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The variability hypothesis states that while men and women have the same median intelligence, they display a greater variability in their performance than females. This could explain both the significantly larger percentage of male criminals and the gap between men and women in certain professions which require very high levels of intelligence.

Is this hypothesis ever acknowledged in public discourse over the gender gap? Or is it always presumed that the distribution of IQ between the genders is exactly equal?

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It depends what you mean by "public discourse". I know of some recent scientific papers that discuss it e.g.

According to the ‘variability hypothesis’, this over-representation of males [in STEM] is driven by gender differences in variance; greater male variability leads to greater numbers of men who exceed the performance threshold. Here, we use recent meta-analytic advances to compare gender differences in academic grades from over 1.6 million students. In line with previous studies we find strong evidence for lower variation among girls than boys, and of higher average grades for girls. However, the gender differences in both mean and variance of grades are smaller in STEM than non-STEM subjects, suggesting that greater variability is insufficient to explain male over-representation in STEM. Simulations of these differences suggest the top 10% of a class contains equal numbers of girls and boys in STEM, but more girls in non-STEM subjects.

One could argue that grades are not a perfect substitute for IQ testing, but it's much harder to get a large sample with the latter (in the US anyway, in countries with mandatory military service, the situation is different in this respect, but I think they don't test women, except maybe in Israel etc.) As for the study quoted above

North American data dominated the dataset, with 70% of the effect sizes.

I don't know if any scientific consensus has been reached though, despite the large number of publications targeting different aspects of gender variability (grades, IQ, creativity, personality etc.) It's apparently a pretty old controversy.

The 1995 Science paper on grater male IQ variability (which finds that it existed in large US samples) cited these two economics papers as discussing the IQ variability implication for economics:

So clearly the implications have been discussed. The (continuing) problem seems to be however it's unclear how much that greater variability really affects the pay or employment gap, given all the other (confounding) factors that affect the latter. I'm not sure if any research has convincingly addressed this. Quite a few other explanations have been offered, e.g. "Men and Things, Women and People: [...] Sex Differences in Interests". I don't know if anyone has managed to put all the alternative hypotheses in one model so as to compare their relative influence on the gap observed.

Pinker also referred to the aforementioned Science paper in a more recent (2005) debate on this, but also to another 2003 paper on Scottish kids:

Finally there's a sex difference in variability. It's crucial here to look at the right samples. Estimates of variance depend highly on the tails of the distribution, which by definition contain smaller numbers of people. Since people at the tails of the distribution in many surveys are likely to be weeded out for various reasons, it's important to have large representative samples from national populations. In this regard the gold standard is the Science paper by Novell and Hedges, which reported six large stratified probability samples. They found that in 35 out of 37 tests, including all of the tests in math, space, and science, the male variance was greater than the female variance.

One other data set meeting the gold standard is displayed in this graph, showing the entire population of Scotland, who all took an intelligence test in a single year. The X axis represents IQ, where the mean is 100, and the Yaxis represents the proportion of men versus women. As you can see these are extremely orderly data. In the middle part of the range, females predominate; at both extremes, males slightly predominate. Needless to say, there is a large percentage of women at both ends of the scale — but there is also large sex difference.

I did notice this latter paper myself before, but I think an issue with it is that it only considered 11-12-year-olds. The authors of this study are also keenly aware of that limitation (they discuss it in the paper in the context of differential developmental issues.)

In a follow-up study in 2008 which additionally considered achievements, the same authors (and using the same Scottish sample) concluded that

Though present at the high end of the distribution, sex differences in variability did not appear to account for sex differences in high-level achievement.

And in more detail in the paper's conclusions:

Males were more heavily represented than females in the distributions representing those with conditions that disrupt general intelligence. Thus, there was greater variability among males than among females at the low ends of the overall distributions of general intelligence. The differences in variability were smaller, but there was also greater variability among males at the high ends of the overall distributions of general intelligence. [...]

Though it is not possible to measure this exactly due to a lack of consistent measurement scales, it appears that the sex difference in variability in general intelligence that we observed would not account for the sex differences in participation at the highest levels of mathematics and science occupational performance. For example, even at the highest levels of general intelligence in the SMS [Scottish Mental Survey] data, the ratios of males to females were only about 2:1. Halpern et al. (2007), however, reported male-female ratios ranging from 6.9:1 to 14.4:1 for tenure-track faculty in elite universities in physical sciences, mathematics, and engineering. Thus, as Lubinski and colleagues have reported for the Study of Mathematically Precocious Youth (e.g., Lubinski & Benbow, 1992, 2006, 2007), sex differences in career motivation and occupational interest likely contribute, as may vulnerability to identity threat from situational cues (Murphy, Steele, & Gross, 2007) and sex differences in self-confidence (e.g., Deaux, 1976; Heatherington et al., 1993). All of these, of course, possibly have roots in biological differences, differences in socialization experiences, and differences in the personal and professional trade-offs required to maintain high-level careers in math and science fields (Halpern et al., 2007). Covert sex discrimination, as reflected in studies such as those that compare ratings of work products or resumes when labeled with male or female names (e.g., Bowen, Swim, & Jacobs, 2000; Davison & Burke, 2000; Swim, Borgida, Muruyama, & Myers, 1989), also likely continues to play some role. This suggests that, to the best of our current understanding of the laws of nature, there remains plenty of room for discussion of the actualization of values.

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  • Regarding conscription, maybe there's relevant data on Norway. – JJJ Apr 14 '19 at 23:58
  • @JJJ: there surely are some studies on GMVH using reasonably large IQ samples (but not in Norway, as far I can tell). The thing is most don't mention the pay (or employment) gap. If one only wants to ask about GMVH, poliics.SE is not the proper forum. – Fizz Apr 15 '19 at 0:24

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