Monday, January 17, 2005

Sex Differences and Science Careers

The president of Harvard, Lawrence H. Summers, has caused an uproar in the blogosophere, with comments about alleged differences between males and females in mathematics and science. Unsurprisingly, those on the liberal side of the blogosphere have been quite harsh in their criticism of Summers. Does he deserve the attacks? Short answer: yes. Long answer: hell yes.

The study of sex differences in cognitive abilities has been muddled, for decades, by political agendas on both sides, but there is a fairly clear picture beneath all the muck, and that clear picture is that there is no clear picture. For a long time, it was believed that the primary area in which robust cognitive differences between males and females existed was in spatial-reasoning1. Spatial reasoning, in turn, was thought to underlie what are sometimes called the "secondary" mathematical abilities, i.e. those that we use for the first time in high school math courses (especially geometry and calculus). Those who held these view were not surprised, then, when sex differences in secondary mathematical abilities were discovered. For instance, Casey et al.2 found that for "high-ability groups" (i.e. those who might someday want to make mathematics or math-intensive sciences their careers), superior performance on mental rotation tasks by males explained the bulk of the difference in performance on the math section of the SAT ("high ability" males perform better on the SAT-M than "high ability" females).

The view that there are differences between mathematical abilities in males and females, and that these abilities are due, in large part, to differences in spatial reasoning abilities (to the exclusion of social and affective explanations) is still prominent, and might even be called the received view3. To be fair, there is empirical support for this view (e.g., the Casey et al. study, and those listed in footnote 3). Yet, for decades, there has also been a substantial amount of research demonstrating a.) that spatial differences don't explain differences in math performance and b.) differences in both spatial and mathematical abilities vary greatly depending on the context and population studied. For example, Goldstein et al.4 demonstrated that the performance of females and males on a mental rotation task only differed in a timed version of the task, indicating that the speeded mental rotation task may not be testing absolute spatial ability, but the speed with which people are able to reason about spatial ability. Further, an extensive review of the literature from a 4 decade period showed no significant correlation between spatial and mathematical abilities, but did find a significant correlation between verbal and mathematical abilities5. This review also found that female college students performed better on math tests than males. Another problem is that there appears to be a high degree of intra-individual variability in performance on both math and spatial reasoning tests. Some have even found that females' performance differs depending on their hormone levels, and thus their menstrual cycle6.

This is by no means an exhaustive review of the literature. Such a review would have to be of book length. Still, this is enough to make my point: while it does appear that there may be some specific sex differences in both spatial and mathematical reasoning, exactly what these differences are, and what causes them, is still very unclear. There is, however, one thing about gender differences in acheivement in mathematics and math-intensive sciences that is undeniable: gender discrimination exists, and it does play a significant role. As research on stereotype-threat theory has shown, the existence and consciousness of stereotypes can significantly affect people's performance on stereotype-relevant tasks7. Specifically, female performance on math tests has been shown to be negatively affected by gender stereotypes8.Furthermore, these stereotypes will, consciously or unconsciously, affect the evaluation of female students and job/tenure candidates, a fact that research on implicit attitudes has demonstrated quite well.

This brings us to the real reason why Summers deserves the harsh criticism. He is probably right that there exist real sex differences, across the entire population, in math abilities, but we know too little about the sources of these differences to be speaking definitively about them in public forums. Furthermore, what he is horribly wrong about is the role of discrimination and stereotypes in the success of women in math and science careers, or even on their performance on math and science tests. As Andrew of Universal Acid aptly notes, the existence of innate differences does not necessarily explain all of the differences in acheivement, and since research has shown that stereoptypes and discrimination are responsible for some acheivement differences, Summers' attempt to discount these as factors can only serve to perpetuate those differences. The effects of stereotypes are mediated, in part, by the authority of their purveyors, and when someone in Summers' position reiterates pernicious stereotypes, their negative effects can only increase.

