Wednesday, January 19, 2005

Invincible Summers

My post on the Summers affair has definitely received some negative attention, much of it based on misconceptions of what I said, so I thought I would clear a few things up.

First, what did Summers say? He made two different points:
  1. One of the reasons that there is a dearth of female professors in the sciences may be genetic differences between males and females.
  2. With reference to the small number of female professors in the sciences, he stated, ''Research in behavioral genetics is showing that things people previously attributed to socialization weren't."
He later stated that the first of these was merely a hypothesis, based on the "scholarly work" presented at the conference. The question, then, is whether it is a viable hypothesis. The second point was much more than a mere hypothesis. It's a pretty strong assertion.

On his first point, is it a viable hypothesis? I was arguing in the first post that it's not, and despite Summers' assertions, we do have plenty of research to assess it. As I said in my first post, the research shows that there are no differences in primary math skills (counting, arithmetic, subitizing, ordinality, numerosity, etc.) across cultures, and these abilities appear to have very little genetic influence. There are, however, consistent differences in secondary math abilities across cultures in the general population, though when more specific populations are tested, the differences vary greatly. Furthermore, there is ample evidence that these differences are largely (though not entirely) due to sociological factors*.
  1. The emergence of secondary math skills is largely dependent on cultural institutions.
  2. The role of discrimination in primary and secondary schools in both math confidence and motivation in females (some of which Clark mentioned in comments to my last post, and Dr. Myers' mentioned in his post), including the evidence presented in the Sherman studies (see footnote 1), as well as the Casey et al. (1997) and the stereotype-threat studies cited in my last post.
  3. Another piece of evidence is the actual differences in performance in males and females on the SAT-M (the primary test used to measure sex differences in math). These differences are largely in the number of correct answers. When the ratio of correct answers are compared, there are no differences (at least in college-bound and college-attending females). Thus, the consistent differences appear to be due to males answering more questions, a result which may indicate that females are slower in mathematical reasoning, but not worse overall (an interpretation that the results from non-speeded mental rotation tests also suggest).
  4. The fact that the effect sizes (which, in the early seventies, were a whopping .3) for the differences between males and females on the SAT-M and similar tests have dropped significantly over the last 30 years (from about .3 to around .14). See Hyde et al. from the previous post.
Taken together, these suggest a strong, though not exclusive (I'll say that again for the commentors on the last post who didn't get it then: though not exclusive) role for socialization in sex differences in mathematical ability. Number 4 is particularly interesting, because it suggests that the bulk of the effect size from the 1970s was either due to social factors, or women have, over the last 30 years, evolved to be better at math.

Number 4 also serves as the best reply to Summers' second point. While there have been arguments for decades that biological, rather than sociological factors are responsible for the small percentage of women in science and math careers, making Summers' statement seem a bit odd, there has also been ample evidence over this time that sociological factors do play a large role (see, for more examples, any of the Eccles publications that you can request from this site). The best illustration of this, to my mind, is effect size. It is extremely unlikely that the small effect sizes in math ability could explain the huge effect sizes in career entrance and success. Even if we look at only the highest scoring males and females, the differences in number are too small to account for the large differences in a wide variety of math-intensive fields, both within and outside of academia.

* See e.g., Sherman, J. (1980) Mathematics, spatial visualization, and related factors: Changes in girls and boys, grades 8-11. Journal of Educational Psychology, 72, 476-82. Sherman, J. (1981) Girls' and boys' enrollments in theoretical math courses: A longitudinal study. Psychology of Woman Quarterly, 5, 681-89.