Hundreds of media outlets - including the New York Times whose Tamar Lewin mentions Lawrence Summers in the very first sentence - uncritically report that "girls are equally good as boys" in math. This highly surprising statement is claimed to be based on a paper in Science magazine.
Janet Hyde herself, a self-described feminist psychologist, seems to be a prototypical 2nd wave feminist, too (click her picture or check her publication record). She thinks that "her biggest contribution to feminist sexology is her college sexuality textbook" (exact quote). She believes that the supposed higher rate of masturbation among boys and men has "enormous implications" which, she believes, was her second "major contribution" to feminist sexology. This difference between sexes goes in the "right" direction so these "scientists" choose to believe it and promote it. We can finally appreciate her third "major contribution". ;-)
All five co-authors are women who have been writing similar cargo cult scientific papers for quite some time.
It is enough to read a brief review in Science to see that the headlines don't follow from the paper at all. The review explains the main reason of the results: they have detected no signal because the tests were too simple. They didn't really test "g" or the ability to think mathematically but rather attainment. And the standards are dropping. David Malakoff writes:
The last sentence says:
Check e.g. California's standardized math test for grade 7 to see how low-brow and mechanical these tests are.
Newspaper articles build their far-reaching statements on grades 2 through 11. The paper by Hyde et al. however did find that boys have an edge in the SAT tests before they enter the college. Hyde herself offers a conceivable but not straightforward interpretation of this fact - one that she chose not to apply in other cases. For a certain reason, this portion of the paper - which is much more important for our understanding of the development of the math talents - is not being reported or, to say the least, it doesn't influence the headlines.
The magnitude of variations
Most importantly, those five co-authors don't seem to discuss the variance of the distributions in the media. The larger second moment of the male distribution is what primarily decides about the small percentage of women in math-loaded occupations (especially the top ones), more than the central value does: see detailed calculations by La Griffe du Lion. Before those five spice girls made their bombshell statements about girls matching boys, they should have made sure that they could match boys (such as Rushton and Nymborg) in mathematics themselves. ;-)
Not to be unfair, their paper does mention that in the 99th percentile, they found the boys:girls ratio to be 2.06:1 (and for the 95th percentile, it was 1.45:1). Incidentally, these numbers roughly agree with Figure 2 in La Griffe du Lion's text about these matters. But Hyde et al. were very careful that this particular result didn't get into the media.
Even if this effect were not enough to explain all the data, one should realize one more obvious thing: there is no reason why the magnitude of math skills gap between the sexes should be exactly universal for all races. Of course that different races have different innate aptitudes for maths and they can also have different differences between the sexes. This would show that the biological factors are more important, not less. In the (highly selective) case of the mathematical Olympiad discussed below, boys have a significant edge among the Asian nations, too.
It's been more than three years when Larry Summers introduced the width of the statistical distributions into the public debate but when you make a Google search, you will see that 99% of people still don't seem to get the point. Most people in the world are just stunningly stupid.
If you're one of them and you're disturbed by all these differences and you want to hear something encouraging about ordinary people, let me tell you that it can be calculated that if you pick a random man and a random woman, the woman will be g-smarter than the man in 45% of the cases. You need to calculate a somewhat tough integral to get this result. As Barbie correctly said, math class is tough. ;-)
Mathematical Olympiads
The girls tell us that the gap is now gone and everything is equal. The only problem is that no airplanes land and the percentage of girls in math-loaded occupations stays comparable to 10% or so and among the Fields medal winners, it is 0.0%.
In order to show you a much more meaningful and transparent measure of the real mathematical talent among American boys and girls, let us look at the winners of the U.S. Mathematical Olympiad. Every year, twelve winners are officially announced. We will start with the year 2007.
Click the picture to zoom in and read more about the 2007 ceremony (click). The guy on the left in an official and the remaining 12 high school seniors are the winners. The young lady in the light blue dress on the right side is the only female winner. Congratulations! She happens to be of East Asian descent. The East Asian people happen to have a higher IQ by about 10 points than the Caucasian people. At least, the PC people could be thrilled about one black guy kneeling in the middle. (Oops, it turns out that he is actually an Indian American, would you believe?) I am thrilled, too - and so am I by the remaining 11 winners.
But let's forget about geography for a while.
If the probabilities that girls and boys become winners were equal, the probability that there will be less than 2 female winners would be equal to 13/4096 = 0.003. That's approximately one part in 300. But yes, you might still say that it is a coincidence. Moreover, 2007 is not the most recent year. Why doesn't Mr Motl look at the 2008 ceremony (click)? It must have been an inconvenient one, right? Well, here it is.
