Greater biological variability cannot explain differences in opportunity

You've probably heard this story many times before: there's some kind of glass ceiling in the world of science and math that hinders women's ability to progress. The latest data confirms that something is going wrong.

The United States ranks 31st on the World Economic Forum's Gender Gap Index and is tied for 21st on Social Watch's Gender Equity Index. Still, the test scores of U.S. high school girls have reached parity with those of boys, and half the undergraduate math degrees awarded in this country go to women.

But after that, something goes off the rails. Just 27% of math Ph.D.s go to women. Exactly the same percentage -- 27% -- of people with careers in science, technology, mathematics, and engineering (STEM) fields are women. Women constitute a very similar number -- 30% -- of STEM college professors.

This is a problem, and not just from an equality standpoint, says math professor Rebecca Goldin, an associate professor of mathematics at George Mason University in Fairfax, Virginia, and director of research at the university's Statistical Assessment Service. "Scientific and mathematical progress relies on the best people doing their best work," she says. "If you discourage half the population [from doing science], then that part is simply not in your pool of who's the best, so the best science doesn't happen."

Now cue the apologists. The most common explanation I hear for the disparity, over and over again, is that it's an accurate reflection of ability: men do better at the higher ranks of science and math because they have better brains. And the most frequent rational for that is the greater male variability hypothesis: the bell curve of performance for women is better tuned to achieve a greater likelihood of median ability, while men are more erratic — they produce more damaged, faulty brains than do women, but at the same time, they produce more brilliant brains. The male population exhibits greater extremes.

This has never made any sense to me.

There are deleterious traits which men have at higher frequency than women: color blindness, for instance, or hemophilia. The explanation for those is that they're X-linked, so males are hemizygous and when they carry a defective allele are less likely to carry a complementary healthy allele at that locus. There is also a known higher incidence for objectively measurable mental defects in males vs. females, diagnosable at birth. Again, the likely explanation is that hemizygosity for all those loci on the X chromosome makes males more vulnerable to developmental and genetic errors.

But how does this lead one to conclude that the greater variability should lead to greater beneficial variability? An expansion of the left tail of the distribution does not imply that there has to be an equivalent expansion of the right tail. For example, males also exhibit greater infant mortality in females. There is no compensatory reduction of male mortality in old age. The mortality curve shifts left for us men; it didn't broaden to give those of us who made it to middle age an advantage over women in our cohort to reach greater old age.

And I note that there is never any specific explanation of a mechanism that would allow greater variability to promote greater intelligence in males. There is much flapping of hands over the greater male frequency of autism, reading disorders, juvenile delinquency, etc. (all true), and then a dangling "therefore…" leading to the conclusion that there must be compensatory intellectual benefits for men. It's basically little more than an appeal to the belief that the universe must be fair, and must grant us guys as a population a benefit to make up for the bad deal we get as babies.

Guess what? The universe isn't fair.

It is conceptually possible that the universe could have screwed over the females or the males of our species. We know, for instance, that human physiology carries specific mechanisms that increase male body size over that of women; you could imagine a species in which there was a similar coupling of hormones to brain growth, and in a science fiction world you could imagine a race with great gender disparities in intelligence. That doesn't seem to be our world, though, and it also wouldn't make sense to explain such a phenomenon by greater noisy variation. But you can't explain that possibility away by saying it wouldn't be fair for our biology to so discriminate against one sex: again, the universe isn't fair.

You have to look at the data. And the data all seem to be saying that men and women who make it to the point of entering the academic world have roughly equal intellectual potential, and that the differences between them are shaped by sociocultural influences, not biology.

To analyze some of the theories put forth for the math gender gap, Kane and Mertz looked at internationally standardized scores for the 2003 and 2009 OECD Program for International Student Assessment math tests and the 2003 Trends in International Mathematics and Science Study. These two datasets include data from 86 countries with a 31-country overlap. If the greater male variability hypothesis, which posits that men have a greater range of intelligence than women, is true, then that variability would persist, consistently, across all 86 countries.

Instead, "For any given country, you quite reproducibly measure the same variance ratio," Mertz says. But between countries the variance ratio changes. Persistent cultural factors, in other words, seem very important in setting variance ratios. "That was one thing that really shocked me," Mertz says.

Some scholars have speculated that coeducational schools put women at a disadvantage in learning math. But Mertz and Kane's research found that gender-segregated schools make no difference in improving math scores for girls or boys.

And while the test scores of children from the poorest countries were affected by poverty, all correlation with per capita GDP ends at $11,500. After that, gender equity -- as measured by the World Economic Forum and Social Watch -- is the only factor they studied that's positively correlated with improved test scores for girls and for boys. "It's very reproducible from exam to exam," Mertz says. "If we were willing to speculate, one thing the U.S. might do to improve math performance would be to pass the Paycheck Fairness Act and the Equal Rights Amendment to the U.S. Constitution."

Well, changing a few laws isn't necessarily going to change people's attitudes, so I'd disagree with her there. But as a reflection of deeper problems in how we perceive science and math and women and men, yes, she has a point.

Mertz cites a shirt famously removed from racks at the American retail clothing chain Forever 21 earlier this year as an example of the unhealthy attitude towards math in U.S. culture. The shirt said, simply, "Allergic to Algebra."

"'Allergic to Algebra'?" Mertz says. "This is what's being sold in the U.S. in 2011? Whereas there's a book in Japan [for teenage girls] called Math Girls. That book is essentially an introduction to topics you would see as a hardcore math major in college, and this is a bestseller in Japan. It's in its 18th printing; they've had three sequels. Can you imagine that in the U.S.?"

There is no denying that the most important factor contributing to academic performance is cultural, not biological. Biology sets the limits, but culture determines what you do within those boundaries, and clearly, we have lots of room for improvement in intellectual accomplishment; most people aren't bumping up against the physical limitations of what their brains can do. What we should be doing is looking at our people, and trying to do better. Less than 30% of the professoriate are women? That doesn't say women aren't as smart, it should be seen as missed potential, and we should be working harder to give every man and woman equal access to the chance to excel. 65% of men and 72% of women graduate from high school? Let's figure out what's holding the men back and fix it.

The great crime here is when people try to claim that these differences are hardwired and nothing can or should be done about them. Brains are plastic to a degree that makes minor potential differences between sexes and races negligible.

(Also on FtB)