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Take that, Larry Summers! December 15, 2011

Posted by mareserinitatis in education, feminism, math, papers, science.
Tags: intelligence, male variability, math
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I came across an article on the new research by Kane and Mertz which supposedly disproves the “greater male variability” hypothesis.  That is, while averages for both genders are approximately the same, males have more variance in their intelligence.  Thus, when intelligence tested, you’ll see more males at both the upper and lower tails of the distribution.

When Larry Summers was talking about the greater male variability hypothesis (GMVH) in his really awful speech, he was talking about those who are at least two standard deviations away from the mean.  If you look at the distribution of IQ for each sex, which is what he was referring to, you can see that the ratio at the 98th percentile is approximately 2:1 male to female.

If IQ were an accurate predictor of success in academia and academics came primarily from that top 2% (neither of which are universally true), you would then expect to see approximately 2 men for every woman in those professions.  Unfortunately, the ratio is much worse than that (from the perspective of women and feminist men, anyway).  This very compelling evidence of social, cultural, and/or economic factors, potentially up to outright sexism coming into play when women are being considered for academic positions.  The fact that it is still so far from this ratio makes me have a lot of issues with Larry Summer’s argument.  Aside from all that, there is the issue that IQ isn’t the best predictor of success.

However, let’s pretend it is…or that it at least that it may be reflected in math achievement for the tests used in the study.  In the study, they took variances from scores on tests like TIMSS and PISA, both of which are given internationally and used to compare various countries’ standing.  Specifically, the paper examined the variance question.

To do this, we can begin by looking at the data from IQ Comparison site, which says that the standard deviation in the WISC IV IQ test was about 14.54 for men and 13.55 for women.  The variance is the square of the standard deviation, giving the variance for men as 211.4116 and women as 183.6025.  If you want to do a comparison, just take the ratio of men’s variance to women’s and you’ll get a variance ratio (VR) of 1.15.  Keep in mind that the data this is taken from the US standardization which was used to norm the test, and it was done in the early 80s.  If you want to compare that to the data presented in the paper, the US VR in 2003 was 1.11 on the TIMSS and 1.19 on the PISA.  In 2007, it had dropped to 1.08 on the TIMSS (no PISA data is given).  Therefore, the VR has changed.

The authors use the math testing data to do this for many countries, not just the US.  You would expect that if the GMVH is true, then you would see VRs of about 1.15 from most countries and that it is constant in time.  What Kane and Mertz find is that the number seem to vary a lot, but many of them have changed.  That by itself gives an indication that a VR of 1.15 is not fixed and that the VR may be somewhat cultural.  Further, they changed through time.  Some of the VRs increased, like in Australia, and some decreased, like Japan’s.

This is the table presented in the paper:

They then attempt to find a correlation between male variance and the VR ratio.  If GMVH is true, you would also expect that a higher VR ratio would be highly correlated with males having a larger variance.  That’s not what they find, however.  The correlation value is fairly low, and the authors state that sometimes a higher VR is actually due to poorer performance on the test by boys.

There is significantly more analysis than I’ve communicated in this post, but the gist is that they found that gender equity in economic and educational arenas were the best predictor of test performance.  This gives a good indication that the GMVH is bunk – performance in math is not biologically destined.

Jonathan M. Kane and Janet E. Mertz (2011). Debunking Myths about Gender and Mathematics Performance Notices of the American Mathematical Society