Click the picture to zoom in. The background is a bit more complicated now :-) - there is one Einstein and 2+2 old officials at the bottom side of the picture. Nevertheless, there is not a single girl here. (There is no longer any guy who looks black here either, but we don't want to analyze geography in this text.) If you assume the 50:50 probability for them to become winners, the probability that there is no female winner equals 1/4096 = 0.000024.
Finally, you can combine the two sets of winners. If you assume that the a priori chances are 50:50, the probability that among 24 winners, there would be less than 2 female winners is equal to 25/2^24 = 0.0000015, roughly one part per million. That's already pretty much a five-sigma falsification of your hypothesis about "equality". Moreover, all these kids have spent all their lives in the atmosphere of political correctness so one would have to be really mad to argue that the small percentage of girls is due to the terror against female scientists. ;-)
At this moment, the egalitarian people have to claim that all the organizers of math Olympiads, including the old lady (Mary McKay) on the 2008 photograph, are despicable sexist pigs.
But because this result is so perfectly reproducible, I could add as many teams as I wanted, reducing the probability that such a thing can occur by chance virtually to zero. For example, among hundreds of known names of Czechoslovak participants of the International Math Olympiad (which I kind of screwed back in 1992, unlike the national level), you only find four female names: the probability is of order 1/2^200 = 10^{-60}. Analogously, there are 4 girls in the 1993-2008 list of the 96 Czech Republic participants, below 5 percent. (Feel free to check other countries.)
(Ms Jana Syrovátková whom I know very well earned a gold medal in 1993 which was amazing. If you care about these things, the last 1992 Czechoslovak team where I competed was the 13rd country which was one of the worst results in history. ;-) On the other hand, the 10th place of the first 1993 Czech team was fine; Slovakia was 12th in 1993. However, after 1993, both Czechia and Slovakia were always much worse than we were in 1992 and recently our teams are both around the 35th place in average. We simply can't compare to Hungary or Romania and I am not sure about the exact reason.)
But whether you like to hear it or not, the idea that there is as much math talent - and I am talking about the higher end - among high school boys and high school girls is utterly absurd. In the fast comments, additional statistics about the International Mathematical Olympiads are discussed. For example, the female percentage in the teams (10% in average in 2008) is heavily correlated with the success of the team. The winning teams are near 1% while the losing teams at the bottom approach up to 30% of girls.
This correlation can't be explained by any bias in education "before the olympiad": you would have to accuse the IMO graders of fraud. Instead, this correlation proves that the average global cutoff for the girls to attend IMO was somewhat lower. Despite this fact, the girls only made up 10% of the participants.
And the significant gap is not dropping in any sense - the two pictures above would indicate just the opposite trend but such a conclusion wouldn't be statistically significant. What may be dropping is the quality of the generic math education in the U.S. which is the thing that the journalists should worry about. But because most of them hate maths anyway, they prefer to focus on (and twist) different things.
The rate of female physics/chemistry Nobel prize winners has dropped, too (there's been none since the early 1960s), for exactly the opposite reason. Relatively speaking, it becomes tougher to earn a Nobel prize "by chance" (sorry, Marie Curie!). This fact doesn't mean that the new discoveries are more revolutionary than the old ones. On the contrary, they may be less revolutionary but they require a lot of systematic high-expertise work. Quite clearly, the more selective your math-related tests become, the lower percentage of females you will obtain (the boys have a greater variance of the distribution).
The high school math Olympiads are more selective than tests accepting undergraduates to colleges but less selective than Nobel prizes. The silly mechanical tests underlying the paper by Hyde et al. are not really selective and if you score well, it doesn't mean that you can do math-loaded things. It only shows that as a child, you were not quite left behind. ;-)
PC = -IQ
Incidentally, another new study found the political correctness of disciplines to be a highly decreasing function of their IQ. The dumber you are, the more politically correct you are. For example, as far as PC goes,
Click the IQ sticker below to see more articles about innate aptitudes and related stuff.
Janet Hyde et al.: Gender similarities characterize math performance
Janet Hyde herself, a self-described feminist psychologist, seems to be a prototypical 2nd wave feminist, too (click her picture or check her publication record). She thinks that "her biggest contribution to feminist sexology is her college sexuality textbook" (exact quote). She believes that the supposed higher rate of masturbation among boys and men has "enormous implications" which, she believes, was her second "major contribution" to feminist sexology. This difference between sexes goes in the "right" direction so these "scientists" choose to believe it and promote it. We can finally appreciate her third "major contribution". ;-)All five co-authors are women who have been writing similar cargo cult scientific papers for quite some time.
