Earlier this week I argued that the gender differences in cognition, while real, are not substantial enough to explain gender disparities in science. We talked about the work of Janet Hyde; it shows that -- contrary to the popular conception of women and men as psychologically disparate -- men and women are actually quite psychologically similar in most respects.
Some of the commenters brought up the issue of the upper tail, and I want to talk about that specifically. It has been suggested that even if the size of the effect -- the differences in averages between a trait like mathematical ability -- is not very large, it becomes magnified at the edges of the distribution. Thus, even a barely statistically significant effect, when observed at the threshold of 4 SD, could result in a several fold skew towards men. The argument goes on that if such a trait were required to participate in a discipline -- like competence in mathematics to become a physicist -- women would then be acting at a natural disadvantage.
This argument assumes two things:
1) A high measure of mathematical ability as measured by cognitive testing is required for technical disciplines like engineering, mathematics, computer science, and physical science college majors and careers. (I shall henceforth refer to these as EMS disciplines because that is the terminology used in the paper I want to talk about.) This is not to suggest that math itself is not involved; rather, I am just pointing out that this argument is predicated on the idea that A) the mathematical ability required for the disciplines is something we can measure and B) the thing we measure is the thing required.
2) Mathematical ability so measured is correlated with participation.
Neither of those propositions are true, as demonstracted by work for NBER by Catherine Weinberger. Her study looked followed high school seniors from 1972 and 1980 through college to correlate mathematical performance with later participation in an EMS discipline.
This study uses data from nationally representative samples of 1972 and 1980 high school seniors, followed longitudinally through the college years to answer the following questions: Is the EMS participation of young women similar to that of young men with the same ability? and: Did most of the men who pursued EMS careers have very high mathematics test scores, or unobserved ability, as high school seniors?
Here is a brief summary of the main point of that paper:
- The level of EMS attainment by women is less than that of men, in line with Census data:
Among 1972 high school seniors, 4.5% of the men and 0.9% of the women graduated college with
an EMS major by the 1979 resurvey. Among 1980 high school seniors, 5.8% of the men and 1.8% of the women completed EMS degrees by the 1986 resurvey. - The numbers of women at the upper tail of the mathematical distribution is less than that of men for both the entire sample and the subset of bachelor's degree graduates:
I now turn to the question of whether EMS participants are drawn from the extreme upper tail of the math score distribution...Figure 3 shows what we already know: there are more men than women at the upper tail of the math score distribution. Figure 4 shows that this is also true within the (more highly selected) group of college graduates. But, within the even more highly selected group of EMS college graduates, the distributions of men's and women's math test scores are much more similar (Figure 5). In fact, among EMS graduates in both cohorts, the women have a higher mean math score and smaller variance than the men. Note that if the relationship between mathematics test scores and EMS participation were the same for men and women, then female EMS participants, drawn from a lower test score distribution, would tend to have lower average scores than male EMS participants. The finding that the mathematics test scores of white women with EMS degrees are not lower than those of the men suggests that women are morecautious about entering unless they have very high scores. (Citations have been removed. Emphasis mine.)
- Here is where it gets interesting. The levels of math achievement for those males that ended up in the EMS discipline were not espcecially high, and by no means prerequisite:
Among all white male 1972 high school seniors employed in the 1979 workforce, only 6% had high school SAT-M[ath] scores greater than 650, while 76% had scores no greater than 550. Although men with high scores are overrepresented in the EMS workforce, they are not the majority. No more than 25% of the EMS workforce had scores above 650. High scores were somewhat more common in the college-educated EMS workforce. Among college graduates employed in EMS occupations, 29% had high scores as high school seniors. Further restricting attention to those who earned an EMS bachelor's degree by 1979 and were employed in an EMS occupation in either 1979 or 1986 did little to change the estimate. Although this group would include those who attended graduate school before entering the EMS workforce, no more than 30% had scores above 650, while 32% had scores no greater than the average humanities major. These estimates lead to the surprising conclusion that less than one-third of the EMS work force had SAT-math scores above the threshold previously presumed in the economics and cognitive psychology literatures. (Citations have been removed. Emphasis mine.)
It would appear that the imputed threshold is not nearly the price of admission that some people would argue. Either we are not measuring the mathematical acumen that is required, or it is not as required as we think.
