Archives

A sample text widget

Etiam pulvinar consectetur dolor sed malesuada. Ut convallis euismod dolor nec pretium. Nunc ut tristique massa.

Nam sodales mi vitae dolor ullamcorper et vulputate enim accumsan. Morbi orci magna, tincidunt vitae molestie nec, molestie at mi. Nulla nulla lorem, suscipit in posuere in, interdum non magna.

Provoking your detractors into being wrong like you

By Thoreau

John Tierney has decided to get himself some attention by writing about the hypothesis that gender differences in science careers can be explained by the variance in mathematical ability distributions being wider among men than women.  This hypothesis is almost certainly wrong*, but not for some of the reasons often offered.  Remember when I took on the race/IQ theorists, and noted that their detractors often over-simplify and thus weaken the pro-equity case?  Well, the detractors of the variability hypothesis do something similar.  Generally they sum up the hypothesis as “Women are bad at math.”  This is an over-simplification of a wrong idea.  The problem with the over-simplification is that it then gives the purveyor of the wrong idea the satisfaction of being able to sit back and say “That’s not what I said” and conclude that his opponents are driven by politics rather  than reason.  I don’t want to give them that satisfaction, so I’m going to present the variability hypothesis in its least bad form and then attack it.

First, the hypothesis is not a blanket statement about women and men, suggesting that every woman is deficient in mathematical ability and every man has an inherent biological advantage.  Most of the opponents of Tierney and Summers get that, but they still sum it up as “Women are bad at math.”  It is instead a statement about distributions, looking at the number of women and men at each level.  The hypothesis is that women tend to be closer to average, with fewer above average but also fewer below average, while men are more likely to have outliers on the high and low sides, with more men at the bottom of the math class and at the top.  Some framers of this hypothesis even suggest that women might actually have a slightly higher average, but because fewer women deviate significantly from their average there will still be fewer women at the top of the mathematical game.

Overall, this is a hypothesis that is only favorable to men at the highest levels.  Unfortunately for the framers, it’s also a hypothesis whose statistical support is questionable at best.  However, I’ll let people who are more immersed in the statistics take up that issue.  Instead, I’ll focus on the “So what?” question:  Even if this hypothesis were (for the sake of argument) correct, does it have any use in explaining disparities in scientific careers?  I’ll argue “no” for 3 reasons:

1)  This hypothesis is, if true, most applicable at the far ends of the distribution.  However, your average college science or engineering classroom isn’t drawn from the very top of the bell curve.  Not every science or engineering department is at Caltech or MIT, alas.  You can go to a science or engineering class at a substantially less selective university and still see a substantial disparity.  If we see this disparity in a group that is closer to the center of the bell curve, you can’t attribute it to the variance hypothesis.  You have to attribute it to other factors.  And since we have seen changes in the demographics of science and engineering over time, and since those changes have coincided with social changes, social variables are a far more plausible explanation than biological ones.

2)  At the upper end, innate intellectual aptitude for abstract reasoning is certainly part of the game.  So is creativity.  So is determination.  So is luck, or, more precisely, the ability to seize on good luck when it happens while riding out bad luck (more of a personality trait than an intellectual trait, in the phrasing of this non-expert).    So is communication ability (since getting ahead in basic research or industry is in part about persuading people that your approaches are good).  And a host of other traits.

Certainly raw talent for math is part of it, but hardly the only part.  The highest echelons of science and engineering are dominated by people who have the total package, and no two people have the exact same mix in their packages.  Some are weaker on one part than another, but they bring enough of each to the game, and they use what they bring, and they get where they go.  A great American engineer and scientist spoke of 99% perspiration and 1% inspiration.  Which is not to say that smarts don’t matter, but that a person could be slightly closer to the center of the bell curve by some measure of smarts and still win by perspiration.

So, knowing how a particular trait is distributed tells you little about how many people have the complete package.  It would be like looking at manual dexterity to the exclusion of all other factors, and trying to predict a person’s career path.  The  most dextrous person around may very well become a heart surgeon.  Or he may become an auto mechanic.  Or an engineer.  Or a sculptor.  Some of those paths have far more money and prestige than others, but looking solely at manual ability would tell you little about that person’s ability to go far and rise in the world.  You’d have to look at the total package.  In fact, even if you looked at a room full of medical students, manual dexterity might tell you who becomes a surgeon, but it wouldn’t tell you who becomes a famous surgeon.  Or who makes the most money.  The one who goes down the R&D path might become famous for an invention, but the one who goes into plastic surgery and makes the right connections in high society might make 10x as much money.  And the one who is just really, really good with his hands but not very inventive or charismatic might go into a less lucrative specialty and never become famous at all, despite having the best hands in the entire class.

