Monday, July 28, 2008

Larry Summers and the case of the gender variance ratio

For the past week or so the newspapers have been trumpeting a new study showing no difference in average math ability between males and females. Few people who have looked at the data thought that there were big differences in average ability but many media reports also said that the study showed no differences in high ability.

The LA Times, for example, wrote:
The study also undermined the assumption -- infamously espoused by former Harvard University President Lawrence H. Summers in 2005 -- that boys are more likely than girls to be math geniuses.

All of these reports and many more like them are false. In fact, consistent with many earlier studies (JSTOR), what this study found was that the ratio of male to female variance in ability was positive and significant, in other words we can expect that there will be more math geniuses and more dullards, among males than among females. I quote from the study (VR is variance ratio):
Greater male variance is indicated by VR > 1.0. All VRs, by state and grade, are >1.0 [range 1.11 to 1.21].
Notice that the greater male variance is observable in the earliest data, grade 2. (In addition, higher male VRS have been noted for over a century). ...

Does this mean that discrimination is not a problem? Certainly not but we need the media and academia to accurately present the data on ability if we are to understand how large a role other issues may play.
--Alex Tabarrok, Marginal Revolution, on what the latest study really says about differences in within-gender ability variance

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