Female representation across broad academic field
Female representation varies across academic field, as illustrated in the figure below [source]. Females earned 46% of all doctoral degrees awarded in 2013, but represented substantially more than that percentage in education (68%) and the social sciences (59%), and substantially less than that percentage in the physical sciences (29%) and engineering (23%). The gray line indicates the percentage of all doctoral degrees that women earned in 2013 (46%).
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I began to look into this topic after reading the Leslie et al. 2015 Science article. I have since come across treatments that better cover the same ground [Scott Alexander, Ceci et al. 2014], so I'll post a few figures here with brief commentary.
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One possible explanation for the variation in female representation across academic field is sex differences in mathematics and verbal performance. The figure below reports SAT-Math scores [source] and SAT-Reading scores [source] by sex in 2009. The figure indicates cumulative numbers, so the point at 40% female representation and a 650 SAT-Math score indicates that females were 40% of all SAT test takers who scored a 650 or higher on the SAT-Math section. The 40% is not adjusted to account for the fact that more females than males took the SAT: there were 224,230 total persons who scored a 650 or higher on the 2009 SAT-Math test: 88,896 females, and 135,334 males.
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Scott Alexander linked to this Hsu and Schombert article, which has this passage:
Thus, a strong interpretation of our result would be that even the most determined student is unlikely to master undergraduate Physics or Mathematics if their quantitative ability is below 85th percentile in the overall population. To have a 50 percent or greater chance of success (i.e., for a person of average conscientiousness or work ethic), one needs SAT-M well above 700, or in the top few percent of the overall population.
In the 2009 SAT data, females represented 36% of SAT-Math test takers who scored a 700 or above, 34% of SAT-Math test takers who scored a 750 or above, and 31% of SAT-Math test takers who scored an 800. So -- presuming no downstream discrimination or sex differences in interest or other non-academic factors -- we'd expect females to represent roughly 1/3 of PhDs in math-intensive fields such as engineering or the physical sciences. But females represent less than 1/3 of PhDs in math-intensive fields: in the 2013 data plotted in the first figure, females were 29% of physical sciences PhDs and 23% of engineering PhDs.
This is where the discussion must involve discrimination, bias, interests, life choices, and life constraints. It seems that the relevant question is the relative effect size of each factor and not the presence or absence of each factor. Ceci et al. 2009 and 2014 are good places to find a discussion of such factors.
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One way to look for evidence of discrimination against women in representation across academic field is to plot sex differences in verbal and quantitative abilities by field. If women with high levels of quantities abilities were being systematically dissuaded from STEM fields such as engineering and the physical sciences into non-STEM fields such as the social sciences and the humanities, then these displaced high-quantitative-ability women should inflate the mean quantitative reasoning scores of women in non-STEM fields. That does not appear to be the case, based on the figure below [source], which plots the mean GRE scores in 2013 in verbal reasoning and quantitative reasoning among male and female GRE test takers in each field. Of course, women with high quantitative abilities might have been systematically dissuaded from STEM fields to non-academic careers; there might also be discrimination upstream that causes observed differences in GRE scores; and there might be selection issues in play with regard to who takes the GRE exam.
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This final figure plots female representation across academic field in 2013 [source] against mean male GRE test scores in verbal reasoning and quantitative reasoning, by broad academic field, in 2013 [source]. The GRE scores are limited to males to account for the fact that some fields such as education have a relatively high percentage of females and a relatively low mean GRE quantitative reasoning score. Patterns for quantitative reasoning scores match those of Randal Olson and Scott Alexander, with female representation falling as male GRE quantitative reasoning scores rise, but patterns for verbal reasoning scores don't match those of Randal Olson: in Olson's data, there is no correlation, but in the data below, there is a positive correlation. One large difference between Olson's data and the data in the figure below is that Olson's data were disaggregated into smaller fields.
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Notes:
1. [2015-01-25 edit] Corrected the spelling of Randal Olson, and revised the SAT graph to read "SAT Critical Reading" instead of "SAT Verbal."