- Some people might argue with the above point that "Hey, well those people who do poorly at math are probably not being as good a physicist right? Maybe they just got a degree but they are not any good at it." Well, Weinbeger shows that if you look at the math scores compared with later earnings, the individuals with low math scores are doing just as well:
The result that the lowest scoring EMS graduates enjoy the same economic returns as graduates with high scores is extremely robust. This finding suggests that many individuals with lower ability, as measured by the SAT-M[ath], are able to complete college level coursework in EMS subjects, and to enjoy the associated wage premium.
Granted this isn't a direct measure like publishing frequency of working physicists, but considering that this is fundamentally an economic issue I think it is a good proxy for success.
- Some housekeeping. Some might argue that SAT-Math is not a good test. Well if you substituted another test, the Cognitivie Test of Mathematics (CTM), results don't change:
Within this sample, the estimated gender differential does not change when SAT-M scores are substituted for CTM scores.
- Say we are just not measuring the right thing. Say there is some "right stuff" that men have that women don't that accounts for their higher participation. How much of a boost would be required to give them this disparity? It turns out it would have to be quite large:
Of course, any possible gender differential could be explained by gender differences in an unobserved ability of some sort. In fact, this is the model underlying the notion that the demographic composition of the EMS workforce reflects the underlying distribution of attributes. In an illustrative example, equal participation conditional on ability is imposed. This exercise allows us to estimate the gender differential in the dispersion of unobserved ability required to sustain this model...In order to sustain the premise of this model, we have to believe that women with math scores at the men's 90th percentile have the same average EMS ability as men scoring at the 78th percentile of male high school seniors. The gender differential in participation can be explained away if we assume that men have quite a bit of "the right stuff," but this is no longer an argument based on gender
differentials in math scores. - Finally, we can mathematically calculate the "threshold" for participation in the EMS field:
The estimated threshold for EMS participation is surprisingly low, 578 SAT-M points. And the estimated dispersion of unobserved ability is so high that 57 percent of men in this sample are estimated to have true EMS ability above the threshold. This estimate of the proportion of men above the EMS ability threshold is more than 50 percent higher than that obtained using CTM scores with the same sample and model. This finding means that, if SAT-M scores were available for a representative sample, the estimated true ability threshold would be far below the 78th percentile estimated using CTM scores.
There remains little room for doubt that many individuals with scores, and ability, well below the "top few centiles" complete EMS college degrees and enter well-paid occupations.
For a threshold that is that low, the disparity between men and women would have to be insanely large to justify the differences in participation. No cognitive test for mathematical ability between men and women has ever found a difference that large.
Here are her conclusions:
It was previously widely believed that entry into bachelor's degree level careers in engineering, mathematics, computer science, or physical sciences (EMS) was limited to individuals who had ability (as measured by high school mathematics test scores) in the top few centiles (Paglin and Rufolo, 1990, Benbow and Arjmand, 1992, Hedges and Nowell, 1995). This belief was so well accepted that no empirical analysis testing this assumption has yet been published.
This study shows that bachelor's degree level EMS participants are drawn from throughout the upper 40% of the mathematics test score distribution. While it is true that there is a high correlation between high school mathematics test scores and EMS participation, many EMS participants had high school mathematics test scores that were not exceptional. For example, fewer than one-third of college-educated white men working in EMS occupations had high school SAT-M scores above 650 (out of 800), while more than one-third had SAT-M scores below 550--the score of the average humanities major--at the 76th percentile of all white men.
The lowest scoring white men with EMS college degrees have the same earnings advantage, relative to college graduates with the same scores, as high scoring EMS participants. This suggests that EMS education is equally beneficial for this lower ability group. When an unobserved component of ability is explicitly modeled, white male EMS participants are estimated to come from the upper 22% of the "true" ability distribution. It can not be determined from this analysis whether the unobserved component of ability is due to under-performance on the math test, or whether the unobserved ability important to EMS success is something that simply cannot be measured by these tests.
The result that relatively few EMS participants were drawn from the top few centiles of the mathematics test score distribution is robust to basing the definition of EMS participation on either educational or occupational attainment, and to using scores from two different standardized mathematics tests. Because EMS participants are not drawn from the very top of the distribution, there are many non-participants with comparable math scores or ability. (Emphasis mine.)
What conclusions do I draw from this?
