In yesterday's post, we discussed sex differences in achievement and ability. Few were identified. For the most part, however, this research discussed average differences. The problem with only discussing averages is that people engaged in science and math careers are far from "average" when it comes to math and science ability. Math and science professors often score in the top 1 percent -- or higher -- on standardized math tests.
It's entirely possible that the top 1 percent looks very different from the average results for the population. Consider this graph of test scores from two different groups:
The vertical axis of the graph is the number of people achieving each score on the test. Even though Group 1 has a higher average score than Group 2, there are still more members of Group 2 at the top of the scale (and at the bottom). Group 2's scores are more spread out, more variable than scores of Group 1, which means that when we focus in at the top of the scale, we find more members of Group 2, even though overall Group 1 performed better on the test.
So, is that what we find when we look at real populations? Are males like Group 2, and females like Group 1, when it comes to mathematical ability?
The Study of Mathematically Precocious Youth observed thousands academically gifted American children who took the SAT test at age 12-14, several years before the usual administration in the 11th grade. In 1983, among those who scored higher than 700 on the test, males outnumbered females by 13:1. This indeed suggests that males have a much wider distribution of scores than females at that age. Interestingly, by 2005, the ratio at that same level had dropped to 2.8:1. Either girls have gotten a lot smarter in the last 20 years, or some of the discrepancy in 1983 can be explained by social differences: different opportunities for boys and girls.
Yet there is still a large, significant sex difference in math scores at the top of the scale (there's no difference in verbal scores). Where does this difference come from? Some evidence suggests that the brightest boys even have an advantage at kindergarten age. Some scholars have speculated that sex roles in humans evolved millions of years ago: while men were out hunting and fighting with neighboring tribes, women stayed closer to home, foraging and caring for children. Since men travelled farther than women, they required better navigation skills -- similar to the visuospatial skills we discussed yesterday. The men who survived were better at navigation, and they passed this trait on to their male children. But others have argued that women needed to travel just as far in foraging. It's certainly possible that differences in ability can be entirely explained by factors unrelated to evolution.
Sex differences in higher education
We've established that in the tiny slice of students with the highest math test scores, there are many more males than females. But how are these boys and girls doing when they grow up and go to college and beyond? While the overall graduation rate from college favors women, in math and science, the numbers tell a different story. The male to female ratio of science majors at MIT in the 1990s was about 1.5 to 1. Among faculty it was higher than 10 to 1. Part of the discrepancy might be due to different social conditions when MIT's faculty was educated. Take a look at this graph:
As you can see, in every field, a larger portion of doctorates was awarded to women in 2001 than in 1980. But women still earn many fewer doctorates than men in physical science and engineering. How can we explain this lingering discrepancy?
Part of it may come down to the relationship between verbal and mathematical skills. The study of precocious youth mentioned earlier actually tracked these children until they became adults. If you take a look at their career choices at age 33, you find that the relationship between verbal and math scores in this group -- all scoring in the top 1 percent -- explained a lot about what fields they went into. Take a look at this graph, which relates career choices to SAT scores:
The blue line represents the point where math and verbal scores were equal. Above that line, verbal scores are better than math scores; below it, vice-versa. As you can see, people choosing the fields most dominated by men, math/computer science and engineering, tended to score much lower on the verbal SAT compared to the math SAT when they took those tests years before. And boys are much more likely than girls to score lower on verbal than math -- for girls, the scores tend to be equal.
But one theme Halpern and her colleagues constantly return in their article is that the issue of women's achievement in math and science is extremely complex. To suggest that the relationship between verbal and math test scores explains all sex differences would be vastly oversimplifying things. We'll cover more on this important topic in tomorrow's post.
Why aren't there more women in science and math? Part 1
Why aren't there more women in science and math? Part 3
Halpern, D.F., Benbow, C.P., Geary, D.C., Gur, R.C., Hyde, J.S., & Gernsbacher, M.A. (2007). The science of sex differences in science and mathematics. Psychological Science in the Public Interest, 8(1), 1-51.
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Regarding the bell curves on the graph:
Is there a typo in the text of this article?
"Even though Group 1 has a higher average score than Group 2, there are still more members of Group 1 at the top of the scale (and at the bottom). Group 1's scores are more spread out, more variable than scores of Group 2, which means that when we focus in at the top of the scale, we find more members of Group 1, even though overall Group 2 performed better on the test."
