The first paper that La Griffe du Lion clarifies was written by veteran feminist author
Janet Hyde (click)and we have already discusses it: she claimed that the math gap between the sexes has evaporated. Lion's conclusions are pretty much identical to ours when he or she writes that
- she uses tests with small children for which the gap has not yet fully blossomed
- the tests are too simple and only measure the ability to understand basic things
- she only talks about the mean differences, not the ratios of the variances; the latter are more important in highly selective contexts.
Culture, gender, math (click, PDF).On their visit to La La Land, the authors argued that the math sex gap decreases in countries where women are more emancipated. La Griffe du Lion confirms that the correlation exists but he also proves that the origin of the correlation is completely different than the four authors suggested. But he shows much more than that.
Click or shift-click to zoom in. Note that in 2006, the Czech Republic became the country that deviates from the interpolating blue line in the upward directions most intensely among all countries. Three years ago, we had the smartest girls, if you wish ;-), but their percentage at level 5 was still below the boys' percentage.
You should notice that all the points are remarkably close to an idealized blue line and this blue line surely doesn't say that the percentages of boys and girls are equal. There exists a two-parameter family of such lines: the shape of the line only depends on the mean difference between the male and female gaussians, expressed in standard deviations; and the ratio of the standard deviations (or variances).
All the countries, regardless of their race, culture, or religion, seem to confirm that the ratio of standard deviations is about 1.15 (boys' distribution is wider) while the mean difference between boys and girls is about 2-3 points (if you normalize boys' abilities like IQ with the average of 100 and the standard deviation of 15). These figures haven't changed for 50 years.
Well, it's clearly noise. Nature wins, nurture loses.
Does La Griffe du Lion show that the correlation found by the four economists (between "emancipation" and the "shrinking male-female gap") doesn't exist? Not at all. He or she confirms that it does exist. But correlation is not causation. More precisely, both of these quantities are correlated not because one of them is the cause but because both of them are effects of something else, namely the general IQ of the nation.
Smarter nations have a higher percentage of men and women whose IQ exceeds 95 (or 100 or 120) while the dumber nations have to probe the "extremely smart tail of the Gaussian" if they want to get to these high IQ values (that are necessary for many purposes in the society). Consequently, the dumber nations will lead to a lower emancipation rate because men's skills will be needed and men dominate in the upper portions of the distribution.
So a higher general IQ of a nation makes the society more emancipated; it makes the male-female gap at any required fixed IQ threshold shrink (because the required IQ is not that selective in a smart nation, and the tails of the Gaussian where the differences matter don't have to be probed). The previous sentence can be tested by drawing the right graph:
That's also the explanation of the correlation found by the four economists. Finally, La Griffe du Lion is able to isolate the contributions of nature and nurture to the particular math sex gap as measured by PISA at level 5 in 2003 and 2006. What he gets is the following:
To find this graph, La Griffe du Lion assumed that the female ratio is equal to the "natural" component plus the "cultural" component that is Taylor-expanded as a function of "discrimination against women", namely (1-GGI) where GGI is an international cultural coefficient between 0 (macho society) and 1 (full emancipation). A least squares fit was performed to find the coefficients.
I think that La Griffe du Lion made a mistake: only the portion of the graph above the "female=male" line should be drawn in blue because for "female=male", there would be no differences, neither natural nor cultural. But even if you fix this bug, the contribution of culture and nurture will be negligible.
And that's the memo.