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  •  Armando misstates what Summers said. (4.00)

    Janet Shibley-Hyde's paper, "The Gender Similarities Hypothesis" is quite interesting, and a useful corrective to difference theorists such as Carol Gilligan, Deborah Tannen, and John Gray. Unfortunately for Armando's dig at Harvard President Larry Summers, however, Shibley-Hyde's paper is not inconsistent with his actual remarks at the National Bureau of Economic Research. Indeed, the approach that Summers entertained, and which Armando mischaracterizes, as one of three possible explanations for the under-representation of women at the highest levels of math and science, is one that Shibley-Hyde concludes "merits continued investigation."

    Shibley-Hyde's gender similarities hypothesis is that

    males and females are similar on most, but not all, psychological variables. That is, men and women, as well as boys and girls, are more like than they are different. In terms of effect sizes, the gender similarities hypothesis states that most psychological gender differences are in the close-to-zero . . . range, a few are in the moderate range . . . , and very few are   large . . . or very large. . . .

    Shibley-Hyde recognizes, however, that her meta-analysis does not answer the question of variability(emphasis added):

    One caveat should be noted, however. The foregoing discussion is implicitly based on the assumption that the variabilities in the male and female distributions are equal. Yet the greater male variability hypothesis was originally proposed more than a century ago, and it survives today (Feingold, 1992; Hedges & Friedman, 1993). In the 1800s, this hypothesis was proposed to explain why there were more male than female geniuses and, at the same time, more males among the mentally retarded. Statistically, the combination of a small average difference favoring males and a larger standard deviation for males, for some trait such as mathematics performance, could lead to a lopsided gender ratio favoring males in the upper tail of the distribution reflecting exceptional talent. The statistic used to investigate this question is the variance ratio (VR), the ratio of the male variance to the female variance. Empirical investigations of the VR have found values of 1.00 -1.08 for vocabulary (Hedges & Nowell, 1995), 1.05-1.25 for mathematics performance (Hedges & Nowell), and 0.87-1.04 for self-esteem (Kling et al., 1999). Therefore, it appears that whether males or females are more variable depends on the domain under consideration. Moreover, most VR estimates are close to 1.00, indicating similar variances for males and females. Nonetheless, this issue of possible gender differences in variability merits continued investigation.

    Against this background, brought to our attention by Armando, let's examine his contention that "Summers . . . said they [men] had greater aptitude in math and the sciences than women."

    By not providing a link to Summers's remarks, Armando makes it somewhat difficult to verify his claim about what Summers supposedly said. The transcript may be found, however, both

    The transcript demonstrates the invalidity of Armando's claim, that is, Summers did not say that men "had greater aptitude in math and the sciences than women." Rather, he entertained the "greater male variability" hypothesis that, according to Shibley-Hyde, "merits continued investigation."

    Summers was addressing "the issue of women's representation in tenured positions in science and engineering at top universities and research institutions." In this connection, he noted that

    the role of women in science is [not] the only example of a group that is significantly underrepresented in an important activity and whose underrepresentation contributes to a shortage of role models for others who are considering being in that group. To take a set of diverse examples, the data will, I am confident, reveal that Catholics are substantially underrepresented in investment banking, which is an enormously high-paying profession in our society; that white men are very substantially underrepresented in the National Basketball Association; and that Jews are very substantially underrepresented in farming and in agriculture. These are all phenomena in which one observes underrepresentation, and I think it's important to try to think systematically and clinically about the reasons for underrepresentation.

    Summer then offered three "broad hypotheses about the sources of the very substantial disparities that this conference's papers document and have been documented before with respect to the presence of women in high-end scientific professions."

    One is what I would call the-I'll explain each of these in a few moments and comment on how important I think they are-the first is what I call the high-powered job hypothesis. The second is what I would call different availability of aptitude at the high end, and the third is what I would call different socialization and patterns of discrimination in a search. And in my own view, their importance probably ranks in exactly the order that I just described.

    Focusing on the "different availability of aptitude" hypothesis, Summers emphasized that, "[e]ven small differences in the standard deviation will translate into very large differences in the available pool." In particular, Summers calculates that a standard deviation of 20% (d = 0.20 in Shibley-Hyde's terms), produces a difference of "five to one, at the high end." Here's the full context of what Summers said on this point (emphasis added):

    If one supposes, as I think is reasonable, that if one is talking about physicists at a top twenty-five research university, one is not talking about people who are two standard deviations above the mean. And perhaps it's not even talking about somebody who is three standard deviations above the mean. But it's talking about people who are three and a half, four standard deviations above the mean in the one in 5,000, one in 10,000 class. 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. Now, it's pointed out by one of the papers at this conference that these tests are not a very good measure and are not highly predictive with respect to people's ability to do that. And that's absolutely right. But I don't think that resolves the issue at all. Because if my reading of the data is right-it's something people can argue about-that there are some systematic differences in variability in different populations, then whatever the set of attributes are that are precisely defined to correlate with being an aeronautical engineer at MIT or being a chemist at Berkeley, those are probably different in their standard deviations as well. So my sense is that the unfortunate truth-I would far prefer to believe something else, because it would be easier to address what is surely a serious social problem if something else were true-is that the combination of the high-powered job hypothesis and the differing variances probably explains a fair amount of this problem.

    According to Shibley-Hyde, a difference in standard deviation of 0.20 counts as "small." (Shibley-Hyde, page 1.) So there's no inconsistency between

    • her claim that "men and women . . . are more alike than they are different";  and

    • Larry Summers's hypothesis that a small difference in the standard deviation of aptitude in math and science would produce a large difference in the availability of men and women "at the high end."

    Please note that I'm not arguing that Summers's hypothesis is correct. Nor that it is the sole or primary explanation for the under-representation of women at the highest levels of math and science. What I am saying, evidently along with Shibley-Hyde, is that the hypothesis is worthy of investigation. I'm also saying that Armando has misstated what Larry Summers said about this highly emotional issue.

    f/k/a one of the people "`Our country, right or wrong!' . . . when right to be kept right; when wrong to be put right." (Sen. Carl Schurz)

    by another American on Wed Sep 21, 2005 at 08:56:24 AM PDT

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