It appears as though there is more of Group 2 at the extreme spectra of the scale. Group 2 has a lower average, but a larger variety of scores (both higher and lower). Am I reading this wrong?
Yes, I totally messed that up. It should be fixed now.
I think the range values for the difference between male and female abilities at the very high end would make me wary of interpreting it as due to any particular cause---the difference between the 13:1 ratio in 1985 and the 2.8:1 ratio in 2005 is substantially larger than the current gender difference itself, which suggests some pretty strong social factors are involved. Unless you have some reason to believe that all of the social factors managed to be washed away in time for the 2005 testing, there's no particular reason to assume that the remaining difference isn't socially influenced as well.
Even if there does appear to be a genetic link, it might not be specifically to do with mathematical ability, for example, one might imagine a situation where girls are motivated to be "normal" while boys are motivated to be "best", and so the girls study right up to the normal achievement level, then stop, while the boys decide on their chances of high achievement and either study as hard a possible, or allocate the time to something else, writing math off as a loss.
As far as choosing graduate studies, the lower numbers of women than men could as well be a rational choice reflecting on hiring discrepancies (10:1 at MIT) as it is a reflection of ability.
I wouldn't claim to have any evidence that that is a factor in the differences, but the fact that various social causes are at least plausible, and the historical trends show evidence of social effects, should be enough, I would think, to discourage researchers from making up fairy tales about hunter-gathers getting lost in the woods to explain SAT scores.
I wonder if the SAT scores themselves are actually predictive, or if they're at least partially causative? Are the students treated the same by parents and teachers after their scores were received? Do students view themselves the same way?
It's hard to imagine that a 10 point difference (the smallest non-zero difference) between math & verbal, which would make a student fall to one side of the line or the other, actually indicates a major difference in ability. This difference keeps the scores well within the range of error of each other. The scores are, for all intents and purposes, the same. Why would that be predictive for a student's career choice?
I've heard -- though of course the person could not say openly -- that the main reason the gap closed among elite math scores is almost solely a function of how many East Asian females were present at the two times. East Asians score higher than Europeans on IQ tests by about 1/3 SD, and they score far higher on just the visuospatial sub-tests.
Since the ceiling is pretty low for SAT Math (easier to get an 800 on it than the Verbal), East Asian males won't boost the male percentage of elite scorers that much, but now the females have a bunch of East Asians who are scoring highly to boost their average.
We've only talked about the "can-do" factors like cognitive abilities, but there are also the "will-do" factors like personality traits. I reviewed the sex differences in personality, in the context of women in science, here:
http://www.gnxp.com/blog/2006/07/women-in-science-part-3595726061058.php
I would be more impressed with a study that followed a representative sample of students through the grades with age appropriate math tests. If they started at Kindergarten comparing a cohort of boys and girls, researchers could more easily consider genetic and social factors. Fraternal twin studies would also be interesting. I think that correlational studies are very weak when attempting to explain causes.
So, Engineers, Mathematicians, and Computer Scientists tend to score better on mathematical aptitude tests than verbal aptitude tests. Men tend to score better on mathematical aptitude tests than verbal aptitude tests. Therefore, it follows that men go into Engineering, Mathematics, and Computer Science.
Is this necessarily the optimal outcome, though? It seems plausible that when you get to the really high scorers (those going on to get PhDs in their fields) there are diminishing marginal returns to being incrementally better at Math, while being better at whatever the verbal tests measure could still help substantially.
Maybe there's an assumption within science fields that the top performers will be the top math performers, regardless of their verbal abilities, while in truth people who get slightly lower, but still high math scores, but who also get high verbal scores would ultimately have made better scientists. This kind of bias would be self-perpetuating, as people in hiring departments would tend to hire people like themselves. It would also be a stable equilibrium, because people who had the slightly lower math and higher verbal abilities wouldn't be as respected by their peers, and might not get the funding or support they needed to be as productive as possible.
But maybe it's not the *best* stable equilibrium. If entire an entire field could move to a new equilibrium where verbal ability is valued too, maybe people in that field would make more important discoveries and contributions.
