To Larry Summers: Correlation Does Not Mean Causation

A week or so ago Larry Summers (noted economist and President of harvard University) apparently argued that the over-representation of males in science and math at elite universities may be grounded in facts about the world. The first part of his argument is that performance among young males in math has a greater variance than it does among young women--that young males are both more likely to be unable to do simple arithmetic and to be math "whizzes" than is true for young women. This, apparently, is true.

What he did next was, I am sorry to say, bad science, and bad statistics. He inferred from this fact that the cause of this difference may well be genetic in nature.

Well, there's clearly a correlation here, between gender and test performance. But Summers knows, I mean he knows, that this does not demonstrate causation.

Consider, for example, an alternative story which yields the same outcome. Suppose that, among young men, outstanding performance in math (or anything else) is highly rewarded, but truly dreadful performance is not particularly condemned. But suppose, among young women, outstanding performance is not rewarded (and may even be stigmatized in some way), while bad performance is, in fact, regarded as unacceptable. One could easily develop some explanations based on the culture of the U.S. that would support this incentive structure.

Then, among young men with math (or whatever) aptitude, there's an incentive to develop the aptitude, whereas among young women, that incentive is much smaller. Conversely, among young men with little interest in math, dreadful perofmance does not lead to negative consequences, while among young women it does.

So wouldn't we expect to see the outcome that we see?

And isn't that outcome at least potentially amenable to social intervention?

What Summers does is something I'm sure he taught his econometrics students not to do. Don't mistake correlation for causation. Don't mistake a plausible-sounding story (not even the plausible-sounding stories that I tell) for reality. Do the hard, necessary research to figure out what's going on.

For making that mistake, he deserved what he got. Even if he didn't get the criticism specifically for that mistake.