Gender & science

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My friend Jake Young has a post up, Contrasting Views on the Gender Disparity in Science:

Second, one of my primary arguments against innate differences in ability between men and women is that you are dealing with traits that have distributions and those distributions largely overlap. Making a statement about any individual man or woman is largely useless. The odds of a women or man selected at random being better or worse at math are not particularly different. This argument applies just as well to differences in preference. Maybe there are differences on average, but they are still distributions that overlap. The key question becomes: to what degree do those distributions overlap? How different on men’s and women’s preferences on average?

James Crow’s Unequal by nature: a geneticist’s perspective on human differences is apropos here:

There is actually a simple explanation that is well known to geneticists and statisticians, but not widely understood by the general public or, for that matter, by political leaders. Consider a quantitative trait that is distributed according to the normal, bell-shaped curve. IQ can serve as an example. About one person in 750 has an iq of 148 or higher. In a population with an average of about 108 rather than 100, hardly a noticeable difference, about 5 times as many will be in this high range. In a population averaging 8 points lower, there will be about 6 times fewer. A small difference of 8 points in the mean translates to severalfold differences in the extremes.

My conclusion, to repeat, is that whenever a society singles out individuals who are outstanding or unusual in any way, the statistical contrast between means and extremes comes to the fore. I think that recognizing this can eventually only help politicians and social policymakers.

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22 Comments

  1. Table 1 (Page 236) of the paper in the URL makes that point clearly. Assuming a normal distribution, it shows that even if men have only small advantages on spatial rotation skills, and/or a slightly higher variance of such skills, you’ll see big differences at the high end. A 5:1 M/F ratio is nothing special, while 17:1 isn’t out of the realm of imagination…. 
     
    So boys and girls will do about equally well at your typical high school, but there’ll be big differences at MIT and CalTech.

  2. All I can say is, thank God I majored in English.

  3. remarkable!! this is spectacular new formulation of the overlap = equality fallacy. several features speak for it to become to new go-to position on the denial of individual human differences: 
     
    first, it has the benefit of being less trivially false than the old fashion alternative, such that you can make it explicit without it being an obvious contradiction. 
     
    second, it is sufficiently complex that it invites repetition by elites along the lines of Lewontin’s fallacy. 
     
    third, it is indirectly playing towards the now inescapable conclusion that genetics can be a powerful force. yet cleverly it does so by arguing that the effect sizes are so small that genetics couldn’t be the explanation. 
     
    of course, you tack onto this position the fallacy that only genetic differences matter, and you have a real winner. your friend may have inadvertently started something big.

  4. Maybe we should provide visuals not of the “overlapping bell curves” kind, since that just reinforces this bafflegab. Our visuals from now on should be male curve minus female curve, which plots male over-representation along the spectrum. 
     
    If we’re talking IQ, where means are the same but male variance is greater, you get an upside-down Mexican Hat function: a negative dip around the mean, and positive values throughout both tails. I think this helps people visualize it more, since you have a bright line — negative vs. positive values show under- vs. over-representation of males.

  5. An important point to keep in mind when considering these issues (e.g., the gender gap in STEM participation) is that while etiology is important, mutability is more important. 
     
    It’s much easier to be convinced that there’s nothing known that can reasonable done about an issue than to be convinced of some particular causal theory.

  6. you probably want male curve / female curve 
     
    x=seq(-4,4,0.1); plot(x,dnorm(x,0,1.05)/dnorm(x,0,0.95))

  7. yeah that looks better

  8. Goddamn Blogger is being retarded about uploading the graphic. Well, check back later and there will be a pretty picture (below the fold) and explanation.

  9. How is it known that a small difference in the mean means large differences at the extremes. This assumes a certain shape of curve. Don’t curves vary a lot?

  10. OK, seriously. 
     
    If you are comparing group behavoural trends, then you look at how groups compare to each other statistically, not how individuals within those groups compare. I don’t think Jake’s approach goes very far towards understanding the differences between men and women in the disciplines they choose.

  11. If you want to explain the point to the unknowing, wouldn’t it be better to use height as an example? Its emotional burden is less.

  12. OK, here is the Male : Female ratio across the IQ spectrum: 
     
    http://akinokure.blogspot.com/2008/05/male-to-female-ratio-across-iq-spectrum.html 
     
    Click on the picture in that post for a larger view. 
     
    When Blogger stops acting retarded, maybe I can add it to this post.

  13. You lot have a point. But I would careful about making predictions that imply any measurable level of precision when extrapolating the bell curve beyond ~2sd. Kurtosis is a bitch.

  14. The differences at the extremes can be striking, even more so with assortative mating.

  15. If men fit a normal distribution, and women fill a normal distribution with a different mean and variance, then PEOPLE do not fit a normal distribution.

  16. the tails are fat. any psychometricians out there willing to correct for that?

  17. Super-smart women are half-men (tall & legs-shaving). L. Cosmides is the exception.

  18. Just something I accidentally read yesterday (but has a date from 2000): 
     
    http://www.sciencedaily.com/releases/2000/09/000913083409.htm 
     
    women tested in single-sex groups scored a 70-percent accuracy rate on math exams; women tested in groups in which they were outnumbered by men scored a 58-percent accuracy rate 
     
    Being outnumbered may cause females to suffer from ?stereotype threat,? a situational phenomenon that occurs when targets of a stereotype ? in this case the idea that women do not perform as well as men in math ? are reminded of that stereotype, 
     
    In the same journal you can find similar aricles of more recent dates: “Women math performance affected by theories on sex differences”, “Are women being scared off math, science and engineering fields” (I know my own dad scared off my very smart sister from becoming an engineer in fact), “Gender stereotypes influence intent to pursue entrepenerial careers”, etc.

  19. “Super-smart women are half-men (tall & legs-shaving). L. Cosmides is the exception.” 
     
    No, they just seem that way compared to super-smart men.  
     
    Anyway, Hedy Lamarr and several of my former classmates would be highly insulted at your silly ass sto-type.

  20. “legs-shaving”? LOL. How many % of women are “full women” according to this criterion?

  21. Luis, have you replicated those findings of “stereotype threat?” 
     
    I didn’t think so.

  22. Luis, have you replicated those findings of “stereotype threat?” 
     
    I didn’t think so.
     
     
    Obviously not, have you falsified them? ^^ 
     
    At the linked article you can find many other similar articles in the same line. Other people have duplicated the study or done something that is about the same, not once but several times.  
     
    Sorry if your macho pride got hurt.

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