Friday, December 5, 2014

Women, Mathematical Skills, Academia

Focus on the so-called STEM departments in academia: that is, science, technology, engineering and mathematics. There is a fairly clear pattern that women are less well-represented in the academic departments that rely on higher mathematical skills. The harder questions are explaining this phenomenon.  Stephen J. Ceci, Donna K. Ginther, Shulamit Kahn, and Wendy M. Williams address these issues in their article "Women in Academic Science: A Changing Landscape," which appears in the December 2014 issue of Psychological Science in the Public Interest. Here's a taste of their conclusions:

We conclude by suggesting that although in the past, gender discrimination was an important cause of women’s underrepresentation in scientific academic careers, this claim has continued to be invoked after it has ceased being a valid cause of women’s underrepresentation in math-intensive fields. Consequently, current barriers to women’s full participation in mathematically intensive academic science fields are rooted in pre-college factors and the subsequent likelihood of majoring in these fields, and future research should focus on these barriers rather than misdirecting attention toward historical barriers that no longer account for women’s underrepresentation in academic science.
Here's an illustrative figure that helps to illustrate the starting point for Ceci, Ginther, Kahn, and Williams. Each of the points is a STEM department. The authors divide up their analysis into what they call the LPS departments, which are the three in the upper right with more females among those who get a PhD and relatively lower math scores on the GRE exam, and what they call the GEEMP departments, which are the departments to the bottom right with a smaller share of females among those who get a PhD in that field and higher average math scores on the GRE exam. These sorts of differences in PhDs granted to females are reflected in large gaps in the number of female professors in these fields.

Ginther and Kahn are economists, while Ceci and Williams are psychologists. Thus, the paper combines economics-style analysis of career development patterns with psychology-style analysis of how people learn. For economists, a standard approach is to look at the "pipeline" to producing tenured professors. For example, you can look at how many females major in STEM subjects in college, and what proportion go on to a PhD, and then to various academic jobs. The idea is to see where there is "leakage" in the pipeline--and thus identify the barriers to women professors.  When they carry out this analysis, the authors offer a (to me) surprising conclusion: the LPS fields have a relatively substantial "leakage" when comparing how females and males move from undergrad majors to grad school and professorships. But in the GEEMP areas--which includes economics--women and men in recent years proceed from undergrad degrees through grad school and into professorships at similar rates. After reviewing a range of evidence, they write:
Thus, the points of leakage from the STEM pipeline depend on the broad discipline being entered—LPS or GEEMP. By graduation from college, women are overrepresented in LPS majors but far underrepresented in GEEMP fields. In GEEMP fields, by 2011, there was very little difference in women’s and men’s likelihood to advance from a baccalaureate degree to a PhD and then, in turn, to advance to a tenure-track assistant professorship. ... [O]nce women are within  GEEMP fields, their progress resembles that of male GEEMP majors. In contrast, whereas far more women than men major in LPS fields, in 2011, the gender difference in the probability of advancing from an LPS baccalaureate degree to a PhD was not trivial, and the gap in the probability of advancing from PhD to assistant professorship was particularly large, with fewer women than men advancing.
The message is that the the most substantial barriers to women in economics and other GEEMP fields arise before college. Why might this be so? One set of explanations focuses on the high scores for boys on a wide range of math tests. The other set of explanations focuses on social expectations about interests and careers. Of course, these explanations become entangled, because getting skills is interrelated with social expectations.

With regard to higher math scores for boys, the paper reviews evidence on how in utero exposure to  androgen hormones is greater for boys, and how certain math-related abilities (like 3D spatial processing) appear to be greater for boys at young ages. I'll skip past that evidence here because: i) as the authors note, it's far from definitive; ii) I lack any particular competence to evaluate this evidence, anyway. Instead, let me stick to several points that seem well established.

In terms of the basic data from math scores themselves, it used to be true that math test scores for boys were higher than those for girls, but on average, high school girls have now caught up. The authors note: "However, by the beginning of the 21st century, girls had reached parity with boys—including on the hardest problems on the National Assessment of Educational Progress (NAEP) for high school students." It also seems true that at the top of the distribution of math test scores, boys substantially outnumber girls: "Thus, a number of very-large-scale analyses converged on the conclusion that there are sizable sex differences at the right tail of the math distribution." One of many studies they discuss looked at the "Programme for International Student Assessment data set for the 33 countries that provided data in all waves from 2000 to 2009. They, too, found large sex differences at the right tail: 1.7:1 to 1.9:1 favoring males at the top 5% and 2.3:1 to 2.7:1 favoring males at the top 1%."

There is an ongoing nature-vs.-nurture argument about how to interpret these higher math scores at the top. Not only have gender differences in math scores changed over time, but they also "vary by cohort, nation, within-national ethnic groups, and the form of test used. ... Moreover, mathematics is heterogeneous, comprising many different cognitive skills ..." At a minimum, these patterns suggest that gender gaps in test scores are quite sensitive to environmental factors. For example, in Iceland, Singapore, and Indonesia, more girls than boys scored at the top 1% of math tests at certain ages.

Some of the evidence the authors cite on the importance of social environment in affecting math scores comes from a Spring 2010 symposium in the Journal of Economic Perspectives on "Tests and Gender." (Full disclosure: I've been Managing Editor of JEP since its first issue in 1987. All JEP articles back to the first issue are freely available on-line at the journal's website.)

