Summer More Extreme Than Others

So Lawrence Summers, President of Harvard University has been in hot water for a few weeks now because of what he said, or supposedly said, about women in science and engineering. While some find questionable certain statements he made about innate differences between men and women, there is one part of what he said that has attracted little controversy; most likely because it seems to be true.

Summers pointed out that men tend to have a greater diversity in science or mathematical skills than women do. This means that even if men and women average (mean) to approximately the same skill level (which they may), that the standard deviation is greater for men. This means that there are more men with extraordinarily week math skills than there are women with such skills, and there are also more men with extraordinarily strong math skills than there are women. Implicitly, therefore, there are fewer men at the mean. You will be hard pressed to find anyone who disputes this; even the woman professor who left Summers' talk claiming to be nauseated by his words does not dispute this part of his statements.

Now, with a little logic, we can see that if there were a test that preferentially selected those with average math skills, such a test would preferentially select women. Similar tests that preferentially selected those with somewhat above average skills, or somewhat below average skills, would select approximately equal numbers of men and women. Any test that preferentially selected those with very low skills, or those with very high skills, will preferentially select men. Summers argument, then, is that being a university professor in math, science, or engineering, preferentially selects those with very high math skills, thereby selecting more men than women.

Note that when I say "average" math skills, I mean it literally. Average is where the majority of the population finds itself. (I know I specified that I was talking 'mean' before, and not 'mode,' but in this case all evidence is that the the two are identical for the subject population.) I don't mean "average" in the sense that it has come to mean in American school system, where anyone scoring "average" is not fully applying themselves. (And one wonders why we have such problems with math as a nation!)

It seems that anyone failing to understand this logic must have significantly below average math skills, and should therefore preferentially be men. (Just kidding.) That those who have been quoted in the media most vociferously excoriating Summers have been women are indications either of media bias (preferentially reporting on women's indignation), or that Summers said something else objectionable, not related to this argument (which seems likely), or that those objecting to Summers' speech are not using their innate math skills to look at his proposition (also a possibility).

I know that as an engineer I have observed throughout my career that women engineers are usually accorded great credit by their peers (although not always by their superiors.) I have always attributed this to a sense that any woman who has succeeded in engineering has faced significant cultural biases and impediments. She must, therefore, really love what she is doing and therefore be unusually good at it. This kind of overgeneralization is not founded on math, logic, or especially sound reasoning, but no one seems to object to it. I know that so far I have not caused any significant trouble for myself or others by believing it and acting as though it were true. I hope someone studies the question someday.