The MSM on the new math/gender study.

Share on FacebookShare on Google+Email this to someoneTweet about this on Twitter

Tabarrok nails it.

Agnostic adds: Here’s a graph using the new study’s finding of same mean for males and females, and taking male to female ratio in variances to be 1.16 (they estimate it between 1.11 and 1.21). This is the ratio of a normal with mean = 0 and s.d. = 1.077 (male) to a standard normal (female). It’s shown for above-average people, but it’s symmetric about 0: males have more geniuses and more idiots. The dashed green line is M:F = 1, or perfect gender parity. Males are underrepresented between -1 and +1 s.d., and overrepresented outside this interval. You may have to click on the image to see it full-size.

Labels:

30 Comments

  1. The qualitative feminist argument about fewer women than men in high-prestige positions is quite good, in my opinion. I haven’t heard a persuasive rendition of a counter-argument that goes “There is no history of relevant anti-woman bias during the past few decades, and even if there was, it wouldn’t have had a significant impact on female employment patterns.” 
     
    The feminist argument turns dogmatic when non-50/50 gender ratios are presented as evidence of discrimination, rather than as markers of possible bias. The premise logically leads to the assertion that only equal representation is sufficient to prove the absence of discrimination. 
     
    This line of reasoning is on display in the comments of the linked Marginal Revolution post.

  2. Eh, sorry, 12:43 2nd paragraph to read 
     
    …The premise leads to the assertion that the absence of career-wrecking levels of discrimination can only be demonstrated by proof of equal representation.

  3. Amac — at risk of digression, an important meta counterargument is that women will usually be less happy if they achieve high status, as they generally want to mate with men of even higher status.  
     
    Overall, telling women to achieve high status a) reduces their time window for childbearing, b) makes it less likely to find a partner, and c) increases the likelihood of feminist indoctrination — triple whammy to fertility. Case in point — watch them struggle over whether a feminist can be in a heterosexual relationship:  
     
    http://www.feministe.us/blog/archives/2008/04/03/feministe-feedback-what-does-a-feminist-relationship-look-like/ 
     
    And Sylvia Ann Hewlitt presents data to indicate that childless CEO-type women wish they’d had kids instead. Conclusion: the most subversive kind of sex ed reform would be telling girls the truth: 48% of women will be infertile by age 35.  
     
    http://www.babycenter.com/0_chart-the-effect-of-age-on-fertility_6155.bc

  4. blah, 
     
    I trained in cell/molecular biology in the late ’80s/’90s. 
     
    > an important meta counterargument is that women will usually be less happy if they achieve high status, as they generally want to mate with men of even higher status.  
     
    Um. I don’t think it would have been such a good idea to have brought up such arguments around the lunch table. At least back then. How to become a social pariah, at a minimum. Maybe things are more relaxed now…

  5. Among white 11th-graders, there were twice as many boys as girls above the 99th percentile?that is, at the very top of the curve. (Asians, however, showed a very slight skew toward females above the 99th percentile, while there were too few Hispanics and blacks scoring above even the 95th percentile to compute their gender ratios.) 
     
    Why is the trend not the same for other ethnicities? What’s up with the Asians?

  6. Why not show both halves of the distribution? 
     
    Probably because I already stated that it was symmetric about 0 and gave that a simple interpretation. The discussion is based on M:F at high levels, so the below-0 range doesn’t matter. If I put the other half in, there would be too much unnecessary visual clutter.

  7. I think the graph assumes a normal (Gaussian) distribution of math ability. Most ability distributions are approximately normal, but depart from strict normality at the extremes. (According to Cyril Burt, anyway, and I don’t think he was making this up.) The true ratio of males to females at the highest ability levels therefore might be very different – either higher or lower – than suggested.

  8. Ironically, by ignoring the standard deviation aspect of this study, the feminists and their media backers have demonstrated…that they suck at math. 
     
    I busted a gut when I read this. I’ve got to call the doc–I think I hurt myself.

  9. The qualitative feminist argument about fewer women than men in high-prestige positions is quite good, in my opinion. 
     
    I don’t share you opinion. You might bring me on-side if you can offer convincing evidence to show that the professoriate in physics, math and engineering is more dastardly sexist than the professoriate of medical schools, law schools, psychology departments, etc which also used to be male-dominated but are now characterized by substantial female presence.