For example, in that issue of JEP, Devin G. Pope and Justin R. Sydnor look at "Geographic Variation in the Gender Differences in Test Scores" across U.S. states and regions. Here's an illustrative finding based on scores from 8th graders on the National Assessment of Educational Progress (NAEP). The vertical axis shows that in every region, the female-male ratio in the top 5% of reading scores is greater than 2, almost reaching 3 in Mountain states. The horizontal axis shows that in every ratio, the male-female ratio in the top 5% of math and science scores ranges from 1.3 in the New England States to 2.2 in the Middle Atlantic states. This finding confirms the fact of a difference in math test scores at the extreme. It also strongly suggests that such differences strongly affected by where you live--and thus are strongly linked to social expectations.

In another paper in the 2010 JEP symposium, Glenn Ellison and Ashley Swanson look at "The Gender Gap in Secondary School Mathematics at High Achievement Levels: Evidence from the American Mathematics Competitions." In a striking finding, the note that most U.S. high school girls who participate in international math competitions come from a very small pool of about 20 high schools. This finding strongly suggests that many other girls, if they were in a different academic setting, would demonstrate high-end math skills. Ellison and Swanson write:
[W]e examine extreme high-achieving students chosen to represent their countries in international competitions. Here, our most striking finding is that the highest-scoring boys and the highest-scoring girls in the United States appear to be drawn from very different pools. Whereas the boys come from a variety of backgrounds, the top-scoring girls are almost exclusively drawn from a remarkably small set of super-elite schools: as many girls come from the 20 schools that generally do best on these contests as from all other high schools in the United States combined. This suggests that almost all American girls with extreme mathematical ability are not developing their mathematical talents to the degree necessary to reach the extreme top percentiles of these contests.
Finally, there is intriguing evidence that a number of women with equivalent math skills may not perform as well in the context of competitive and high-stakes math testing.  In the 2010 JEP symposium, Muriel Niederle  and Lise Vesterlund look at a range evidence on "Explaining the Gender Gap in Math Test Scores: The Role of Competition." I was especially struck by this study:
They examine the performance of women and men in an entry exam to a very selective French business school (HEC) to determine whether the observed gender differences in test scores reflect differential responses to competitive environments rather than differences in skills. The entry exam is very competitive: only about 13 percent of candidates are accepted. Comparing scores from this exam reveals that the performance distribution for males has a higher mean and fatter tails than that for females. This gender gap in performance is then compared both to the outcome of the national high school graduation exam, and for admitted students, to their performance in the first
year. While both of these performances are measured in stressful environments, they are much less competitive than the entry exam. The performance of women is found to dominate that of men, both on the high school exam and during the first year at the business school. Of particular interest is that females from the same cohort of candidates performed signififi cantly better than males on the national high school graduation exam two years prior to sitting for the admission exam. Furthermore, among those admitted to the program they find that within the first year of the M.Sc. program, females outperform males.
A possible reason here is a well-known phenomenon called "stereotype threat"--that is, if reminded of a negative stereotype about a group to which you belong before a test, people often perform worse. Here's one study that Ceci, Ginther, Kahn, and Williams cite along these lines: "For example, female test takers who marked the gender box after completing the SAT Advanced Calculus test scored higher than female peers who checked the gender box before starting the test, and this seemingly inconsequential order effect has been estimated to result in as many as 4,700 extra females being
eligible to start college with advanced credit for calculus had they not been asked to think about their gender before completing the test ..."

To recap the argument to this point, the basic question is why women are underrepresented in academic disciplines in certain STEM fields where math scores are higher. For current students, the main underlying reasons seem to trace back to the choices that college students make about undergraduate majors. In turn, a possible explanation is that more males get high scores on pre-college math tests than do women. In turn, a substantial part of this difference seems to trace to social expectations about gender and math, and about gender and test-taking. If more women felt more positive about math before reaching college, then majors in GEEMP areas would presumably tend to rise.

But there is also a different set of arguments about why fewer women sign up for the GEEMP disciplines as undergraduates, which suggests that whole issue of math test scores may be a distraction. For example, it's not clear how much the gender difference in math scores at the extreme top end should matter for academia. As the authors point out above, the typical GRE math scores for those in the math-oriented GEEMP fields was about at the 75th percentile--not the top 1%. Another intriguing fact is that women have now been receiving 40-45% of math Ph.D's for the last few decades. This alternative view focuses less on math skills and more on perceptions about self and occupation. The Ceci, Ginther, Kahn, and Williams team points out (some citations omitted):

Psychologists have charted large sex differences in occupational interests, with women preferring so-called “people-oriented” (or “organic,” or natural science) fields and men preferring “things” (people- and thing-oriented individuals are also termed “empathizers” and “systematizers,” respectively. This people-versus-things construct ... is one of the salient dimensions running through vocational interests; it also represents a difference of 1 standard deviation between men and women in vocational interests. Lippa has repeatedly documented very large sex differences in occupational interests, including in transnational surveys, with men more interested in “thing”-oriented activities and occupations, such as engineering and mechanics, and women more interested in people-oriented occupations, such as nursing, counseling, and elementary school teaching. And in a very extensive meta-analysis of over half a million people, Su, Rounds, and Armstrong (2009) reported a sex difference on this dimension of a full standard deviation.
In other words, the reason that fewer women choose the GEEMP disciplines as undergraduates--and thus the reason that women are underrepresented as faculty in those areas--may be less related to math skills and more related to this distinction between people-oriented and thing-oriented.

In the context of economics, it seems to me true, and also deeply frustrating, that this distinction does capture something about how the field is perceived. Economics is the stuff of life: full of choices that people make about work, consumption, saving, parenthood, and crime, as well as about the structure and decisions of organizations like firms and government that affect people's daily lives in profound ways. But the perception that many students have of economics, which is sometimes unfortunately confirmed by how the subject is taught, can lose track of the people, instead viewing the economy as a thing.