It is enough to read a brief review in Science to see that the headlines don't follow from the paper at all. The review explains the main reason of the results: they have detected no signal because the tests were too simple. They didn't really test "g" or the ability to think mathematically but rather attainment. And the standards are dropping. David Malakoff writes:
The study's most disturbing finding, the authors say, is that neither boys nor girls get many tough math questions on state tests now required to measure a school district's progress under the 2002 federal No Child Left Behind law. Using a four-level rating scale, with level one being easiest, the authors said that they found no challenging level-three [strategic thinking] or [level]-four [extended thinking] questions on most state tests. The authors worry that means that teachers may start dropping harder math from their curriculums, because "more teachers are gearing their instruction to the test."That's what the media should actually worry about - decreasing quality of American kids' math skills - but no one does. It's just too bad if there are no challenging problems. The tests they have processed had nothing to do with strategic thinking and extended thinking. It wasn't really about the math that matters in math-loaded occupations.
The last sentence says:
Among students she's observed, she says "the boys tend to be a little more idiosyncratic in solving problems, the girls more conservative in following what they've been taught."Yes, that matches my experience, too. The latter approach is normally called "a lack (or shortage) of creativity." If you combine this observation about boys and girls with the statement that "more teachers are gearing their instruction to the test", you may guess whether it is the boys or the girls whose scores will be raised.
Check e.g. California's standardized math test for grade 7 to see how low-brow and mechanical these tests are.
Newspaper articles build their far-reaching statements on grades 2 through 11. The paper by Hyde et al. however did find that boys have an edge in the SAT tests before they enter the college. Hyde herself offers a conceivable but not straightforward interpretation of this fact - one that she chose not to apply in other cases. For a certain reason, this portion of the paper - which is much more important for our understanding of the development of the math talents - is not being reported or, to say the least, it doesn't influence the headlines.
The magnitude of variations
Most importantly, those five co-authors don't seem to discuss the variance of the distributions in the media. The larger second moment of the male distribution is what primarily decides about the small percentage of women in math-loaded occupations (especially the top ones), more than the central value does: see detailed calculations by La Griffe du Lion. Before those five spice girls made their bombshell statements about girls matching boys, they should have made sure that they could match boys (such as Rushton and Nymborg) in mathematics themselves. ;-)
Not to be unfair, their paper does mention that in the 99th percentile, they found the boys:girls ratio to be 2.06:1 (and for the 95th percentile, it was 1.45:1). Incidentally, these numbers roughly agree with Figure 2 in La Griffe du Lion's text about these matters. But Hyde et al. were very careful that this particular result didn't get into the media.
National Post (Canada) explains that these findings of the paper about the variations support e.g. Lawrence Summers' statements...In the paper, they also say some "likable" stuff about the ratio being different for Asians: some people argue that this shows "complex cultural factors". That's of course complete rubbish. The ratio is closer to one for Asians simply because the Asian boys and girls have a higher central value, and the 99th percentile of the whole society therefore cuts their distributions closer to the bulk where the difference in variances doesn't play such a role.
Even if this effect were not enough to explain all the data, one should realize one more obvious thing: there is no reason why the magnitude of math skills gap between the sexes should be exactly universal for all races. Of course that different races have different innate aptitudes for maths and they can also have different differences between the sexes. This would show that the biological factors are more important, not less. In the (highly selective) case of the mathematical Olympiad discussed below, boys have a significant edge among the Asian nations, too.
It's been more than three years when Larry Summers introduced the width of the statistical distributions into the public debate but when you make a Google search, you will see that 99% of people still don't seem to get the point. Most people in the world are just stunningly stupid.
If you're one of them and you're disturbed by all these differences and you want to hear something encouraging about ordinary people, let me tell you that it can be calculated that if you pick a random man and a random woman, the woman will be g-smarter than the man in 45% of the cases. You need to calculate a somewhat tough integral to get this result. As Barbie correctly said, math class is tough. ;-)
Mathematical Olympiads
The girls tell us that the gap is now gone and everything is equal. The only problem is that no airplanes land and the percentage of girls in math-loaded occupations stays comparable to 10% or so and among the Fields medal winners, it is 0.0%.
In order to show you a much more meaningful and transparent measure of the real mathematical talent among American boys and girls, let us look at the winners of the U.S. Mathematical Olympiad. Every year, twelve winners are officially announced. We will start with the year 2007.
Click the picture to zoom in and read more about the 2007 ceremony (click). The guy on the left in an official and the remaining 12 high school seniors are the winners. The young lady in the light blue dress on the right side is the only female winner. Congratulations! She happens to be of East Asian descent. The East Asian people happen to have a higher IQ by about 10 points than the Caucasian people. At least, the PC people could be thrilled about one black guy kneeling in the middle. (Oops, it turns out that he is actually an Indian American, would you believe?) I am thrilled, too - and so am I by the remaining 11 winners.