1) I continue to believe that the cognitive differences between men and women are a genuine and important area of study. The effects of gender on the brain are another important part of understanding the totality of brain function. However, the evidence continues to suggest that the gender differences between men and women in several cognitive traits are not sufficient to explain the disparity of participation between them in scientific occupations.
2) The entire idea that a single axis model of mathematical ability could explain achievement was always fundamentally flawed. Do you sincerely believe that whether someone is a good physicist or a good mathematician can be explained so simply? I don't.
The reality is that many things go into making a good scientist, most of them complicated. Part of it is a raw ability, but that ability is can measured in a variety of different ways and can certainly not be boiled down to a single number (if it can be measured at all). But also part of it is also intuition, drive, wisdom, and experience. These things are not well quantified by tests, and there are certainly not documented differences in them between men and women.
The sooner that we abandon a simplistic notion that single value X equals ability to do physics, the sooner that we will realize that the impediment to women in science is us -- and it is so easily amended.
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Long version: http://www.gnxp.com/blog/2006/07/women-in-science-part-3595726061058.php
Short version:
Success / eminence / genius in any artistic or scientific field is surely more complex than just cognitive ability, such as mathematical skills in science or visuospatial skills for painting or sculpture. However, the other variables involved -- crucially including personality traits -- also show a male advantage. With the personality traits, there are actually differences in the means, aside from any difference in variance. For example, any empirical study of the personality traits of eminent scientists (and artists) shows that they tend to score low on what the "Big Five" model calls Agreeableness, meaning they're not as cooperative, tend to have a more antagonistic personality, rather than deeply empathizing with others & trusting the good-will of people. This personality trait shows the largest difference in means between the sexes: men are more dis-Agreeable than women, with a difference in means of 0.57 SD -- for comparison, if this were true for IQ, it would equal 8.55 IQ points.
Moreover, all empricial studies of eminence in a creative field (science or art) show that the distribution is log-normally distributed, indicating that the component variables interact multiplicatively rather than additively. That is, failure to meet the threshold for any single variable will result in overall failure. So, if a given woman has an IQ of 145, has a doggedly disciplined work ethic, is passionate about what she does -- that will be all for naught if she doesn't also possess a deep intellectual curiosity / penchant for the abstract or non-utilitarian. In this case, she might make a top-notch lawyer or other professional, but not a scientist or artist. If she was smart, hard-working, intellectually curious -- but conformist rather than tending toward iconoclasm -- then the same applies: she'd make a good lab worker, but not a pioneering researcher.
The same goes for men who fail to meet the treshold for each variable, obviously. It's just that, wherever there are male "advantages" in the component traits, there will be a more male-favoring skew. I put advantages in quotes since these traits are downright harmful in other fields like accounting or teaching -- we hope our accountants and teachers will be friendly and down-to-earth rather than antagonistic and nutty.
My comments are extremely anecdotal, but possibly interesting, side notes.
The women in my family (both mother's and father's sides) are highly intelligent--I would guess that all of them scored >650 on the SAT "verbal" (quotes for emphasis). None of them (I'm thinking of my mother plus my two aunts, two sisters, and four female first cousins) is particularly good at math except me--my score was 712 math (verbal was higher). My mother was given the hormone DES (diethylstilbestrol, a male hormone) when she was pregnant with me, due to earlier miscarriages. (This practice was discontinued prior to 1960 because of negative side effects.) A few years ago, a study showed that "DES daughters" scored higher than other women in math. (I don't have a citation for this, I read it in the newspaper.)
As to who goes into EMS--especially the E part: In my twenties I worked at an engineering company (Bechtel Corp), and subsequently went to Berkeley as an engineering undergrad, something that would never have occurred to me as a high school graduate. When I worked at Bechtel, I wondered whether engineering school made engineers "like that" or whether they were born "like that". "Like that" meaning, with the classical engineer personality. (Search for "engineer identification test" (in quotes) for a good description.) My conclusion, at Berkeley, was that they are born like that--the incoming freshmen fit the mold as well as the graduates. My experience at UCB (and in later engineering working environments) is exactly that described in the study you mentioned: engineers have a math IQ distribution that is shifted a few points to the right (higher) than the population as a whole. They also (not addressed in that study) have a social IQ that is shifted by a much larger number of points to the left (lower). (Let me just say here, by way of the usual self-defense, that I have many friends who are engineers, and enjoy their company). The whole phenomenon of the engineering personality is fairly well captured, I think, by the term "geeky". (This term has started to spread itself out to "acting geeks", "policy geeks", etc--but people using it in these extended senses should back off. We need the term "geek" for its original purpose--engineers. And the original sense definitely included "socially challenged", which actors are certainly not.) Silicon Valley, where I work, has a high incidence of autism--said by many, jokingly or not, to be a function of inbreeding engineers.