I think it would be hard to verify or falsify my speculation, but it's still worth keeping in mind the overarching point: if men are scoring better than women on the tests we think scientists should do well on, maybe there's something wrong with the tests.
Not yet considering the effect of pregnancy and raising family on the sexes? If females are performing better at the undergraduate level, but "achievement" at the graduate level and beyond into careers dwindles for females, this is certainly a factor that can't be ignored.
The Math tests aren't really cognitive ability tests, so it's kinda apples-and-oranges to compare them with Verbal, which is a cognitive ability. The Verbal questions that best detect the smarties are analogies (they are the most highly "g-lodaed"), but non-verbal analogies are just as tough. So, if we know that A got 1 more math question than B, but B got 3 more analogy questions than A, I'd bet on B. Analogical reasoning is just pervasive in the sciences, especially math.
if men are scoring better than women on the tests we think scientists should do well on, maybe there's something wrong with the tests.
You can only have this suspicion on the assumption that men and women are equally likely to become top scientists, i.e. their distributions for all relevant traits (not just cognitive abilities) are equal in mean and variance -- the very proposition we're investigating. For once, we can correctly apply the term "begging the question." But we know the male & female distributions aren't equal, hence no suspicion.
If there were a unisex basketball league, it would be virtually all-male due to height requirements. We wouldn't say, "Hmm, maybe there's something off about selecting pro basketball players to be on average 6'7 (which is what they are)." We evaluate the selection criteria on how well they detect the top candidates, compared to other criteria, with zero attention to the effect it has on representation of women or Blacks and Hispanics. Assuming we want the best candidates, of course.
That's why top physics programs will never allow in a cohort whose average GRE math score is 700 or below -- at most top places, the average is probably 800, since it's not that hard to get if you know your stuff. If you get far less than that, you're just not good enough with numbers to do well in a top physics program. All the dept will do is waste some money hiring a VP for diversity outreach; nothing will change substantively in the selection process. Harvard won't shoot itself in the foot just to make activists happy.
regarding this sentence: "Some scholars have speculated that sex roles in humans evolved millions of years ago: while men were out hunting and fighting with neighboring tribes, women stayed closer to home, foraging and caring for children."
As an anthropologist, it's frustrating to see this kind of inaccurate statement mindlessly repeated in a science blog. Modern humans evolved no more than 200 THOUSAND years ago. MILLIONS of years ago (2 million?) there were at least 2 species of Homo (H. erectus and some last populations of H. habilis) or one highly variable species sometimes classed as H. erectus. We don't have a lot of data as to sex differences in foraging for H. erectus, and some scientists (Alan Walker) believe that the growth pattern for H. erectus is closer to apes than modern humans. Until we start testing for sex differences in math and spatial abilities in ape brains and behavior, I wish we could stop repeating the supposed evolutionary correlation.
Agnostic:
The differences between ethnic groups you alluded to (or the speaker you heard) are an artifact of the Flynn effect. The 'East Asian' group (Chinese, Japanese, Korean) tended to be tested later, compared against earlier US norms, and the secular changes over time are most pronounced on the visual-spatial subtests. Hence, this pattern. The most egregious example I can think of was adopted children of Asian background, raised in Belgium, who showed a huge advantage (greater than 1 standard deviation) on the Raven's matrices, as compared to a vocabulary measure. There was no control grop, however. Later work showed that Belgian children, in general, showed a similarly huge advantage on the Raven's matrices, again due to the Flynn effect, not any genetic cause. Always use a control group. (The paper was in Personality & Individual Differences, 1989 or 1990). Flynn gave an excellent lecture, presented here. http://www.thepsychometricscentre.co.uk/publications/BeyondTheFlynnEffe…
The data I'm familiar with (from the last 5 years) shows little or no overall effect. In some countries, those of Asian background show a relative advantage in measures of psychomotor speed, but this isn't true in the US. It's not true for tests of reasoning, however.
Go read the whole article by Benbow, Eagly and colleagues (it's also in Scientific American). It's excellent and covers all bases well, as expected by something written by researchers who have owned this field for nearly 30 years, and whose work has been cited by all knowledgable parties to this debate. As someone who started graduate school in a class just over half female, and who could look at previous classes that were predominantly male, I don't see how the genetic composition changed that much in 10 years.