So Lawrence Summers Was Fired For Being Correct?

So, apparently Lawrence Summers was correct:

Wall Street Journal -- Girls
and boys have roughly the same average scores on state math tests, but
boys more often excelled or failed, researchers reported. The fresh
research adds to the debate about gender difference in aptitude for
mathematics, including efforts to explain the relative scarcity of
women among professors of science, math and engineering.

latest study, in this week's journal Science, examined scores from
seven million students who took statewide mathematics tests from grades
two through 11 in 10 states between 2005 and 2007.
researchers, from the University of Wisconsin and the University of
California, Berkeley, didn't find a significant overall difference
between girls' and boys' scores. But the study also found that boys'
scores were more variable than those of girls. More boys scored
extremely well -- or extremely poorly -- than girls, who were more
likely to earn scores closer to the average for all students. The study found that boys are consistently more variable than girls, in every grade and in every state studied
(see crude diagram above - showing distributions where mean
intelligence is the same, but the standard deviation of male
intelligence is greater than female intelligence).

In Minnesota, for example, 1.85% of white boys in the 11th grade hit the 99th percentile, compared with 0.9% of girls -- meaning there were more than twice as many boys among the top scorers than girls.

Of course, Summers did not get in trouble for being incorrect.  He got in trouble for saying something he was not supposed to say.  And it seems that the media are trying to avoid the same mistake, reporting what they want to believe, and not what the study actually says.

As I write in a post at Climate Skeptic, this is part and parcel of a new post-modernist science, where (as MaxedOutMamma writes) "If a
research finding could harm a class of persons, the theory is that
scientists should change the way they talk about that finding".


  1. Doug:

    I remember Charles Murray giving a talk at AEI about this sort of stuff shortly after Summers had been fired. Murray mentioned this same idea that there is a difference between the "intelligence" of guys and girls; there are a lot more guys that are geniuses and idiots, but there are a lot more girls who are of "average" intelligence. I think this study which produced such fat and skinny bell curves proves Murray's point.

  2. gadfly:

    The Harvard Crimson ran an editorial discussing the "aftermath" (apparently no pun intended on their part) of University President Lawrence H. Summers' resignation in which the editorial board noted that some media outlets blamed "a hard-left faculty of 'feminazis' for the heat that caused the resignation.

    Rush Limbaugh must be proud to find some indirect recognition inside those ivy-covered walls.

  3. Jim Hu:

    From what I recall at the time, Summers didn't get axed for his conference statements so much as the statements provided cover for those who wanted to get rid of him for more prosaic intra-university power struggles.

    There are two fundamental problems with the variance defense of Summers: 1) he said it was innate. I don't have a problem with some of it being innate, but it seems unlikely to me that kids are culture-free by the time they can take these tests. 2) the measured variance doesn't account for the observed gender ratio unless you assume that the mean IQ for scientists is way the hell out in the tail. There are certainly people out there in the scientists, but that doesn't mean that the average scientist at Harvard is 4 sigma off the mean. Maybe in ego, but not in IQ. I'm an academic scientist fwiw.

    In the particular case of Summers and Harvard, it was also in the context in a drop in female hiring and promotion when he became President. Which only fits with his explanation if he raised Harvard's lax standards or there was an implausible change in the demographics of talent over a very short time.

  4. Dan:

    "the measured variance doesn't account for the observed gender ratio unless you assume that the mean IQ for scientists is way the hell out in the tail."

    Isn't it?

    I think it's easy for smart people to forget exactly what average intelligence is. Just for example, average SAT scores for Math and Verbal each hover around 500 points. Most scientists would probably consider that a dismal score. And remember, this is only measuring people who bother to take the SAT, which is already a self-selected group who intend to go to college.

    I would bet that your typical university science professor is *at minimum* around the 85th-90th percentile for intelligence.

  5. Jim Hu:

    "I would bet that your typical university science professor is *at minimum* around the 85th-90th percentile for intelligence."

