[sanxiyn]

One usual citation is Global Sex Differences in Test Score Variability (DOI: 10.1126/science.1162573).

It uses standardized test scores. I quote findings below. Remarks inside parentheses are mine.

"The third column in table S1, reports the estimated male/female variance ratios with standard errors in parentheses. In all but five countries (There are 41 countries) we can reject the hypothesis that the variance ratio is equal to one at 5% level. In all the countries where this hypothesis is rejected, the variance ratios are larger than one indicating that the male variance in reading is higher than the female variance."

In other words, male variance > female variance with 95% significance level in 36 countries, and no statistically significant difference in 5 countries. There is no countries where female variance > male variance with statistical significance.

There are various interpretations of this result. The usual interpretation is that there is a sex difference in variability. Another interpretation is that since variability difference is not universal (in 5 countries it is not statistically significant), variability difference is cultural. The later interpretation is argued in PNAS paper cited below.

[viola11]

Reading the supplementary material (since that isn't paywalled) I not that these are not IQ tests, but results from mathematics and reading comprehension tests.

I also found this little thing that implies that the score distributions aren't symmetric (I think):

"There is no clear pattern in the male to female ratios at the bottom 5% of the math distribution. This ratio is different from one in only 15 countries but in some countries it is larger than one and in others smaller. On the other hand, at the top 5% the ratio of boys to girls is larger than one in 35 countries with the highest estimated ratio in Korea (2.55). In these 35 countries, boys are clearly over-represented at the top end of the math distribution. The quantile differences at 5th and 95th quantiles confirm the same finding, with no clear pattern at the 5th quantile but positive and significant differences in all but five countries at the 95th quantile. "

Doing a quick test, I took some random normal numbers with variance ratio 1.4, and found that the variance ratio is not very sensitive to if I calculate it using the full sample, the bottom half or the top half. In other words, for a normal distribution the reported ratios for the 5th and 95th quantile should be the same within the errors, but this is never the case for mathematics so the scores simply aren't normal.

[alextgordon]

> Another interpretation is that since variability difference is not universal (in 5 countries it is not statistically significant), variability difference is cultural. The later interpretation is argued in PNAS paper cited below.

How do they reach this conclusion? 36 for, 5 against at 95% significance level would expected given random variation, no?

[nshepperd]

A significance level says very little, if anything, about the probability of getting an "insignificant" result given that the null hypothesis is false. That's all about statistical power. It's entirely possible that those "5 against" were just underpowered (sample size too small). Or that the sample sizes were systematically too small, and those 5 just happened to be the ones that failed to reach statistical significance. Or that the study was actually well-powered and the difference really is localized geographically.

Either way, a 95% significance level by itself tells us little about how we should interpret those 5 against.

[boyaka]

I should look at this study more carefully before commenting, but I would assume there are genetic as well as cultural differences in those 5 countries with no statistical male/female IQ difference.