1 See Vandenberg, S. G. & Kuse, A. R. (1978) Mental rotations, a group test of three-dimensional spatial visualization. Perceptual and Motor Skills 47: 599-604, for an old review of the mental rotation literature, on which most of the sex difference theories were and continue to be based.
2 Casey, M.B., Nuttall, R., Pezaris, E., and Benbow, C.P. (1995). The influence of spatial ability on gender differences in mathematics college entrance test scores across diverse samples. Developmental Psychology, 31, 697-705.
3 See e.g., Casey M.B. (1996). Understanding individual differences in spatial ability within females: A nature/nurture interactionist framework. Developmental Review, 16(3), 241-260; Geary, D.C., Saults, S.J., Liu, F., & Hoard, M.K. (2000). Sex differences in spatial cognition, computational fluency, and arithmetical reasoning. Journal of Experimental Child Psychology, 77, 337–353; Hyde, J.S., Fennema, E., & Lamon, S.J. (1990). Gender differences in mathematics performance: A meta-analysis. Psychological Bulletin, 2, 139-155; and Casey, M.B., Nuttall, R.L., Pezaris, E. (1997). Mediators of gender differences in mathematics college entrance test scores: a comparison of spatial skills with internalized beliefs and anxieties. Developmental Psychology, 33(4), 669-680.
4 Goldstein, D., Haldane, D., & Mitchell, C. (1990). Sex differences in visual-spatial ability: the role of performance factors. Memory and Cognition, 18(5), 546-550.
5 Friedman, L. (1995). The space factor in mathematics: Gender differences. Review of Educational Research, 65(1),22-50.
6 Silverman, I. & Phillips, K. (1993) Effects of estrogen changes during the menstrual cycle on spatial performance. Ethology and Sociobiology, 14, 257-270.
7 Steele, C. (1997). A threat in the air: How stereotypes shape intellectual identity and performance. American Psychologist, 52, 613–629.
8 Osborne, J.W. (2001). Testing stereotype threat: Does anxiety explain race and sex differences in achievement? Contemporary Educational Psychology, 26, 291-310.


Anonymous said...

As I mentioned when in college my professor made us read a lot of studies on how people learn. On of the more interesting ones, beyond how distrustful intuition was, was concerning the effects of early childhood bias on math learning. I truly wish I had the paper, but it basically was looking at gender differences in math. The conclusion of the paper (about all I can recall, more than a decade later) was that there was big worry that teachers in elementary school were biasing young women. Often these biases were unconscious. (i.e. call on boys more than girl, express "fear" of math to girls, but expectations to boys) An other problem was that people in elementary teaching often were very afraid of math themselves which manifest itself in subtle ways.

As I said, I can't recall the study. However it seems plausible, if speculative, that if this took place when language areas of the brain were still wiring themselves that this could have a big impact by the time high school or college rolls around. Of course the more pernicious problem is the emotional connotations that these girls associate with math.

Back in college they did a lot to try to attract women to the sciences. Math did probably the best of all the hard sciences as I recall. (Yeah, not technically a science -- but you know what I mean) Physics was among the worst. That, despite a lot of incentives. There were only a handful of women. Some were of course brilliant - far more intelligent than me. I remember a woman I dated from the physics department who had perfect SAT scores. But they still were by far the minority and it wasn't at all uncommon to have a class with no women in it.

As I recall at the time, it was simply difficult to recruit women to these fields.  

Posted by Clark

Anonymous said...

I remember choosing the lower math class in 7th grade, feeling pressure to not be as smart as I was, as a girl, that math was for boys and I was a reader. Algebra in high school was hard because I couldn't just memorize the theorems, I needed to understand why they worked. Somehow I could never get it. Now it seems clear.

As an adult I can look back and see how I shorted myself due to trying to fit in and how the adults around me shorted me by not expecting me to get it. The didn't care or know something was wrong if I wasn't geting it. All I did was wander through school reading science fiction.

I have also literally been offered 70 cents to the 100 a man was making.

There is no way to understand or know biological differences between the sexes until we break these long held gender beliefs. But commercials still have girls baking and boys playing with trucks. And boys are still tough and girls are still too emotional to think "logically."

Oh and I now fix computers for a living. And realize I do know math. And wondering if any of this is interesting input.  

Posted by marsha

Anonymous said...

This brings us to the real reason why Summers deserves the harsh criticism. He is probably right that there exist real sex differences, across the entire population, in math abilities, but we know too little about the sources of these differences to be speaking definitively about them in public forums.Leaving aside your erroneous position that Summer was speaking definitively, this type of statement drives me nuts because of the blatant hypocrisy inherent in your mindset. See here for Pinker's rejoinder.

If only you could adhere to the same standards that you seek to impose on Summers. 

Posted by TangoMan

Anonymous said...

What you don't mention is that when it comes to those with high math skill, there are _far_ more males than females. Consider the 2004 SAT takers, at

There were more females (53%) overall, but a lot more males when it came to high math scores: 21k males vs. 9.9k females scored 750-800; 39k males vs. 24k females scored 700-750, 64k males vs. 47k females scored 650-700. The same is true for the GRE (see McGillicuddy & De Lisi, _Biology, society, and behavior: The Development of Sex Differences in Cognition_)

Stereotype threat, by the way, explains only a tiny amount of performance differences. 

Posted by tc

Anonymous said...