But let's forget about geography for a while.
If the probabilities that girls and boys become winners were equal, the probability that there will be less than 2 female winners would be equal to 13/4096 = 0.003. That's approximately one part in 300. But yes, you might still say that it is a coincidence. Moreover, 2007 is not the most recent year. Why doesn't Mr Motl look at the 2008 ceremony (click)? It must have been an inconvenient one, right? Well, here it is.
Click the picture to zoom in. The background is a bit more complicated now :-) - there is one Einstein and 2+2 old officials at the bottom side of the picture. Nevertheless, there is not a single girl here. (There is no longer any guy who looks black here either, but we don't want to analyze geography in this text.) If you assume the 50:50 probability for them to become winners, the probability that there is no female winner equals 1/4096 = 0.000024.
Finally, you can combine the two sets of winners. If you assume that the a priori chances are 50:50, the probability that among 24 winners, there would be less than 2 female winners is equal to 25/2^24 = 0.0000015, roughly one part per million. That's already pretty much a five-sigma falsification of your hypothesis about "equality". Moreover, all these kids have spent all their lives in the atmosphere of political correctness so one would have to be really mad to argue that the small percentage of girls is due to the terror against female scientists. ;-)
At this moment, the egalitarian people have to claim that all the organizers of math Olympiads, including the old lady (Mary McKay) on the 2008 photograph, are despicable sexist pigs.
But because this result is so perfectly reproducible, I could add as many teams as I wanted, reducing the probability that such a thing can occur by chance virtually to zero. For example, among hundreds of known names of Czechoslovak participants of the International Math Olympiad (which I kind of screwed back in 1992, unlike the national level), you only find four female names: the probability is of order 1/2^200 = 10^{-60}. Analogously, there are 4 girls in the 1993-2008 list of the 96 Czech Republic participants, below 5 percent. (Feel free to check other countries.)
(Ms Jana Syrovátková whom I know very well earned a gold medal in 1993 which was amazing. If you care about these things, the last 1992 Czechoslovak team where I competed was the 13rd country which was one of the worst results in history. ;-) On the other hand, the 10th place of the first 1993 Czech team was fine; Slovakia was 12th in 1993. However, after 1993, both Czechia and Slovakia were always much worse than we were in 1992 and recently our teams are both around the 35th place in average. We simply can't compare to Hungary or Romania and I am not sure about the exact reason.)
But whether you like to hear it or not, the idea that there is as much math talent - and I am talking about the higher end - among high school boys and high school girls is utterly absurd. In the fast comments, additional statistics about the International Mathematical Olympiads are discussed. For example, the female percentage in the teams (10% in average in 2008) is heavily correlated with the success of the team. The winning teams are near 1% while the losing teams at the bottom approach up to 30% of girls.
This correlation can't be explained by any bias in education "before the olympiad": you would have to accuse the IMO graders of fraud. Instead, this correlation proves that the average global cutoff for the girls to attend IMO was somewhat lower. Despite this fact, the girls only made up 10% of the participants.
And the significant gap is not dropping in any sense - the two pictures above would indicate just the opposite trend but such a conclusion wouldn't be statistically significant. What may be dropping is the quality of the generic math education in the U.S. which is the thing that the journalists should worry about. But because most of them hate maths anyway, they prefer to focus on (and twist) different things.
The rate of female physics/chemistry Nobel prize winners has dropped, too (there's been none since the early 1960s), for exactly the opposite reason. Relatively speaking, it becomes tougher to earn a Nobel prize "by chance" (sorry, Marie Curie!). This fact doesn't mean that the new discoveries are more revolutionary than the old ones. On the contrary, they may be less revolutionary but they require a lot of systematic high-expertise work. Quite clearly, the more selective your math-related tests become, the lower percentage of females you will obtain (the boys have a greater variance of the distribution).
The high school math Olympiads are more selective than tests accepting undergraduates to colleges but less selective than Nobel prizes. The silly mechanical tests underlying the paper by Hyde et al. are not really selective and if you score well, it doesn't mean that you can do math-loaded things. It only shows that as a child, you were not quite left behind. ;-)
PC = -IQ
Incidentally, another new study found the political correctness of disciplines to be a highly decreasing function of their IQ. The dumber you are, the more politically correct you are. For example, as far as PC goes,
Psychology > Sociology > History > Political science > Biology > Mechanical engineering > Electrical engineeringAs far as IQ goes, these disciplines are sorted exactly in the opposite order. Check the previous two links! ;-)
Click the IQ sticker below to see more articles about innate aptitudes and related stuff.
Janet Hyde: boys = girls in math? Not really
Reviewed by DAL
on
July 24, 2008
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Reviewed by DAL
on
July 24, 2008
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