    That sounds reasonable - but remember that 2 standard deviations above the mean is roughly the 97th percentile. 95% of the population in a Gaussian distribution is within 2 sigma, and then add in the bit more than 2% who are more than 2 sigma below the mean. To reach the 15% women on variance alone, I estimate you'd need a minimum IQ around 140 for the scientist subpopulation, and that's just slicing off that hunk of the bell curve. If IQ is normally distributed within the population of scientists, you'd need something significantly higher as the average to account for the observed gender ratio. For comparison, the Mensa cutoff is around 138 (98th percentile). Summers (quoted at Marginal Revolution) rationalized by talking about the gender ratios at 3.5-4 sigma, which is above the 99.9th percentile. In the Science paper, the difference in variance gave a 2x gender difference at the 99th percentile.

    Trust me, we aren't that smart on average. Maybe the high end physicists, mathematicians and philosophers, but not the average prof in a science or engineering department.

    I'm not denying that IQ variance isn't real or that it makes no contribution. But the data for discrimination is just as good and I'm sure it makes some contribution too. I think other factors explain more of the gender numbers than either variance or discrimination.

  6. Jim Hu:

    Arg - typos. Should be "I'm not saying" not "I'm not denying"; there are probably other errors...

    See, I told you we aren't that smart.

  7. Xmas:


    Marginal Revolution has a nice discussion of this using some numbers...

    If you assume that top scientists are in the top percentile, then a small difference in Standard Deviation results in large differences at the tail ends.

  8. Xmas:

    Agh, it's too early in the morning for my reading comprehension. Jim already has a link to the MR post.

  9. Gringo:

    More extremes at the other end, also. Such as more mentally retarded males.

  10. David Zetland:

    I heard that Summers was *really* fired for using Harvard $$ to bail out Andrei Shleifer from his Russian fraud charges... (AS was LS's student)

  11. Jim Hu:

    Full disclosure: more evidence that I'm not that smart - Steve Hsu points out that my Excel calcs of the numbers are off by a lot. The 4 sigma number is more like 5-10K not 250. Over at MR, we argue about whether that changes the bottom line.

  12. loki on the run:

    So Jim,

    If culture has such a powerful effect on outcomes, I can imagine some lineages having evolved the ability to control the development of new culture to cause the great majority of people to waste valuable effort obsessing over their putative cultural oppression rather than attending to the continuation of their lineage.

    Damn, they told me not to spill the beans.

    (PS, also psychometricians have obsessed over culture fair tests for a long while now ...)

  13. Neo:

    Vive la différence!

  14. Neo:

    In "The Bell Curve" (in part) by Charles Murray, he argued that if there was a class that had lower that usual scores (in anything) that it would be a problem that would be unaddressable due to political pressure not to offend that class.

    Of course, this is a prescription for a permanent underclass.

  15. markm:

    The trouble is, a variance difference of 1.85 explains some disparity in the male/female ratio in the math, hard science, and engineering faculty, but it doesn't explain an 85%/15% split unless you assume that all the professors are geniuses - which anyone who majored in one of those fields knows is not true. They are smart (90th percentile and up), but few of them hit the 99th percentile, and I'd expect that the very best often choose to take their skills into industry where they have a chance of becoming millionaires rather than settling for a guaranteed middle-class income that's pretty much unrelated to their accomplishments once they've crossed the threshold of tenure.

    I think there's another reinforcing factor - women with high math ability, like women in general, are far less likely to combine that with a serious defiency in social skills, etc., and hence don't need to hide from the real world in academia...

  16. Ron Hardin:

    I don't believe that variability has much to do with it.

    You don't have to be unusually smart to excel in science, but you do have to be absolutely dedicated to it, in particular preferring it to any social life, which girls are almost never likely to choose. Therein lies the difference that shows up in science.

    Vicki Hearne put this and other significant diffences in writing, in her book Bandit, wondering why ``vicious'' dogs bite boys many times more often than girls, and wondering why boys give up horseback riding at puberty

    A bit relevant to science copied out here

  17. Brandon Berg:

    That chart is misleading, as it doesn't show the tails of the distribution. A literal reading suggests that there are large areas in the extremes with many males and no females at all, which is wrong. Rather, the tails tend to have few males and even fewer (but some) females.

  18. E:

    Where in that study does it prove or even imply that these differences are biological in nature? He was fired for saying something stupid, but that stupid statement was not that men excel in math and science more than women. The stupid statement was that the cause for this discrepancy is innate predispositions; that men are naturally, biologically better at these subjects than women (and by inference, naturally more intelligent, more apt to be "in charge", etc.), a rather disturbing sort of manifest destiny if you ask... well, most intelligent individuals.