Thursday, January 04, 2007

Sex difference in g   posted by the @ 1/04/2007 09:25:00 PM

A new La Griffe is up: Intelligence, Gender and Race.

Inspired by Jackson and Rushton (Intelligence 34 (2006) 479-486), La Griffe (Prodigy?) seeks to use a version of the "method of thresholds" to estimate the female distribution of g relative to males. The details are well spelled out in the article. Combining a variety of data sources, the article arrives at a least-squares estimate of the parameters defining the distribution of g first for blacks and then for women.

A white-black mean difference in g of 1.09 SD exists in favor of whites, equivalent to 16 IQ points. The black g distribution is narrower than the white, with a variance ratio (B/W) of 0.888.

A male-female mean difference in g of 0.164 SD exists in favor of men, equivalent to 2.46 IQ points. The female g distribution is narrower than the male, with a variance ratio (F/M) of 0.916.

Contrast the sex-difference estimate with Jackson and Rushton's estimate of 3.63 IQ points. At the time of publication of the Jackson and Rushton paper, I noted that no attempt was made to take into account the very well documented difference in variability of IQ between men and women. We can now compare Jackson and Rushton's estimate with La Griffe's. Above a +1 sd threshold, women would make up only 40% of the population using Jackson and Rushton's estimate and assuming equal variance. Notably, using La Griffe's estimates of mean and variance, women would make up 39% of the population above a +1 SD threshold.

Even small differences in mean and variance can have large effects at the tails. To give an idea of the effects, I've generated a table listing the percentage of women in a population above +1 SD for values of female mean in standard units (listed in the first column) and the ratio of female to male SDs (listed in the first row).

 1 0.975 0.95 0.925 0.916 0.9 0.875 0.85 0 50% 49% 48% 47% 46% 46% 44% 43% -0.025 49% 48% 47% 46% 45% 45% 43% 42% -0.05 48% 47% 46% 45% 44% 43% 42% 41% -0.075 47% 46% 45% 44% 43% 42% 41% 39% -0.1 46% 45% 44% 42% 42% 41% 40% 38% -0.125 45% 44% 43% 41% 41% 40% 38% 37% -0.15 44% 43% 42% 40% 40% 39% 37% 36% -0.164 44% 42% 41% 40% 39% 38% 37% 35% -0.175 43% 42% 41% 39% 39% 38% 36% 34% -0.2 42% 41% 39% 38% 37% 37% 35% 33% -0.225 41% 40% 38% 37% 36% 35% 34% 32% -0.242 40% 39% 38% 36% 36% 35% 33% 31% -0.25 40% 39% 37% 36% 35% 34% 33% 31% -0.275 39% 38% 36% 35% 34% 33% 31% 30% -0.3 38% 37% 35% 34% 33% 32% 30% 28%

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