## Sex, Mathematics, And Political Correctness

### The Key Is The Distribution

Many more men than women become lead engineers and theoretical physicists. Is the reason, as feminists assert, that society, the universities, and the mathematical professions discriminate against women? Or is the reason that men are naturally better at mathematics?

Those who believe discrimination to be the cause point out that the male mean (i.e., average) score on the math section of the Scholastic Aptitude Test is only slightly higher than the female mean--not enough higher, argue believers in discrimination, to account for the massive preponderance of men in jobs requiring high mathematical ability. The discrimination justifies affirmative action, goes the reasoning, in order to put equal numbers of women into mathematical jobs.

Maybe not.

The key is to understand that the average score does not in itself predict performance. The *distribution* is crucial. As an unrealistic example to illustrate the point, imagine a group of twenty women each of whom has an IQ of 100. The mean for the group will be 100. Now imagine a group of twenty men, ten of whom have IQs of zero, and ten of whom have IQs of 200. The average will again be 100--but the consequences would be very different. Half will be geniuses, and half will be idiots.

Look closely at the actual scores. (They are from the research library of the Educational Testing Service in Princeton, NJ, which administers the SATs. The tests consist of math and verbal sections, with scores on each running from 200 to 800.)

From the 1983-84 testing period through 1988-89, the ratio of the absolute numbers of girls to boys scoring above 600 on the math section, a fairly high score, is 1.84 boys to girls, almost two to one. The ratio above 700, a quite high score, is 3.13 boys to girls. Above 750, which begins to be high indeed, 4.79 boys to girls. For scores of 800, there are 7.61 boys to girls. (The distribution is symmetrical: Men also predominate on the low wing of the distribution, which, along with greater aggressiveness, probably accounts for the roughly ten-to-one preponderance of males in prisons.)

From the very high scorers come the prominent engineers and research scientists. This goes a long way toward accounting for the predominance of men in the hard sciences. (On the verbal test, the differences are much smaller. For example in the same testing period there are 1.32 males per female with scores of 800.)

If the scores correlate with innate ability, and if the gap continues to widen with increasing ability, which in fact it does, then mathematicians on the order of Newton, Gauss, and Galois will almost always be male.

This distribution is well known in the testing community, and occurs across a wide range of tests. Because the reality is so politically incorrect, considerable effort goes into altering tests to disguise the difference, as for example the recent renorming of the SATs.

But, one might ask, do the scores measure real differences in ability? And how much of the difference is due to innate ability?

The SATs fairly obviously measure a mixture of intelligence and achievement. Separating the two isn't easy. People achieve more at things that interest them. Are boys more interested in mathematics, as they are in carburetors?

If the disparities between the sexes were slight, one might easily explain them as the result of such things as a culturally ingrained tendency for girls to take fewer math courses. Since more girls than boys take the test, one might suspect that their test population contains more students of low ability, which would bring down the female mean. (Here, however, the ratios are calculated using absolute numbers of scorers at given levels, obviating the objection.) On the other hand, girls in high school study more and make better grades, which would favor the girls. In short, there is enough slop in the statistical gears to make doubtful any conclusions from small differences.

But the differences are not small. They are huge. What is the explanation?

Three possibilities come to mind. First, perhaps the tests are biased against females. If so, one must conclude that ETS, which is aware of the differences, deliberately designs its tests to keep women out of the mathematical professions. The idea is absurd. Second, perhaps secondary schools, even society as a whole, somehow fail to prepare extremely bright girls to compete against extremely bright boys, while preparing girls of ordinary ability about as well as boys of ordinary ability. Well, maybe. If very bright girls for whatever reason take English courses instead of math (though when I was in high school, all college-bound students took the same courses), they presumably will do less well than boys who do take math. But then why do more boys than girls make 800s on the verbal test?

Third, perhaps men are just plain better at mathematical reasoning. If so, nothing can be done. This is the least politically correct explanation but it is also, I think, the one most in accord with the evidence.

If men are better mathematically, the implications for policy are substantial. In particular, quotas by sex cease to make sense. Firms, as for example defense contractors, should not be required to hire people who don't exist. If an engineering company refuses to hire a particular woman who is demonstrably the best qualified candidate, she has a legitimate complaint. If the company fails to ensure that half of its hires are women because it can't find qualified women, no one has a complaint.

This in turn implies that perhaps advancement should be awarded by ability, not by race, creed, color, sex, and national origin. Affirmative action--i.e., the enforced hiring of the unqualified--might almost make sense (but probably wouldn't) if native ability were equal. If ability isn't equal, the results will be high overhead, inefficiency, and incompetence for companies, and enormous resentment from the qualified who are passed over. And in the long run, it won't work.

Finally, perhaps it is time to rethink the hallmark tenet of today's compulsory political propriety, namely that all groups are in all ways equal. What if they aren't?