Bell curves

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, 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 maneuvers 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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156 Responses to Bell curves

  1. macho says:

    Your penultimate paragraph should be posted above the entrance to every physics department. In large font.

    It is also worth pointing out that it’s not clear yet how many young women are dissuaded from (or not successfully recruited into) majoring in physics after they enter college. The AIP survey found that the drop-off occurs somewhere between high school, where almost half of physics students are female, and the awarding of bachelors degrees, only about 22% of which go to women (and at least one major research university for which I’ve seen the numbers has graduated only about 13% women in physics in recent years).

  2. Arun says:

    First question – is the phenomenon that Xie and Shauman report upon universal across the first world societies, or is it American only?

    Second question –
    Could it simply be the fact that fewer of their cohorts are going into science be what dissuades young women from going into science?

  3. andrew jones says:

    First question – is the phenomenon that Xie and Shauman report upon universal across the first world societies, or is it American only?

    it’s pretty much everywhere:
    Japan, in physics and most communities

    “It is also necessary to build a framework that encourages women to pursue careers in science and engineering.” – Korea

    “However, the problem is worse than that. Many of the women who do take physics end up running away from it. Statistics show that a higher proportion of women than men leave physics at each stage of their career – a phenomenon that is often dubbed the “leaky pipeline”. –

    What’s worse is that in England they were considering (and might have passed) a law that segregates girls from boys in mathematics (and also possibly students of African heritage).

    just google science and women, gender inequality, there’s thousands of papers on this. Women in the sciences is a global issue, but at least it’s being addressed.

    Anyway, according to this there’s 9.8 million women working in the science fields in China, although I’d assume some of that is health care and research assistants:

    “According to a survey made by Hong’s federation, there are 9.88 million women working in science and technology, accounting for 36.91 percent of the total.

    As the status of women in China improves, more and more women are breaking the glass ceiling and taking on senior level positions.

    The Chinese Academy of Sciences and Chinese Academy of Engineering now have 87 female members, or about 5.1 percent of the total. “

  4. Frank says:

    I have the impression that it pays off a lot in physics to be extremely self-confident; do you know of any Bell curves and variances for measures of self-confidence?

  5. Winston Churchill says:

    I found this post quite confusing. The purported study of Xie and Shauman claims that high-scoring girls are less likely than boys to want to pursue science. Perhaps this is true, though it is common for social science studies to often be flawed and later contradicted. But suppose it is true: I don’t understand why Carroll is triumphantly claiming that this means the dearth of women scientists is not explained by the smaller numbers of women at the high end of test scores. The fact that there are smaller numbers of women at the higher end means that already they will be underrepresented no matter whether the women in the end choose to follow science. So even if high-end women are more likely to be discouraged, the dearth of women has already partially been explained by Summer’s point.
    Of course, in addition, the dearth of female physicists is explained by the fact that the few women at the upper end are less likely to pursue physics (as Carroll points out in the post). However, this is simply a complimentary observation, and it alone does not explain the dearth of women, as Carroll seems to be suggesting.
    But perhaps I misunderstand Carroll.
    Though I am no fan of Andrew Sullivan, as far as I can see his comment is perfectly fine.
    However, I would like to make an independent comment on this blog. I think having a blog for the general public in which scientists describe their work in a realistic manner– and detail what goes on behind the scenes– is a great idea. There is so much scientific illiteracy out there.
    However, that is not this blog. Rather than being a blog that extols the importance of critical thinking and the questioning of assumptions, this blog is a Daily Kos/Atrios-light written by those who are professors by day. We get narrow-minded posts about Hurricane Katrina which seem uncritically copied from any of the plethora of left-wing sites that exist. Or we get a post like this one, whose arrogant tone (I’m sorry but that’s the way this post and so many posts sound) is so off-putting to someone who is interested in this issue but doesn’t understand why it needs to become a partisan issue.
    It’s great the writers of this blog have political beliefs; all the physicists I work with do too. However, why replicate what other left-wing blogs already do– (again, I’m sorry) and do so much better?