Tango, I've addressed his reply in the comments section on his blog. I stand by what I said there, and here: a.) the gender differences are fairly small, unexplained, and contain a high degree of variability, and b.) the role of discrimination does not deserve to be diminished. It's true that stereotype-threat cannot explain the bulk of the variance, but that was not my point. My point was that stereotype threat is only one example of how discrimination affects people, and by reaffirming those stereotypes, as Summers did, whether you like it or not, you can only increase the role of stereotype-threat.

Which brings me to my real point (and this is for tc, as well), which both you and the folks you linked seem not to understand: innate differences probably do play a role, but highlighting these, and diminishing the role of discrimination, is stupid. When Summers says these may be responsible, he's wrong, period, unless he makes it clear that at most, they are responsible for a small portion of the variance in career success (and entrance). The sociopolitical factors play a huge role, and no amount of research on sex differences will show this to be false, because even those who recognize the sex differences in secondary math skills also recognize the large role that sociopolitical factors play (see some of the references in footnote 3, for example). Furthermore, since we can't do anything about what innate sex differences do exist, and we can do things about the atmosphere of discrimination and stereotype, we should place more emphasis on these, rather than less. 

Posted by Chris

Anonymous said...

role of discrimination does not deserve to be diminishedDeserve? That's a value judgement, not a scientific one, and to forestall your criticism, I haven't read anyone in this debate, including Summers himself, saying that the role of discrimination deserves to be diminished.

I'm forever baffled by the presumption, which it appears to me that you harbor, that adhering to a position of 100% environmentalism sides you with the angels and to even posit otherwise sides one with the devil.

When Summers says these may be responsible, he's wrong, period, unless he makes it clear that at most, they are responsible for a small portion of the variance in career success (and entrance).You employ an interesting debate tactic in holding Summers to your arbitrary standards. He need not jump through your conditional hoops in order to be right. Biology plays a huge part in the shaping of our lives - we are not blank slates - and for Summers to introduce this issue speaks to his affinity for dealing with the reality of the situation rather than the fiction you'd like to see the world as.

The sociopolitical factors play a huge role, and no amount of research on sex differences will show this to be false, because even those who recognize the sex differences in secondary math skills also recognize the large role that sociopolitical factors playTo entertain biology in no way diminishes these findings. If you wish to adhere to your 100% environmental models you'll be in for much unpleasant news for the research that's being conducted in labs today will simply be a sustained assault on the way you see the world. These views aren't going away.

Furthermore, since we can't do anything about what innate sex differences do exist, and we can do things about the atmosphere of discrimination and stereotype, we should place more emphasis on these, rather than less.Should? That's your opinion. I say we should base our policies on the "reality based persepctive" not the Bushian view of the world. 

Posted by TangoMan

Anonymous said...

The role of descrimination does not "deserve" to be diminished because it plays a big role. If he doesn't want to be beholding to the data, that's fine, but if he does, then he must admit that (and he certainly doesn't seem to be admitting that).

My standard is the scientific one: the innate differences are too small to account for the huge differences in career success and entrance. If Summers doesn't want to be held to the scientific standards, then he shouldn't reference scientific concepts (like innate differences) which he knows nothing about.

Since I've made it clear that my model is not 100% environment, both in the post and in the comments, I won't address any replies to my nonexistent belief that the differences are 100% environmental.

My final statement in the last comment was based on reality: the reality is, both biology and discrimination play a role, with sociopolitical factors playing a bigger role, in this case, than the environment (as is easily demonstrated, and as the research has demonstrated, if only by showing how small and variable the biological sex differences really are). I am the one being realistic here. I'm focusing on the factors we can do something about, and recognizing that even with biological factors, the ones we can do something about are very important. 

Posted by Chris

Anonymous said...

Sex differences are 'small and variable?' You mean like the 2 standard deviation difference in mean height between the sexes, acconting for about 50% of the variation in human height? The differences in physical stength?

And the fact is it does *not* take a terribly large difference to create a substantial disparity. Taking a simplified model here, say it takes a minimum math IQ of 130 to get into some field. The Math/Verbal IQ's of men and women are (say) 102/98 and 98/102 respectively. Given a standard deviation of 15 in math IQ and a normal distribution, 3.1% of men and 1.6% of women will have math IQs over 130--a ratio of nearly 2:1. This is in spite of only about a 1/4 standard deviation gap in mean math ability, or about 1.7% of the variation in math ability. This model does not even take into account the possibly greater variability of male intelligence, giving an even more heavily male bias to the right (and left) tails of the ability distribution. 

Posted by dude

Anonymous said...

The first sentence of the second paragraph should read "And the fact is it does *not* take a terribly large [mean] difference to create a substantial disparity." 