The bottom line is that even if (for the sake of argument) this hypothesis regarding the extremes of the distribution is correct for one particular trait, it tells us little about how many people of each gender will be able to succeed in science and engineering.  And it tells us nothing about the vast majority of people trained in science and engineering, who are smart but not on the extremes.

*By writing “almost” in front of “certainly” in a post on a provocative topic I do run the risk of being paraphrased as “I absolutely cannot rule out…”  Let’s try to avoid that.

26 comments to Provoking your detractors into being wrong like you

  • DCA

    My memory is that Summers was, as President of Harvard, talking about the implications of such a difference in distributions for the hiring of Harvard professors: that is, even with equitable hiring, at the very top of the distribution you might still see an imbalance. This might pose a problem for a few elite universities, but has no implications for any other setting. And this is a hypothetical (I think Summers even posed it as such) that would be, as you say, very difficult to establish.

  • hf

    Well, Prof. T, that was well written but isn’t likely to satisfy anyone on either side of the debate.

    The core of your argument seems to be merely that there are many different factors influencing success in STEM. I hope you won’t take offense, but that sounds awfully close the the familiar argument “there are many factors influencing climate, so everyone has to STFU about man-made global warming”.

    In addition, your “whole package” theory doesn’t really invalidate the basic argument of the differential-distribution theory. They could just change their hypothesis to say that women (for whatever reason, it could even be institutional bias in earlier education) have a different distribution of performance on the “whole package”.

    And while I don’t think it’s a useful thing to focus on, I’ll have to admit to the following based on long experience teaching a lot of classes:

    – female students, while fewer in number, are definitely more likely to pass with a successful grade.
    – the best student is almost invariably male.
    – the worst students are almost entirely male.

    Colleagues who are willing to talk about this have the same experience. And yes, maybe it’s because we’re sexist in some complicated way that causes the women to have a higher but tighter distribution.

    Having said all that, I agree that differences in enrollment (as opposed to performance) are an order of magnitude too large to explain away using the distribution argument. The simplest and most obvious explanation is that women don’t go into STEM because there aren’t a lot of women in STEM already, and there is a clear path to correcting that. We noticed a sharp jump in female enrollment after we got our first woman on the faculty.

  • hf-

    OK, I grant that the second point may boil down to “It’s complicated” but at the very least I think it’s an adequate response to those who focus on math scores to explain the whole thing. If they wish to make a hypothesis based on variance, they will have to bring data for other traits besides math ability. Since most of those advocating the variance of the distribution as the key factor are indeed focusing on math, I think it’s an adequate response to the hypothesis as currently formulated in most public discussion.

    I share your observation about the male students almost inevitably being worst. However, I wonder if the scarcity of female students at the extremes of our anecdata may simply be due to the scarcity of female students overall. Alternatively, I can explain the male students at the bottom of the grade roster with 1 word: Playstation.

  • Barry

    “My memory is that Summers was, as President of Harvard, talking about the implications of such a difference in distributions for the hiring of Harvard professors: that is, even with equitable hiring, at the very top of the distribution you might still see an imbalance. This might pose a problem for a few elite universities, but has no implications for any other setting. And this is a hypothetical (I think Summers even posed it as such) that would be, as you say, very difficult to establish.”

    Summers is a f*cking Harwh*re. He basically skipped over every other possible explanation like the sort of guy who trashed the world’s economic system out of stupid Econ 101 glibertarianism. Considering that Summers was in Harvard in the 1970’s, and was witness to the massive surge of female students into field after field after field, it’s just sexism.

    As for his ‘just speculating’, I’ve heard that, starting back in the Bell Curve days, where various racist and sexist guys would paint their lies in a thin coat of pseudo-science. And *that* was invented centuries ago.

  • hf

    “anecdata” – thanks for the new and useful addition to my vocabulary.

  • Summers is a f*cking Harwh*re.

    a who is a what now? (i know you gotta censor for the sake of panera bread but what’s a har-hooah?)

  • alkali

    Philip Greenspun has commented, persuasively in my view:

    Having been both a student and teacher at MIT, my personal explanation for men going into science is the following:

    1. young men strive to achieve high status among their peer group

    2. men tend to lack perspective and are unable to step back and ask the question “is this peer group worth impressing?” […]

    What about women? Don’t they want to impress their peers? Yes, but they are more discriminating about choosing those peers. I’ve taught a fair number of women students in electrical engineering and computer science classes over the years. I can give you a list of the ones who had the best heads on their shoulders and were the most thoughtful about planning out the rest of their lives. Their names are on files in my “medical school recommendations” directory.

  • Honk! Honk!

    You sound like a lawyer defending a client. A client that’s guilty as hell.

  • Sherri

    Inevitably, the distribution arguments are shorthand for “see, there’s not really a problem, and anyway, it’s not our fault!”