  6. Dissident says:

    So what’s “dissuading high-school girls from choosing to become scientists”? Perhaps the simple realisation that a science career is not particularly appealing compared to all the available alternatives. Men may understand this too, perhaps even as quickly as women, but being less individualistic and more status-conscious, they choose to “soldier on”, Summers style, for the privilege of becoming underpaid thirty-something postdocs. “Smarter”? Heh…

  7. Cassandra says:

    Despite popular belief one does not need high end test scores to be a scientist. So to say that the lack of women in science is due to a lack of high scoring women, is uhh… wrongheaded.

  8. Fyodor Uckoff says:

    Exciting sociology research just out proves that, contrary to intuition, it *is* possible to revive a dead horse by beating it a sufficient number of times. Examples here, here, here, here, here, here, here, here, here, here, here, here, here, here, here, here, here, here, here, here, etc.
    Now let’s talk about something new.
    How about that hurricane in New Orleans, eh?

  9. Arun says:

    Sorry, the question really was – given a set of people with the same high scores, were girls as a percentage of their group less likely to continue into science than boys as a percentage of their group – universally?

    And in any case, just how good a predictor is high scores for boys?

  10. Wolfgang says:


    > revive a dead horse by beating it a sufficient number of times
    this is just an attempt to get a discussion with Lubos going …

    > How about that hurricane in New Orleans, eh?
    … so hurricanes and global warming will be discussed next 😎

  11. slanted tom says:

    OT but there is no science IF:
    Court case may determine how evolution is taught in US

  12. Arun says:

    Xie and Shauman find that the majority of men who get baccalaureate degrees in science or engineering pursue those degrees throughout their college years, whereas most of the women who graduate in these fields enter science and engineering during college after starting on non-science tracks.
    The gender gap in mathematics achievement is small and has been declining, and girls not only take as many maths and science courses as boys, but also get significantly better grades in them.

  13. Arun says:

    To me, the finding highlighted in 12. above breaks any obvious causal link, for women, between getting a Bachelor’s degree in science and engineering and test scores received at the end of high school. There is another breakdown of Summers’ argument.

    From the URL in 12, Xie and Shauman’s chief breakthrough may be breaking with

    the more familiar conceptualization of career trajectories in science and engineering is a “science pipeline”. This pipeline is unidirectional: participants enter the pipeline by taking maths and science courses at school, and leak from it at various points when they stop pursuing coursework or careers in science.

    I would need to read the book to be sure.

  14. jls says:

    Fyodor: sexist attitudes and misconceptions about women in science were a problem six months ago and remain a problem today. Big underlying sociological problems don’t fix themselves in six months.

    Dissident: “oh, women are so smart and let the poor, stupid men exhaust themselves slaving away at this unappreciated and underpaid work.” If women are so much more “individualistic” than men and wiser about their choice of careers (a statement which is sexist and misconceived to start with), why do women predominate in the work of raising children, which is much, much, more unappreciated and underpaid than science research careers?

    Gah. Thanks for trying, Sean.

  15. Bob says:

    In science we have often learned that it is easier to view 2 dimensions by viewing it from a 3 dimensional aspect. Likewise, this situation may be no different.

    What is it that frightens a lot of people of both genders in all cultures from science? They could be afraid to admit that they have been using science right from the time that motion was first their cradles..

    All of children’s play involves experimenting with the laws of motion. I think that sports and all shop courses in schools should come under the umbrella of Newtonian Physics and should be labeled as such..Home economics should fall under biochemistry and injuries that need trips to a medic should be seen as contributing to medicine. Kids can be intimidated by words from the science community but need to be reminded that learning the language of science is no different than learning a foreign language. When they remove such barriers, they become less afraid of pursuing science studies.

  16. spyder says:

    There are some pretty serious philosophical issues surrounding this topic, winston churchill notwithstanding. They lead to any number of critical questions that need to be asked and addressed as well as those that Arun put forward. Is there a need for more women “in” the sciences? Why is there such a need, and to what purpose and to fill what capacity does such a need serve? Are we sustaining this position(the need for more women in the sciences) from some enlightened ideal? Is the need best addressed through an increase in the number of women in academic roles at universities? Is the need best addressed through an increase in the number of women in research roles in the corporate structures(pharmaceutical and chemical corporations, governments sponsored physics researches, and so forth)?

