorically wrong. As most of the feminist meanies already knew, women aren’t inferior to men in ability to learn math, science, or anything else. And now we have the data to prove it.

This is very wrong. First off, Fecke's characterization of Summers' argument is almost libelous in its inaccuracy. Summers gave three hypotheses for the underrepresentation of women in math and science, in what he believed was descending order of importance:

1. Women are, on average, less willing or able (e.g., because of the demands of motherhood) to make the commitment of time and energy needed to succeed in highly competitive careers.

2. Although men and women are roughly equally intelligent on average, the male intelligence distribution has higher variance, so men are overrepresented at both tails of the distribution, which is where academics come from*.

3. Differential socialization.

Nowhere did Summers say anything about women being inferior to men, either in general or in terms of math ability. A study finding that boys and girls perform on average equally well on a test of basic math skills is perfectly consistent with everything Summers said.

A couple of commenters pointed out this error, but were quick to assert their feminist bona fides by saying that Summers was wrong about the variation too--that men aren't really overrepresented at the tails of the intelligence distribution. This is wrong. They are, and the study in question backs this up, even though the press release explicitly says otherwise:

Some critics argue, however, that even when average performance is equal, gender discrepancies may still exist at the highest levels of mathematical ability. So the team searched for those, as well. For example, they compared the variability in boys' and girls' math scores, the idea being that if more boys fell into the top scoring percentiles than girls, the variance in their scores would be greater. Again, the effort uncovered little difference, as did a comparison of how well boys and girls did on questions requiring complex problem solving.

I guess it depends on how you define "little." According to this supplement (PDF), the study did find that at the 99th percentile, white boys outnumbered white girls 2 to 1:

For whites, there are 1.45 times as many boys as girls above the 95%ile in grade 11, and twice as many boys as girls above the 99%ile.

Interestingly, this pattern did not hold among Asian Americans:

For Asian Americans, however, at the 99%ile, the gender ratio is 0.91, meaning that more girls than boys scored above the 99%ile.

Also, if you look at table S2 in the supplement, you'll see a fairly large negative effect size for maleness specific to blacks and American Indians--that is, they scored on average 8-9% lower than their female counterparts.

See also the table on page 9 of this document (PDF) from the College Board. In 2004, boys were 2.2 times as likely as girls to score 750+ on the math section (97.8th percentile). The study mentioned above comments on the fact that the average SAT score is higher for boys than for girls and chalks it up to sampling bias (more girls than boys take the SAT), but there's no mention of the sex imbalance in the 700+ range.

To point out what should be obvious, the fact that males outnumber females at the tails of the math ability distribution doesn't mean that we have to tell girls who are good at math that they can't become physicists or mathematicians or software engineers**. It just means that we can't take underrepresentation of women in these fields as a priori evidence of systematic discrimination.

See also Bob Hayes, who should quit slacking off and get back to blogging.

*No comment on which disciplines draw from which tails.

**I'm all for more women in my workplace, albeit for distinctly non-feminist reasons.

Share this

Smart Asians

Interestingly, this pattern did not hold among Asian Americans:

For Asian Americans, however, at the 99%ile, the gender ratio is 0.91, meaning that more girls than boys scored above the 99%ile.

Reading through the comments on Alex's entry at Marginal Revolution, I found this comment by JL:

Here is a question, are those asians the top 1% of asians, or are they the asians that made it into the general top 1% of students? Because those two sets are not the same due to higher average asian achievement compared to whites. If the study used asians in the top 1% of the general population, then it is entirely possible that that set includes far more than 1% of asians. Thus we would be talking about less standard deviations above the asian mean of achievement.

Heather MacDonald writes about this study here. She points out that,

Among white 11th-graders, there were twice as many boys as girls above the 99th percentile—that is, at the very top of the curve. (Asians, however, showed a very slight skew toward females above the 99th percentile, while there were too few Hispanics and blacks scoring above even the 95th percentile to compute their gender ratios.)

So it seems that you're right: more than 1% of Asians in the study are probably above the "99th percentile". This might explain the lack of Asian male overrepresentation comparable to white male overrepresentation at high percentiles. It's possible that the 99th percentile of the general population is the 95th percentile for Asian, or something like that.

Seems as though it might explain it. But it's not entirely clear from the above what the researchers did: did they look specifically at the Asian-only distribution, or did they look at the whole-population distribution, comparing Asians in the top 1% of the whole population. Whether JL's comment explains it will depend on that.

What he said.

Have you seen Roy Baumeister’s 2007 address to the American Psychologoical Association, “Is There Anything Good About Men?” He provides 12 pages of review of gender disparity data as well as an explanation routed in evolutionary psych. I’m not really qualified to evaluate it, but it sounds plausible to me:

Oh yeah, and what you said about Hayes.

The variance difference has been substantially decreasing

From ""Sex, Math, and Scientific Achievement" by Halpern et al. in Scientific American Mind, November 2007"

Although it has drawn little media coverage, dramatic changes have been occurring among these junior math wizards: the relative number of girls among them has been soaring. The ratio of boys to girls, first observed at 13 to 1 in the 1980s, has been dropping steadily and is now only about 3 to 1.

I find this fascinating, and it argues against the variance difference being mainly biological, which I find quite surprising.

both tails

"men are overrepresented at both tails of the distribution, which is where academics come from"

Yep. My experience has been that academics come from both tails of the intelligence distribution. In any given academic field, it often seems that most come from the lower tail of the distribution. But, this tail is actually under-represented in practicing academics because administrators are preferentially selected from it.

Summers is too PC

Ages ago when I was majoring in Physics in college, the campus feminists discovered that women were seriously under-represented in that discipline. They started a major campaign against the Physics Dept because of it. Of course the students were bewildered; nothing could be more false than that a bunch of Physics nerds didn't want any girls around. Likewise for the professors. I thought the whole thing was pretty silly.

Summers understates things in my opinion. There are actually significant differences in the sexes in the sorts of abilities you need for disciplines like Physics and computer hardware engineering (although not for software engineering, apparently). This is plain to see, in any computer company. The alternative hypothesis, that companies across the board discriminate when selecting computer hardware engineers (discarding feminine talent in that area), but not software engineers, is rather implausible.

Get over it, feminists - men and women are not the same. Each have their own areas of expertise and latent talent.

The alternative hypothesis,

The alternative hypothesis, that companies across the board discriminate when selecting computer hardware engineers (discarding feminine talent in that area), but not software engineers, is rather implausible.

That is not the alternative hypothesis. The alternative hypothesis is that although girls are as genetically gifted to do computer hardware engineering, they do not generally end up in those jobs. Discrimination is only one possible alternative explanation, it could be that parents educate girls differently, etc.

I'm pretty much convinced that
- it's genetic
- for the most part a matter of taste (they can but don't want to), and to a lesser extent a difference in abilities.

Just pointing out that your argument is flawed.


The underrepresentation of women in high-level math and science must be genetic, because there's nothing else stopping women from getting up there.

Nowadays, any American girl who shows the slightest interest in these subjects is not-so-gently pushed toward the pursuit of academic stardom. Scholarships abound, along with enrichment summer programs for girls in math, science, space exploration and other stuff most girls find sort of dull and impersonal.

I don't know about variation across races, but these sex differences seem to come from what we've selected for as mating characteristics. Women are attracted to brilliant men who have lots of practical knowledge and gain status through achievement in the labor market. Men are attracted to hotties. Thus, it would be counterproductive for a girl to spend 15 hours/day in a chemistry lab, even if she had the requisite abilities.