Posted by dude

Anonymous said...

dude, 1.) height differences are irrelevant, and 2.) populations that overlap as extensively as males and females on mathematical reasoning ability shouldn't yield a 90 to 10% difference in engeineering departments. Especially since the differences for college-going females are even smaller (and don't range over all math skills). 

Posted by Chris

Anonymous said...

It would be one thing to say Summer shouldn't be speaking publically on this issue, if the other side didn't take the position that "disparate impact" is prima facia evidence of prejudice and discrimination. To be labeled a bigot nowadays is not that much different than being labeled a nigger in days gone by. Grow up! 

Posted by Luke Lea

Anonymous said...

"2.) populations that overlap as extensively as males and females on mathematical reasoning ability shouldn't yield a 90 to 10% difference in engeineering departments. Especially since the differences for college-going females are even smaller (and don't range over all math skills)."

I don't know about this. You have to remember that one's choice to go into a field doesn't involve pure ability; one may have the skills for a certain field but not have much interest in it. Part of the issue here is not just that a lower percentage of women can hack it in engineering/math/physics, it's also that a fair number who *could* hack it don't have much interest in the field--they might prefer medicine, law, or some other field.

Would you say, for example, that the large predominance of males in DXing (long-distance radio reception) or ham radio is due solely or even largely to 'discrimination?' I mean, it's not like there's much social benefits to being in such groups (high pay, prestige, etc), and pretty much anyone who's interested can be involved. Is it really so hard to believe that women might be innately less interested in electronics than men? 

Posted by dude

Anonymous said...

Dude, you're right that preferences influence career choice, but the question still remains, do sociological factors influence these choies? The answer, to me, is obviously yes, and significantly so. 

Posted by Chris

Anonymous said...

Wow. I may be more oriented towards conspiracies than most, but I wonder if some of the above posters were consciously spamming nonsense, perhaps with some devious hidden purposes. Because, if they "honestly thought" what their posts suggest, and even worse they judged their thought to be true or valid or well founded... well, what the hell can I say!?!?

Take the definition of sanity as: "soundness of judgement or belief, or atleast the recognition when judgement or belief is unsound."

Surely we are all insane. But, how many of us, these days anyways, even strive for sanity? I suspect less than .001% 

Posted by Concerned US Citizen

Anonymous said...

This brings us to the real reason why Summers deserves the harsh criticism. He is probably right that there exist real sex differences, across the entire population, in math abilities, but we know too little about the sources of these differences to be speaking definitively about them in public forums.Beautiful - time permitting, I have to quote that.

In doing so, I will probably make the point that we (excuse me, the rest of us) don't actually know what Summers said, or how "definitively" he said it. I will then segue (gracelessly, no doubt) to some point or other about free academic inquiry and its apparent inappropriateness within the "reality based community".

Summers also mentioned the theory that men have more variabilty in their ability, and tend to be over-represented at the top and bottom of math tests. If you addressed that in your post, I missed it - sorry. 

Posted by Tom Maguire

Anonymous said...

We do know some of what Summers said (I quoted it in a later post). I don't think he mentioned variability. That was Pinker, who defends Summers on the ground that the existence of a disparity doesn't automatically indicate discrimination if there is an alternative explanation. However, we already know, from empirical research, that there is discrimination, so why Pinker would imply that this might not be the case is beyond me. 

Posted by Chris

Anonymous said...

My comment about variability was based on a story in the NY Times, but why should I trust them?

In citing a second factor, Dr. Summers cited research showing that more high school boys than girls tend to score at very high and very low levels on standardized math tests, and that it was important to consider the possibility that such differences may stem from biological differences between the sexes. 

Posted by Tom Maguire

Anonymous said...

Except it wasn't a public forum, it was a private luncheon. Papers contacted Summers asking him to provide transcript of what he said. He refused, so they went with (frequently skewed) recollections of invited members. 

Posted by Yaroslav Bulatov

Tisiwoota said...

Really late to comment on this, but
it seems the undercurrent of the discussion is a disagreement about whether we should be more concerned that Summers' comments might promote gender discrimination, or that suppression of his ideas might promote blank-slatism.

Both valid concerns in their own right, so I think the debate would be greatly clarified by making sure to distinguish concerns about this particular situation (and I think in that regard it is relevant that these comments occurred in what was meant to be a private context) from the wider issues that it has invoked.

Personally I think it's a shame that Summers comments got out, and I think the bulk of society's efforts should be devoted to reducing gender discrimination. But I also don't think that should come at the price of embracing blank-slatism wholesale and shutting down certain routes of research just because they might not give us politically correct results.

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