    Once these questions are more fully understood and discussed, they lead to still more questions about the education of our children in general, as it applies to gender more specifically, and as it relates to how educational systems themselves “produce” or “fail to produce” the desired outcomes. As someone from that strain of academia, i can say that we in teacher education and public education reform, take these questions very seriously. There is a concerted effort by zealots of the right wing who deeply believe, and work to advance(through gaining seats on curriculum decision committess and district school boards) their views, that women in our society belong in the home tending to the basic nuclear family needs supporting their husbands in everyway that they are asked. Can you say promise keepers??

  17. If every single woman physics grad student that I have had enough close contact with to talk to me about it hadn’t felt intimidated, cajoled, and belittled because of her gender, I could have more sympathy for Winston’s remarksI don’t think it’s a conscious effort, but, at least from the perspective of MY university, it ends up with women feeling quite unwelcome studying physics. I came into grad schoo, four years ago, alongside 7 women. ONE of them is still int eh graduate department. And it has nothing to do with natural ability.

  18. Samuel Crane says:

    Winston Churchill, if that is your real name, why do you insist on haranguing these people for their blogging manners? The funny thing about blogs is that they are personal. Amazing!

    Who cares that they are physics professors except for the fact that this brings an particular lens to their views. Which in and of itself makes this site different than something like Daily Kos. I mean, if FOX is reporting on the hurricane than i guess that should free up the New York Times to cover other news stories, right? What an imbecilic suggestion that Cosmic Variance is wasting their time because you happen to think that they’re hacks.

    Blogs are personal soap boxes. I think it’s wonderful that I can pick up the news from the official outlets and then stop in at a diversity of blogs, from science-orientated places like CV and Pharygula to politics-oritentated places like Daily Kos, to see what the people think. Diversity of opinion and view point. Such is the advantage and value of blogs—which you seem to have a problem with.

    Here’s a suggestion, stop reading this blog if you think it sucks so much! And then make your own and run it how you want to—sans arrogance and partisanship. I for one don’t think i’d be reading your blog very much… too boring.

  19. Chris Crawford says:

    Let’s look at the significance of all this. While we’re busy arguing over genetic differences between men and women that affect behavior (and yes, there ARE such genetic differences), we might consider the real issue in the background: are women being unnecessarily held back from pursuing careers in science? The answer to that is certainly affirmative. However, let’s acknowledge that most of the of these restraints are not voluntary on any person’s part, in the sense that we’re not talking about sexist professors gleefully rubbing their hands together as they denigrate women students. The primary forces at work here are subtle and may not be so easily corrected. Indeed, correcting those forces may require changes in society that we might balk at.

    Consider, for example, the competition/cooperation axis. Testosterone pushes people (males) towards agonistic behavior. Men bull their way through problems that women prefer to talk their way through. For society in general, the female cooperative approach is more desirable. Indeed, a recent study demonstrated that corporate executives score much higher than average people on tests for psychopathy. However, that male bullheadedness can provide some benefit when it is directed at problems beyond the reach of normal efforts. Young males are the most dangerous creatures on the planet, because they are driven by testosterone to dominate. Some turn to crime, others to physics — but the basic drive is the same. And that drive, usually so destructive, can rarely lead to stellar achievement. Do you think that Einstein, Beethoven, Michelangelo, Newton, Darwin, or Shakespeare were laid-back guys engaging in pleasant intellectual diversions? Do you think it a coincidence that all great male thinkers achieve their boldest breakthroughs during their twenties, when that testosterone-driven urge to acquire females peaks? Males don’t reach the pinnacle of achievement by being naturally smarter — they do it by pushing themselves to the very limits of their abilities, by sacrificing everything else in their lives in pursuit of that grand goal.

    Men are not smarter than women. They’re sicker. For the great majority of men, this leads to some sort of personal disaster. For a lucky few, it leads to stellar achievement. As a group, males pay a steep price for their collective achievement. Let us not begrudge them that.

  20. Arun says:

    The causal connection between the “testosterone-driven urge to acquire females” and Newton’s accomplishments seems tenuous to me, especially, since as far as we know, Newton did not “acquire any females”. In general, I would think it would be easier to “acquire females” than to do what these folks did.

    Regarding Beethoven and Michelangelo, it is not clear to me what their “boldest breakthroughs” correspond to. They were productive through out their lives well beyond the testosterone.