  10. The qualitative feminist argument about fewer women than men in high-prestige positions is quite good, in my opinion. 
     
    when i looked at cross-cultural data the proportion of women in math professions varied a lot. in places like mongolia where men are discouraged from higher education there was parity. but an important point was this: in all the countries i found data for [mostly EU, but some like mongolia, et.] the males were most well represented in mathematical/mechanical sciences, far less in other “high prestige” domains such as law and medicine. the ratio might have varied, but the rank order remained pretty invariant. norm of reaction? i also added the mechanical part because i noticed that mechanical engineering was often more male than mathematics, so it isn’t just math aptitude here. 
     
    there may be some discrimination on the margins which are greater in the mathematial sciences than the biomedical sciences (where women graduates are more than 50% in the USA last i checked), and some of this may be due to multiplier effects from small initial differences, but these “lack of women in math and science” conversations have a tendency of ignoring the fact that in the USA there are huge areas of academia where women are now substantial, or majority, presences. not all of them low status, such as law and medicine. 
     
    p.s. apparently cognitive psychology and psychometrics are the areas in psychology where men are numerous.

  11. Razib, I think the strongest part of the argument (expressed on that MR thread) is based on time series, e.g. the proportion of physicians in the US who were women was very small in the 1940s, and it has grown progressively closer to 50% in the decades since, as social acceptance of professional women increased. Such trends would support the notion that there was nothing inherent about women’s aptitudes that accounted for their low participation in this profession in the 1940s, say (in the absence of affirmative action programs).  
     
    This is an observation that can only be made in retrospect, obviously.  
     
    And though feminists would (presumably) disagree, it seems to me that the qualitative feminist argument can make no strong claims as to – 
     
    (a) The extent to which changeable social factors (eg discrimination, norms, socialization) rather than differences in aptitude or innate preferences determine gender distribution. This may (well, does) vary from situation to situation (eg schoolteacher, accountant, psychologist, firefighter, theoretical physicist). 
     
    (b) The argument does not imply that 50/50 gender balance is a natural or desirable or just outcome in any given situation.

  12. (b) The argument does not imply that 50/50 gender balance is a natural or desirable or just outcome in any given situation. 
     
    no shit, since in medicine, law a non-mathematical sciences women are already more than 50% of the graduates now! ;-)

  13. I couldn’t locate the volumes I had in mind, but the newsletters of my professional society (American Society for Cell Biology) often remonstrate against the continuing gender discrimination in the field. Raising kids and advancing towards tenure is not a natural or easy combination, and to some extent this is a gender issue… in other regards, it isn’t. Even that is too much to say out loud in polite company.

  14. in other regards, it isn’t.  
     
    well…yeah. there are people who helped their retarded friends do OK in organic chemistry via free tutoring who are on post-doc #3 unable-to-afford-a-house while their retarded friend is starting make a lot of money as an MD and is married to a hot-thang.* there are serious issues staring you back in the face when it comes to a science-career. but at the end of the day here is the question that matters: but is it good for science??? the percentage of women, minorities, the quality of life of scientists, the ability to raise a family, etc. etc. all pale in comparison to this. the continued economic productivity gains which fuel the consumer society are driven in large part by the gains accrued via science & technology. so is it good for science has an implication for is it good for civilization. if, for example, we go hard on quotas to make sure there are the “right” proportion of lawyers and doctors people would be natural consumers and discriminate against women and minorities under the assumption that they’d provide substandard services (to which many women and minorities who aren’t substandard would figure out ways to advertise that they weren’t substandard). there isn’t such an easy “demand side” solution for the distortions of the culture of science. to some extent our civilization hangs in the balance when it comes to the perpetuation of the scientific culture which started with dead white males. there were lawyers and doctors during the days of rome. scientists, not really IMO. 
     
    (this by the way is why i’m pretty OK with scientists taking drugs to increase their IQ if that means shorter life expectancy; 5 years in one persons’ life for the greater good of mankind. let’s take that if that’s the choice people make) 
     
    * i’m not dissing MDs here, i’m saying that i know many circumstances where moderately bright people are very successful in terms of status and money, while somewhat brighter people who took the “pure” science route are far less so.

  15. I haven’t read much into the “women in science” debate, but here are my current thoughts: 
     
    There surely exist environmental biases against women both within academia, and on the way there (i.e. in the acquisition of the abilities/grades/etc. required to be at the top in academia.) These biases have reduced over the year, resulting in increased female representation. These biases don’t prevent women from reaching equality in fields like psychology, and outnumbering males in fields like linguistics or sociology. Thus, the argument for environmental bias being the primary cause of the math/science gender gaps is logically required to claim that said biases grow stronger as the fields become more algorithmic. 
     
