Be afraid, be very afraid. If there was a cheesy documentary made about the side effects of political correctness, that’s your opening voice-over. What’s sobering about the person whose plight I highlight is that he was one of, if not the, beautiful people. A brief description of Larry Summers from a 2007 NYT article:

At age 52, he has already finished his first three careers. The son of two economists at the University of Pennsylvania and the nephew of two Nobel-winning economists, he enrolled at M.I.T. when he was 16. Then came the swift rise to tenure at Harvard, a flurry of research papers on seemingly every major topic in economics and an award called the John Bates Clark Medal, given every other year to the best economist under 40. “I’ve been around some pretty smart people,” said Jonathan Gruber, an M.I.T. economist and a former student of Summers’s. “But it’s a different level with Larry.”

His PC crime? In 2005, as president of Harvard, he wondered whether there were some innate differences between men and women which accounted for men dominating the field of science. An uproar ensued and he was forced to apologize and then resign … yada yada yada. My favorite reaction was that of the MIT professor, Nancy Hopkins, who said the following:

When he started talking about innate differences in aptitude between men and women, I just couldn’t breathe because this kind of bias makes me physically ill.

OK, so we got a brilliant scholar who gets his privates cut off for thinking out loud. Big deal, academia is the birthplace of PC, this stuff is common. Posner’s blog even makes the case that CEO types shouldn’t really expect to enjoy freedom of speech. But that’s not the punch line. The punch line is that he was right.

Right as in proven. Right as in various independent studies confirmed his hypothesis. If I was ever that right about something I had been vilified about, the victims of my subsequent I told you so’s could probably light up a suicide hotline’s switchboard. But I hate to brag and digress.

Anyways, it gets better. As the data and studies accumulate which prove Mr Summers correct, reputable news publications continue to state the opposite. Like lower-weight Mexican boxers, PC soldiers don’t go down easily! See the post from the Marginal Revolution blog copied below:

Summers Vindicated (again)

For the past week or so the newspapers have been trumpeting a new study showing no difference in average math ability between males and females. Few people who have looked at the data thought that there were big differences in average ability but many media reports also said that the study showed no differences in high ability.

The LA Times, for example, wrote:

The study also undermined the assumption — infamously espoused by former Harvard University President Lawrence H. Summers in 2005 — that boys are more likely than girls to be math geniuses.

Scientific American said:

So the team checked out the most gifted children. Again, no difference. From any angle, girls measured up to boys. Still, there’s a lack of women in the highest levels of professional math, engineering and physics. Some have said that’s because of an innate difference in math ability. But the new research shows that that explanation just doesn’t add up.

The Chronicle of Higher Education said:

The research team also studied if there were gender discrepancies at the highest levels of mathematical ability and how well boys and girls resolved complex problems. Again they found no significant differences.

**The Marginal Revolution blog continued; “All of these reports and many more like them were false.” **

In fact, consistent with many earlier studies (JSTOR), what this study found was that the ratio of male to female variance in ability was positive and significant, in other words we can expect that there will be more math geniuses and more dullards, among males than among females. I quote from the study (VR is variance ratio):

Greater male variance is indicated by VR > 1.0. All VRs, by state and grade, are >1.0 [range 1.11 to 1.21].

Notice that the greater male variance is observable in the earliest data, grade 2. (In addition, higher male VRS have been noted for over a century). Now the study authors clearly wanted to downplay this finding so they wrote things like “our analyses show greater male variability, although the discrepancy in variances is not large.” Which is true in some sense but the point is that small differences in variance can make for big differences in outcome at the top. The authors acknowledge this with the following:

If a particular specialty required mathematical skills at the 99th percentile, and the gender ratio is 2.0, we would expect 67% men in the occupation and 33% women. Yet today, for example, Ph.D. programs in engineering average only about 15% women.

So even by the authors’ calculations you would expect twice as many men as women in engineering PhD programs due to math-ability differences alone (compare with the media reports above). But what the author’s don’t tell you is that the gender ratio will get larger the higher the percentile. Larry Summers in his infamous talk, was explicit about this point:

…if one is talking about physicists at a top twenty-five research university, one is not talking about people who are two standard deviations above the mean…But it’s talking about people who are three and a half, four standard deviations above the mean in the one in 5,000, one in 10,000 class. Even small differences in the standard deviation will translate into very large differences in the available pool substantially out.

If you do the same type of calculation as the authors but now look at the expected gender ratio at 4 standard deviations from the mean you find a ratio of more than 3:1, i.e. just over 75 men for every 25 women should be expected at say a top-25 math or physics department on the basis of math ability alone (see the extension for details on my calculation). Now does this explain everything that is going on? I doubt it. As Summers also pointed out it takes more than ability to become a professor at Harvard and if there are variance differences in characteristics other than ability (and there are) we can easily get a even larger expected gender ratio.

Does this mean that discrimination is not a problem? Certainly not but we need the media and academia to accurately present the data on ability if we are to understand how large a role other issues may play.

Addendum: Andrew Gelman points out that perhaps alone among the media, Keith Winstein at the WSJ reported the story correctly.