I don't know many people who are career mathematicians, physicists, biologists, etc; my impression is that they are a little bit geeky, but not very. And, as I think is well expressed by the Engineer Identification Test--it is very clear that the reason engineers go into engineering is that they love it--which has a mild correlation with SATM scores. My guess is that you could find other testable qualities with a much higher correlation--for example the "box-folding" section they used to have in the SAT, and some types of logic puzzles.
Regards,
Sally
jake,
one axis is not sufficient. but it maybe necessary. e.g., i have seen engineering schools suggest that you should have at least a 550 on your mathematical SAT to expect to excel in their degree program. that does not mean that 550 would be sufficient.
Segregation on the basis of gender is not scientifically (I am not even considering morally or ethically) correct, because an ability or achievement in any given field is a combination of many different, multifactorial traits. However, it is important to keep in mind - while analyzing data on this - that the male and female brains are significantly different in hemisphere usage and higher, complex brain functions that impact both physiologically, as well as psychologically, such as language, multiple memory systems, spatial abilities, deductive and inductive reasoning and so forth. This inherent different may be a major factor in determining which individual, male or female, finds a given environment comfortable and conducive to expression of talents or abilities. Therefore, equal opportunities is a great concept - that of a level playing field, where any man or woman can perform according to his or her abilities.
On the other hand, there is this age-old debate about men being better (if not safer) drivers than women... ;)
There is also the point that men and women may have similar high-level competencies and skills, but assemble them from slightly different cognitive components. The SF editor John Campbell demanded: "Show me something that thinks as well as a man, but not like a man." Well, how about a woman? ;-)
Sarah H: There's another issue to consider: There is a condition called Non-Verbal Learning Disorder. It's fairly common as learning disorders go, and some people think it fits on the autistic spectrum (I differ, but not too vehemently). It appears that in this condition, various sections of the brain normally devoted to various "sub-conscious" facilities seem to get "re-committed" to verbal and abstract abilities.
The "shorted" abilities vary from case to case, but often include social cues and modeling, bodily and/or manual coordination, and emotional awareness. Sound familiar? Yup, the typical symptoms of this condition strongly echo the classic stereotype of "the geek"! Of course, not all "geeks" have NLD, but it's worth considering how many of them might have wandered over from a rather different bell curve....
I love you.
It also wouldn't surprise me if _some_ of the distribution of women's mathematical scores is affected by disparate tracking and social discouragement / lack of encouragement in K-12 education.
Awesome post, Jake, thanks!
I am a female engineer. I have a stereotypical engineering personality. I have sometimes wished that I was male, and not female (although not enough to change my gender). I agree that personality has a lot to do with being an engineer. You also have to be smart enough to get through university.
Do men and women really have different brains? Not sure. Does this affect intelligence, or personality? ...Or both?
Are men and women expected to meet stereotypical gender roles? Yes. Not just in school, as Blu suggests, but in life. Our SOCIETY makes it is difficult for a woman to become an engineer, because people do not fit into binary categories.
I am also a female engineer (aerospace, how's that for geeky) and I have to agree with Sally that I was "born this way". It definitey helps to have the engineer personality to get through school. A lot who don't, end up flunking out.
But, and this is a huge but, I agree with Mastermind about the difficulty of becoming a female engineer, at least 20 years ago when I started.
If a HS guy was good at math, the counselors would automatically suggest that they become engineers. If a HS girl that was good at math suggested to a counselor that they wanted to become an engineer, the counselor would often look at them with that "Are you an alien look". It is very discouraging. Twenty years ago, you really, really, really had to want to become a female engineer if you had a chance of making it through all the, mostly unspoken, discouragement.
Twenty years on, I haven't seen that anything much has changed. I see my 4th grade daughter getting teased for being exceptionally good at math. My 6th grade son, who is also exceptional at math, has not been hassled nearly as much.
Jake, thank a lot for the well researched documentation.i would agree that there is disparies in brain functions in men and women,however,performance especially in chemistry is by large a function of the society as opposed to genetic make-up