    I would caution against falling prey to this kind of reductionism. It produces many just-so stories, very satisfying and all, but likely wrong. Everything doesn’t reduce to DNA or testosterone or high school math test scores.

    Anyway, even if you don’t agree with a word of the above, the following, and the essays preceding it, at the link below, are well worth the time spent reading.

    Study at one level determines the possible, the study at the next higher level determines the actual.

    We cannot understand a Newton from his testosterone.

  21. Wolfgang says:


    > Some turn to crime, others to physics — but the basic drive is the same.

    Great observation !

  22. Chris Crawford says:

    Arun, I had a look at the link you provide and was not much impressed. The analysis offered there lacks depth; it caricatures those beliefs it wishes to question.

    It’s true that Newton (and many other great achievers) did not explicitly seek to acquire females. I am talking about the effects of testosterone, which functions biologically to drive males to acquire access to lots of females. This effect is not something we can directly measure in the lab, but it certainly shows up in the behavior of males. This male thing I’m talking about is a drive to get to the top of the heap, to excel, to dominate. Every male goes about it in a different way. I mention acquisition of females only because that’s the evolutionary logic behind it. The individual male doesn’t perceive matters that way; Newton didn’t smile wickedly to himself as he wrapped up the Principia, saying, “I’m gonna be rolling in hot babes when this is published!” But the underlying drive came from that evolutionary force.

    Yes, there are lots of examples of people making great contributions after their thirtieth birthday. But when you look at the overall statistics of creativity, the 20’s are the prime decade for creative achievement. Creative achievement can certainly occur later, but the best time is the twenties.

    Lastly, your reference to reductionism brings up a troublesome issue. It seems to me that some people are using that term to apply to all science, all logic, or even all rationalism. For this reason, I no longer take that term seriously. Yes, it’s easy to abuse data in search of proof for a favored hypothesis. But that doesn’t mean that we abandon rationalism. We need only be careful with each application. This entire issue of female achievement in the sciences is particularly vulnerable to this kind of failure. Ultimately, the logic we use relies on the broadest possible collection of material from many fields. We cannot prove anything about any individual, and it’s even difficult to establish numeric values for groups. But we can still apply reason to the problem.

    Let me suggest that there are three primary causal factors for the dearth of women in science:

    1. Institutional selection against women.
    2. Self-deselection by women.
    3. Innate differences in talent between men and women.

    We all know that the first and second factors are real. Some people would deny any substance to the third hypothesis; the myriad established differences between males and females lead me to dismiss their denial. I am confident that the innate difference between men and women as regards to the drive to dominate does play some role in the issue, but I do not know its magnitude. My hunch right now — and it is only a hunch — is that the second factor plays the largest role, and the first factor now plays the smallest role (although it wasn’t very long ago when that first factor played a much larger role.)

  23. Kea says:

    “For well I understood in the prime end
    Of Nature her th’ inferior, in the mind
    And inward Faculties, which most excel,
    In outward also her resembling less
    His image….” Milton (Paradise Lost)

    Thanks again, Sean.

  24. Kea says:

    Chris Crawford

    Instead of trusting your intuition, you might try ASKING a few
    women in physics about their experiences.

  25. Arun says:

    You illustrate my point perfectly, Chris:

    1. Institutional selection against women.
    2. Self-deselection by women.
    3. Innate differences in talent between men and women.

    If Xie and Shauman are correct about the following

    …most of the women who graduate in these fields enter science and engineering during college after starting on non-science tracks.

    then for explaining
    a. Institutional selection against women and
    b. Self-deselection against women
    could have worked only after high school and was undone in part in undergraduate school

    c. differences in innate ability –
    does not explain either why women undergraduates transfer into the science and engineering stream.

    Of course, Xie and Shauman may be misled or may be misleading us. If not, we have to at least say at least that a., b., c., operate at certain times and are reversed at other times.

    It would be very interesting if the drive to dominate manifested itself purely in intellectual activity and not in character. Was any of these characters you name a dominating type? And can’t I equally well postulate that a quest for some kind of immortality (i.e., fear of death) was the underlying biological drive for these guys?

    Finally, how did evolution make this sexual drive appear that manifests itself in a rather asexual way?

    Without showing the causal links between things we are not saying anything very different than stories about gods on Olympus.