    It’s certainly easy to come up with an explanation as to why women would be underrepresented at the lower end of the distribution: a woman is likely to be better in math than a man before she even considers going into a STEM field, given the subtle and not-so-subtle discouragements she faces. The absence of women at the higher end of the distribution could also be affected by those same discouragements, which do tend to undermine confidence over time.

    It’s been a long time since I was in school (physics undergrad, CS grad school), and I would have hoped for greater gains since then, but the numbers haven’t really gotten much better over the last 30 years. Now I have a 15 year old daughter who loves math and is good at it, but so far, isn’t thinking about STEM in her future.

  • Sherri-

    As I understand it, the variation argument is usually about skills as measured in middle schoolers or high schoolers, i.e. before the self-selection that goes into a choice of major.

    Or were you referring to the anecdata on female students rarely being the worst in the class? If so, I think you have a good point. However, let us not underestimate the explanatory power of video games as we try to understand why men are at the bottom of the class.

    You sound like a lawyer defending a client. A client that’s guilty as hell.

    Just so we’re clear, are you referring to the part where I present a slightly less weak version of the variation argument, or the part where I argue that it’s wrong? When I post things like this, I sometimes get hit from both sides, with some people thinking I’m a sexist and others thinking I’m caught in PC dogma.

    I’ll love it if you feel that way about both sides of my argument. I’ll totally feel like Cathy Young at that point. :)

  • However, let us not underestimate the explanatory power of video games as we try to understand why men are at the bottom of the class.

    Wouldn’t surprise me.

    So, knowing how a particular trait is distributed tells you little about how many people have the complete package.

    Inevitably, the distribution arguments are shorthand for “see, there’s not really a problem, and anyway, it’s not our fault!”

    The problem I think with this discussion is that there is a subtle suggestion that those who suggest some levels of difference in innate ability simply want to leave it at that and to push the issues under the rug. Certainly, I doubt that anyone who suggests the “variance” hypothesis is saying that we cannot study the issue more.

    I think the real reason that these things are getting brought up more and more is that a lot of people are tired of constantly being told that all differences between groups are the result of discrimination, and that ensuring that outcomes are equal is a top priority.

    I think a lot of people in our society are starting to feel like the science professor you referenced in an earlier post.

  • Sherri

    I was referring to the anecdata on female students rarely being the worst in the class, which is also consistent with my memory from long ago in STEM classes. Video games weren’t really a good explanation back then; there were only arcade games, so availability was limited.

  • Video games weren’t really a good explanation back then; there were only arcade games, so availability was limited.

    Yes, but the male students presumably had access to D&D, televised sports, pr0n (print or VHS), and comic books. All of these things can suck up time.

  • However, let us not underestimate the explanatory power of video games as we try to understand why men are at the bottom of the class.

    Let’s not overestimate it either. Before videogames there were comic books, and television, and sports, and pot, and alcohol, and D&D. To blame videogames doesn’t actually explain anything, it just pushes the question elsewhere. To wit: “Why is it the men rather than the women who decide they’d rather waste time in leisure pursuits than do their schoolwork?”

    Men have always been the bulk of the unemployable dropout moron/criminal class as well as the bulk of the award-winning Nobel Laureate/professor/inventor class. Your IQ-variance-doesn’t-really-matter-to-performance theory needs to explain *both* ends of that scale, and “guys play a lot of videgames” doesn’t do that.

    Heck, you could even go one step further and claim guys like videogames because videogames are designed to appeal to guys and that *still* wouldn’t do it. *why* are videogames designed to appeal to guys? Why aren’t the products that are designed to appeal to girls as compelling to girls as videogames are to guys? Why did guys constitute most of the goof-off dropout slackers even *prior to* the 1970s?

  • One could probably explain high achievement and low achievement by positing that males get sorted into different groups by various social factors, with extreme outcomes being likely for some of those groups, while women are less likely to be steered into the extremes. I wouldn’t need to appeal to IQ variance at all.

    One could also theorize that women try harder than men (hence avoiding the trap of pot and D&D) because they have to in a hostile world (and that hostility makes it less likely that they’ll be able to reach the very top).

    I don’t know that either of these approaches is actually right, but the existence of a variety of plausible theories shows that we should not simply glom onto one poorly supported biological theory for alleged lack of any better alternatives.

  • Oh, and I think that there is much wisdom in the Greenspun essay that alkali linked to.

  • albatross

    Thoreau:

    In these discussions (race and gender differences or lack thereof in intelligence), I always have the sense that you are several times more skeptical and demanding of proof from one side than the other. That’s natural with stuff you have strong feelings about, but it doesn’t strengthen your argument.

    Assuming the different-variances argument is true (the best discussion I’ve seen of it is http://www.lagriffedulion.f2s.com/math.htm), you have to look at the ratio of variances *and* how selective some distinction is (whether that’s graduating in EE from a middling state university or getting a PhD in math from MIT). You can’t just assert that the difference could only matter at the far right end of the bell curve.

