It is frequently claimed that men show greater variance in the distribution of their general intelligence factor (g) ("IQ") than women.
Is that claim accepted by the scientific community?
It's frequently quoted, this seems to be the main research used:
Sex differences in mental test scores, variability, and numbers of high-scoring individuals.
Hedges LV, Nowell A. Science. 1995 Jul 7;269(5220).
From the abstract: "...the test scores of males consistently have larger variance"
You ask about IQ, but a closely related question is even more commonly found - that men show greater variance in the distribution of their mathematics skills than women. I am hoping that, with only a slight wave of the hand, you will consider an answer in this area to be highly relevant.
Ed Yong wrote an article for the Not Rocket Science blog, which covers this area so well, I had to stop myself from simply quoting it all. I recommend reading it.
It looked at, and summarised the article:
The fact that men outnumber women in the highest echelons of mathematics (as in science, technology and engineering) has always been controversial, particularly for the persistent notion that this disparity is down to an innate biological advantage.
Now, two professors from the University of Wisconsin – Janet Hyde and Janet Mertz – have reviewed the strong evidence that at least in maths, the gender gap is down to social and cultural factors that can help or hinder women from pursuing the skills needed to master mathematics.
They looked at a number of factors - e.g. the performance of the genders in the general population, as well as the mathematically-talented (i.e. at the upper end of the distribution.)
gender differences in maths performance don’t really exist in the general population, with girls now performing as well as boys in standardised tests. Among the mathematically talented, a gender gap is more apparent but it is closing fast in many countries and non-existent in others. And tellingly, the size of the gap strongly depends on how equally the two sexes are treated.
Since 1894, some scientists have suggested that men have a greater variability in intellectual ability than women, a simple statistical quirk that would result in more male prodigies. This was the controversial hypothesis that Lawrence Summers mentioned in his now-infamous speech at the National Bureau of Economic Research Conference in 2005:
“Even small differences in the standard deviation will translate into very large differences in the available pool substantially out… In the special case of science and engineering, there are issues of intrinsic aptitude, and particularly of the variability of aptitude, and that those considerations are reinforced by what are in fact lesser factors involving socialization and continuing discrimination.”
To test that, Hyde looked at data from maths tests in Minnesota and compared the numbers of boys and girls who scored in the top 5% of their year. The ratio was 1.45, meaning that for every two girls in this elite group, there were around three boys. In the top 1%, the ratio was 2.06, meaning two boys for every girl. That seems to vindicate the Variability Hypothesis, but those figures only applied to white American children. In other ethnic groups or, indeed, in other countries, the picture was very different.
For Asian-Americans the ratio was actually 0.91, meaning more girls than boys in the top 1%. International studies have found similar trends. One analysis of tests from the Program for International Student Assessment (PISA) showed that 15-year-old girls matched or outnumbered their male peers in the top tiers within Iceland, Thailand and the UK. Two studies found that 15-year-old boys and girls were equally varied in their mathematical skills in most of the countries taking part in PISA and the Trends in International Mathematics and Science Study (TIMSS). In some, like the Netherlands, girls actually turned out to have the wider range of ability.
So much for the idea that a greater variation in ability underlies the larger number of men in the top ranks of mathematics – if that had any biological basis, it should apply to all populations regardless of ethnicity or nationality. Clearly, that’s not the case. Instead, the evidence suggests that whatever gender differences exist are mostly down to social factors.
In conclusion, if we accept that the claim that men have a greater distribution in IQ has the same basis as the similar 1894 claim that men have a greater distribution of maths skills than women, then we can see that there is strong evidence to suggest any such discrepancies in skill are cultural and not innate.