    There are several plausible lines of argument that can be made along such lines. Just to name one for example, it might be argued that women are socialized to be more empathetic/people oriented, and are thereby repelled by nerdish subcultures. (I don’t buy the argument that this is environmental based on what I’ve currently read, although I’m open to the possibility. At the very least it seems likely that there is a genetics-environment interaction between innate factors and things like stereotypes and gender roles.) 
     
    What I don’t understand, however, is how anyone can claim significant discrimination against females by teachers/administrators at any grade level–kindergarten to grad school.

  16. it might be argued that women are socialized to be more empathetic/people oriented 
     
    The kind of socialization you probably have in mind doesn’t matter: boys who are raised and socialized as girls do not behave at all like girls.

  17. agnostic, 
     
    i agree that studies like that point to a genetic component. i don’t see how they rule out a gene-environment interaction, though. 
     
    as a sidenote: the summaries i’ve read of those studies indicate that the boy-girls prefer to play with trucks, rough-house, etc. thus, i’m not sure how one can claim that these behavioral studies say much of anything about math aptitude. like i said before, i haven’t read enough about this subject so i wouldn’t be surprised if my understanding of the scope of these studies is off.

  18. no shit, since in medicine, law a non-mathematical sciences women are already more than 50% of the graduates now! ;-) 
     
    What in the world is a non-mathematical science? Do you mean social sciences? Even biology needs math, often in addition to just basic statistics. 
     
    How’s the male/female ratio for non-health science biologists(such as population ecologists, cell biologists or geneticists)?

  19. when i looked at cross-cultural data the proportion of women in math professions varied a lot. in places like mongolia where men are discouraged from higher education there was parity. but an important point was this: in all the countries i found data for [mostly EU, but some like mongolia, et.] the males were most well represented in mathematical/mechanical sciences, far less in other “high prestige” domains such as law and medicine. the ratio might have varied, but the rank order remained pretty invariant. norm of reaction? i also added the mechanical part because i noticed that mechanical engineering was often more male than mathematics, so it isn’t just math aptitude here. 
     
    Is the M/F ratio for Asians like Chinese and Tamils closer to one? I always got the impression that the West had the most exaggerated variance for males.

  20. thus, i’m not sure how one can claim that these behavioral studies say much of anything about math aptitude. 
     
    upon re-reading your comment i see you weren’t claiming that those studies speak to math-aptitude specifically, just to socialization. my bad.

  21. BTW, the next time you hear some dopey and loudmouthed Baby Boomer or Gen X-er whining about how we need to socialize the young in the desired direction, ask them how well older people managed to socialize them. It’s just a bunch of goddamned nonsense. 
     
    And now Gen Y-ers, or whatever they’re called, are acting independently from the Boomers and X-ers. At least for these matters (what career to go into, what music to listen to), people pay attention to their peers, which isn’t the same as imitating them 100% of course. 
     
    “I’ll do whatever I feel like, Mom!”

  22. these discussions tend to veer off course, even at gnxp. 
     
    short term, it doesn’t matter what the cause of the m:f ratio of high math performance is (7:1 with SAT-M > 760 in the study of mathematically precocious youth), unless academic hiring practices are themselves the cause. otherwise, the pressure for quotas in science hiring needs to be ended. 
     
    long term, figuring out what causes sex differences is really hard. there are fewer clear-cut natural “experiments” to work with than in individual or racial group differences. Correlations with sex hormone measurements are fairly good evidence. Pathological cases of ambiguous or mixed-up sex are less robust. The age of onset of some differences is good evidence. The psychometric structure of the differences — some male and some female advantages — are not predicted by simple discrimination theories.

  23. What a quandry. To demonstrate to what extent one group produces more great mathematicians than another, we must use mathematics.  
     
    Can’t we put it in an episode of Sex in the City?

  24. well…yeah. there are people who helped their retarded friends do OK in organic chemistry via free tutoring who are on post-doc #3 unable-to-afford-a-house while their retarded friend is starting make a lot of money as an MD and is married to a hot-thang.* 
     
    Ironic, isn’t it? though i do think the med guys do at least tend to be decently bright and studious. i’ve known a lot of really smart math/science guys that chose medicine when they weighed the economic benefits…… the retarded kids tend to wash out in undergrad and switch to business or public health. there’s big time weeding out between freshman and senior year.  
     