    (As a caveat, I fundamentally don’t buy this analysis (at least the claimed precision in it) by Griffe du Lion, because it (like most of his stuff) depends so heavily on the tails of real-world distributions working like the tails of a normal distribution. Real world distributions often look normal in the middle, but usually not so much at the tails. I don’t know which direction his analysis is likely to be off by, alas. I’d need to know more about what the tails of intelligence distributions look like, and I am not even sure how you’d analyze that. Note that what we’re concerned with here is the distribution of intelligence, not of artificially created IQ scores which are synthesized out of a bunch of individual test scores whose correlation with one another and with performance in school or work is built mostly on people in the middle.)

    Your second reason (you never got to #3) struck me as just tossing out plausible things that may fall either way for anyone. Yes, for any kind of success in school or work or life, you need social skills and communications skills and a good work ethic and good luck, along with the requisite talent and intelligence. But what can we assume about those things? Girls tend to do *better* in school in terms of grades, be more conscientious, do their homework more regularly, and so on. I don’t see why luck should be distributed more one way than another. Women tend to be better than men overall at communication (at least verbally, women have higher average scores/abilities than men). This model would seem to predict that women should be *overrepresented* in math-heavy fields, relative to their talent.

    On the other hand, it’s clear that women are discouraged at various levels from going into hard science/math fields. For social, economic, or inborn preference reasons, women may also prefer fields that are less mathematical. I have no idea how to measure the effects of all these things and decide which of them dominates. But without doing that, it’s kind of hard for me to see how you can exclude the possibility of differences in abilities, either on average (spatial skills) or because of differences in the distributions that create big imbalanced at the tails of the distribution.

  • Wonks Anonymous

    “This hypothesis is almost certainly wrong”
    Shouldn’t you provide some support for that strong claim?

    Barry, Summers most certainly did not skip over every other alternate explanation. He even said there was much Harvard (or society more broadly) could do to better serve female STEM faculty. Like most of his detractors you appear to be quite unfamiliar with what he actually said. I suppose ignorant denunciations are so fun that informing yourself is unnecessary.

  • DannyK

    Thoreau, shouldn’t you make some notice that Tierney is using the Summers argument to knock attempts to address gender issues in science and engineering? That’s the real reason people always get mad at these statistical arguments about the abilities of Black people or women — they inevitably get used for (what are seens as) unsavory political purposes.

    Your discussion of the variability hypothesis is very interesting, but the anger doesn’t make sense without the political context.

  • DannyK-

    You’re absolutely right. I already had a long post going, and since I had already presented why I consider the hypothesis wrong I didn’t feel like going into a discussion of the ways the hypothesis is often utilized.

  • No Nym

    The distributional argument dates from at least 1910. It has as little evidence in its favor now as it did then.

    http://psychclassics.asu.edu/Hollingworth/sexdiffs.htm

  • Thoreau, could you link to your earlier presentation?

    Wikipedia reports that male IQs have significantly higher variance:
    http://en.wikipedia.org/wiki/Sex_and_intelligence#Variance_in_IQ

  • Bruce Baugh

    I’m not the only one to bring this up, but it’s such a compact, solid piece of data.

    Professional orchestras have gone from a standard of auditioning by musicians on display to the evaluators to one of performers doing their auditions behind a screen, so that they can be heard but not seen. Women have gone from being 10% of the population of professional orchestra players to 35%, in the course of about 20 years, and the percentage continues to rise. At several of the top-tier symphonies, they’re closing in rapidly on parity of genders in new hires.

    It’s really, really difficult to account for the earlier standing as anything but discrimination by auditors seeing women and discounting their performances.

    Given this datum, I feel comfortable in being skeptical about essentialist claims about women’s incapacity in other fields, and wish to see some comparable demonstrations before I feel obliged to give them, well, any credence at all. I don’t know what it would take, in lots of cases, to construct a comparable really, really effective screen against early discrimination on the basis of perceived factors other than performance, but I know I’d like to see a whole lot more work at trying.

  • Bruce Baugh

    Oh, and as a classic demonstration of DOIN IT RONG, the Vienna Philharmonic’s rationales for opposing blind auditions are really impressively bad.

  • marcel

    Thoreau wrote:

    Even if this hypothesis were (for the sake of argument) correct, does it have any use in explaining disparities in scientific careers? I’ll argue “no” for 3 reasons:

    1) This hypothesis is, if true, …
    2) At the upper end, innate intellectual aptitude …

    Late to the party, but I’ll bite. What is 3)? Or is this just a bit of sarcasm, Thoreau’s (who I believe is male) pretending that he is at the extreme low end of the mathematics ability distribution?

  • I used the search-bar for this blog, and it seems like Thoreau was agnostic on Summers’ most controversial claim in his first post here:
    http://highclearing.com/index.php/archives/2006/08/09/5356