Estimating sex intelligence difference based on high-IQ samples?

To my knowledge this has not been so extensively done, but it seems like an interesting line of evidence.

Here is a random sample i came across:

Lubinski, Webb, et al., 2001, Journal of Applied Psychology,
86, 718-729). A 10-Year Longitudinal Study of the Top 1 in 10,000
in mathematical or verbal reasoning (N = 320) identified in the
early 1980s (at age 13) [SMPY Cohort 3]. // found via Long-Term Effects of Educational Acceleration in A Nation Deceived: How Schools Hold Back America’s Brightest Students volume 2, p. 114.

M=225, F=59, total = 284, so some must be missing from the follow-up. I skimmed but didnt find the sex ratio about initial participants. But it seems unlikely that all the dropouts were women such that the data are completely bogus for estimating.

If there is a sex difference in mean ability, then this difference becoms progressivly larger as one goes further and further away from the mean of 100. This can be used to go backwards and estimate the sex difference. The ratio in the data above is 3.81:1, M:F.

Assuming that there is no difference between sexes in variation (in contrast to what was earlier believed), then one can calculate expected ratios:

Sex ratio Mean diff Men >180 Women >180 Men mean Women mean
9.0596324742 6 1.42E-007 1.57E-008 103 97
7.5396273569 5.5 1.30E-007 1.73E-008 102.75 97.25
6.2746501907 5 1.19E-007 1.90E-008 102.5 97.5
5.2219106584 4.5 1.09E-007 2.09E-008 102.25 97.75
4.3457994826 4 9.96E-008 2.29E-008 102 98
3.6166820496 3.5 9.11E-008 2.52E-008 101.75 98.25
3.0098949676 3 8.32E-008 2.77E-008 101.5 98.5
2.5049120246 2.5 7.60E-008 3.04E-008 101.25 98.75
2.0846535716 2 6.95E-008 3.33E-008 101 99
1.7349029347 1.5 6.34E-008 3.66E-008 100.75 99.25
3.7521222492 3.6 9.27E-008 2.47E-008 101.8 98.2
3.8925671421 3.7 9.44E-008 2.43E-008 101.85 98.15

I did it semi-manually using this site (my data is here), as i didnt want to go thru the trouble of finding the math way to solve it backwards. Thru iterating one can get pretty close, and the ratio is not that significant anyway with such a small sample set. But given the data, the sex mean difference is around 3.6-3.7. This number fits well with other studies (random example).

Edited to add: This sample was tested at age 13, thus before men have the ~4 IQ advantage per the developmental theory. But the data still fits. It wud be better if one cud find samples that are based on inclusion tests at a later age, say 20. Data from high-IQ societies may be distorted due to self-selection effects.

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