    Oh and lots of hot thangs are becoming docotors now. Something like half of all new doctors are female. :)

  25. Oh and lots of hot thangs are becoming docotors now. Something like half of all new doctors are female. :) 
     
    I will never understand the drive, or maybe inertial force, to assort by profession. If you want to marry a good-looker who is smart enough to talk about smartie things with, network with ballet people until you win over a dancer.

  26. Table 2 of the article list the sample size of 219 for Asians. Which means (from the percents scoring above 99th reported in the table, 1.37 for girls and 1.25 for boys) that the authors’ statement “Even at the 99th percentile, the gender ratio favoring males is small for whites and is reversed for Asian Americans” is based on 3 girls and 2.74 boys. Sheesh … some statistics. (And what’s up with the 2.74 boys?)

  27. The top 1% of achievers in maths is also disproportionately white male. I haven?t seen anyone claim yet this means white folks are smarter; presumably it?s obvious to everyone that socio-economic factors play a pretty big role in test scores.

  28. One of the most striking pieces of evidence regarding this matter is the list of high scoring people in the Putnam Mathematical Competition. This competition is written every year by the best undergraduate mathematics students in USA and Canada, and the people who do well are the best of the best, and truely must in the extreme upper fringes of mathemaatical ability.  
     
    http://en.wikipedia.org/wiki/William_Lowell_Putnam_Mathematical_Competition 
     
    The top 5 students every year (or top 6 in the case of a tie) are given the distinction “Putnam Fellow”. The names of Putnam Fellows are published every year.  
     
    http://www.maa.org/awards/putnam.html 
     
    Since 1992 there has been a special award for the top scoring female in the competition. From 1992-2007 a woman acheived the Putnam Fellow distinction only 4 times, while men have been awarded this distinction about (5*16)-4 = 76 times. So the M:F ratio is 76:4, or 19:1. (I am basing the gender count on the assumption that in a year when a woman is a Putnam Fellow, she will also be the winner of the Elizabeth Lowell Putnam Prize for the highest scoring women. Because many of the names are not Anglo-Saxon, I can’t tell from the names alone). 
     
    More data could be obtained, because a list of the top 500 contestants is published every year, and likely the gender of most could be determined using the first name (if a team of people familiar with names in different cultures looked at them).  
     
    I wrote the contest in 1993 and scored in the top 500, which is how I know about the list. I’m also a female.  
     
    Before you men get too smug, keep in mind that a lot of men in the upper fringes of mathematical ability seem to have strange, antisocial personalities–they might have Asperger’s or something like that (which is more common in men). And a lot of them are just bat-sh*t crazy.

  29. Note that if test scores are some ability plus noise, and if the noise variance doesn’t change much between genders, then the gender ratio of ability variance will be larger than the observed gender ratio of score variance. So a graph like this for ability would be even more dramatic.

  30. Voyageur Occidental sez: 
     
    “What in the world is a non-mathematical science? Do you mean social sciences? Even biology needs math, often in addition to just basic statistics.” 
     
    As razib has pointed out numberous times in the past, physicians don’t use math. That’s because medicine is not a science, more like “son/daughter of science.” While there are plenty of research scientists in the field of medicine (a four year medical degree is one of the best ways to get into biological research) most physicians apply the results of the science on a one to one basis with their patients. Hence the lack of statistical sophistication since the highest level of math most physicians use was ground into their brains in the fourth grade. 
     
    Women are now slightly dominate in medical schools and residency programs because they are capable of sustaining the high work rate and good grades needed to get into medical school and have had the chance to get in over the past 30 years. This is a factor of change in our society, not something inherent to men. When I applied to medical school in 1965, 10% of medical students were women. The trick was to beat out all those white males. When my son applied in 2000, he was applying to about 40% of the seats available (you subtract 50% women and 10% misc. including 6 year students, and other considerations.) It was probably a lot harder for him to get in. 
     
    But the math requirements for med students remain the same: you take a statistics course for a few weeks and promptly forget it. 
     
    There have been alterations in the demographic make-up of students since I was matriculated but the quality does not seem to have changed based on my experience teaching in medical schools.  
     
    But they still don’t teach you to be a scientist.

a