The reaction in the left blogosphere to the recent study of math performance in US schools is interesting. The post at Alas seems fairly representative; boys and girls are the same at math, Larry Summers was an idjit, etc. In fairness to Jeff and others, they are probably taking their interpretations from media reports of the study, which were quite often fundamentally dishonest about one of the study’s key findings.

The study doesn’t show what Jeff Fecke, media figures, and others think that it shows. Yes, it does indicate that the overall performance of boys and girls is equivalent - the average boy and the average girl are at about the same level of mathematical ability. But Summers (and most informed observers) never claimed that “boys are better at math”. Instead, the claim has always been that the increased variability of male performance means that there will be more boys at both ends of the spectrum. The bell curve is flatter for boys, probably for genetic reasons, and there are more geniuses and more poor performers than we find among girls. That effect, in turn, means that at the extreme right-hand side of the bell curve, where (for example), math and science professors tend to come from, we’re going to see more boys as a natural consequence of the statistical reality. That was Summer’s (often-maligned, and in fact, often completely reversed and misrepresented with shocking dishonesty, point.) It would be amusing, if it weren’t so distressing, to see so many people who allegedly know how to read and think interpreting Summer’s comments, which boiled down to “there’s a difference in the number of brains that can hit the target, and there’s also discrimination against the brains that happen to belong to females”, as “there is no discrimination and girls are stupid!”

Unfortunately for egalitarians, though, the study shows that the conventional wisdom about variability is, once again, proven to be a real phenomenon. The study found consistently more variability among boys than among girls, at every grade level, in every state. (Marginal Revolution explains the findings quite coherently here.) The study findings are consistent with the bulk of previous work in the field; it is simply no longer a controversial point that there is greater variability among males than among females in mathematical ability.

But that won’t stop egalitarians from claiming the intellectual high ground, and accusing people of idiocy, for the crime of being 100% correct about a reality that egalitarians find distressing. Larry Summers may have been wrong about his weighting of the three factors he proposed for the differential numbers of men and women in math and science (female reluctance for whatever reason to engage in the horrible grind that many math and science jobs represent, ability-based differences in the population of those able to fill those jobs in the first place, and overt discrimination). He left out the fact that many women who have incredibly high math skills also have incredibly high verbal skills (in contrast to males, where my understanding is that it is more common to find men with just one or the other) and thus have access to other high-status career fields.

But he was right about the fact that at two, three, four or more standard deviations above the median, the small difference in male variability translates to large differences in the number of males with that level of performance versus the number of females. He was pilloried for it - and future scholars who stubbornly persist in recognizing the truth when they see it will no doubt be pilloried for it - but he was right. Efforts at producing a 50-50 outcome at the highest level are going to founder against this population effect. Campaigners for equality - may God bless them - should recognize this fact and move their focus towards ensuring that any woman of aptitude who seeks a career in math or science isn’t discriminated against. Open opportunities, and let outcomes fall where they may.