Bell curves

By Sean Carroll | September 22, 2005 8:14 pm

Back at the old blog we used to occasionally chat about the notorious speech by Harvard President Larry Summers, in which he suggested that intrinsic aptitude was a more important factor than discrimination or bias in explaining the dearth of women scientists. Examples here, here, here, here, here, here, here, and here. There was a lot of posturing and name-calling and oversimplification on either side of the debate, of course, which tended to obscure the basic fact that Summers was, as far the data goes, wildly wrong. Two favorite goalpost-moving manoeuvers from his supporters were first to pretend that the argument was over the existence of innate differences, rather than whether they were more important than biases in explaining the present situation, and then to claim that Summers’ critics’ real motive was to prevent anyone from even talking about such differences, rather than simply trying to ensure that what was being said about them was correct rather than incorrect.

It was a touchstone moment, which will doubtless be returned to again and again to illustrate points about completely different issues. Here’s an example (thanks to Abby Vigneron for the pointer) from Andrew Sullivan:

DAILY KOS AND LARRY SUMMERS: It’s a small point but it helps illuminate some of the dumbness of the activist left. “Armando” of mega-blog/community board, Daily Kos, takes a dig at Larry Summers, and links to a new study on gender difference. I’m not getting into the new study here, but I will address Armando’s description of Larry Summers’ position. In a bid to be fair, Armando writes:

NOTE: Yeah I know Summers didn’t say men were smarter than women, he just said they had greater aptitude in math and the sciences than women. Huge difference.

This is one of those memes that, although demonstrably untrue, still survives. Read the transcript of Summers’ now infamous remarks. His point was not that men are better at math and the sciences than women, as Armando would have it. His point was that there is a difference not in the mean but in the standard deviation:

Even small differences in the standard deviation will translate into very large differences in the available pool substantially out. I did a very crude calculation, which I’m sure was wrong and certainly was unsubtle, twenty different ways. I looked at the Xie and Shauman paper – looked at the book, rather – looked at the evidence on the sex ratios in the top 5% of twelfth graders. If you look at those – they’re all over the map, depends on which test, whether it’s math, or science, and so forth – but 50% women, one woman for every two men, would be a high-end estimate from their estimates. From that, you can back out a difference in the implied standard deviations that works out to be about 20%. And from that, you can work out the difference out several standard deviations. If you do that calculation – and I have no reason to think that it couldn’t be refined in a hundred ways – you get five to one, at the high end. (My italics.)

Summers was addressing the discrete issue of why at the very high end of Ivy League math departments, there were too few women. His point, as the Harvard Crimson summarized it was that, in math and the sciences, “there are more men who are at the top and more men who are utter failures.” Armando is wrong; and he needs to correct the item. In fact, this is a good test of leftist blog credibility. Will he correct? I’ll keep you posted.

Ah yes, the good old standard-deviation argument. It’s the absolute favorite of those in the intrinsic-differences camp, since (1) it sounds kind of mathematical and impressive, and (2) they get to insist that it’s only the width of the distribution, not the mean, that is different between men and women, so really the argument doesn’t privilege men at all, while it manages to explain why they have made all the important contributions in human history. In a debate with Elizabeth Spelke at Edge, Steven Pinker rehearses the argument somewhat pedantically.bell curves
But let’s look at what the argument actually says, both explicitly and implicitly.

  1. Standardized tests scores reflect innate ability.
  2. Boys’ scores on certain tests have a larger standard deviation than girls’ scores, leading to a larger fraction of boys at the high end.
  3. The dearth of women scientists is explained by their smaller numbers on the high end of these tests.

Now, everyone who is familiar with the data knows that point 1 is somewhere between highly dubious and completely ridiculous; Summers himself admits as much, but it would ruin his story to dwell on it, so he soldiers on. But point 3 is interesting, and deserves to be looked at. It’s a nice part of the argument, because it’s testable. Is this difference in test scores really what explains the relative numbers of men and women in science?

Summers’ data comes from the book Women in Science: Career Processes and Outcomes by Yu Xie and Kimberlee Shauman. Interviewed shortly after his remarks, both Xie and Shauman were quick to criticize them, using words like “uninformed” and “simplistic.” We were fortunate enough to have Kim Shauman herself as a speaker at our Women in Science Symposium back in May. She pointed out that the studies Summers refers to can indeed be found in her book, right there in Chapter Two. But if you wanted to know whether the standard-deviation differences were actually what accounted for the dearth of women in science, you would have to read all the way to Chapter Three.

Here’s the point. By the time students are in twelfth grade, there is a substantial gap in the fraction of boys vs. girls who plan to study science in college. So it’s easy enough to ask: how much of that gap is explained by differing scores on standardized tests? Answer: none of it. Girls are much less likely than boys to plan on going into science, and Xie and Shauman find that the difference is independent of their scores on the standardized tests. In other words, even if we limit ourselves to only those students who have absolutely top-notch scores on these math/science tests, girls are much less likely than boys to be contemplating science as a career. Something is dissuading high-school girls from choosing to become scientists, and scores on standardized tests have nothing to do with it.

Now, looking at Sullivan’s post above, there’s nothing he says that is strictly incorrect. He is simply characterizing (accurately) what Summers said, not actually endorsing it. Still, he is certainly giving the wrong impression to his readers, by repeating a well-known allegation without mentioning that it is demonstrably false. It’s a small point, but it helps illustrate some of the disingenuity of the activist right. Sullivan is misleading, and he needs to correct the item. In fact, this is a good test of quasi-right-wing blog credibility. Will he correct? We’ll keep you posted.


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Cosmic Variance

Random samplings from a universe of ideas.

About Sean Carroll

Sean Carroll is a Senior Research Associate in the Department of Physics at the California Institute of Technology. His research interests include theoretical aspects of cosmology, field theory, and gravitation. His most recent book is The Particle at the End of the Universe, about the Large Hadron Collider and the search for the Higgs boson. Here are some of his favorite blog posts, home page, and email: carroll [at] .


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