7 ms·

This post has many empirical problems, but let's start by looking at the male/female deck by Terri Oda. The only data in the entire deck is on slide 21, and the

by temphn 15y ago

This post has many empirical problems, but let's start by looking at the male/female deck by Terri Oda. The only data in the entire deck is on slide 21, and the caption reads: Two normal distributions that are 0.15 standard deviations apart (i.e d=0.15. This is the approximate magnitude of the gender difference in mathematics performance, averaging across all samples.) In other words, what is plotted there is actually NOT data but simply the textbook Gaussian curves for two distributions. So let's take a look at actual data. Here is a significantly more rigorous analysis: http://www.lagriffedulion.f2s.com/math.htm http://www.lagriffedulion.f2s.com/math.htm This actually uses data from three different tail populations: Female mathematicians in the NAS, Fields Medalists, and Putnam Competition winners. Lo and behold, a simple Gaussian model predicts that small differences in average mathematical ability produce significant sex differences in the tail[1]. And these predictions tally with reality (e.g. the empirical proportion of females in the NAS). Ms. Oda also does not consider two other crucial aspects, which are: 1. The large difference in spatial ability between men and women: http://goo.gl/SGhDw On the whole, variation between men and women tends to be smaller than deviations within each sex, but very large differences between the groups do exist–in men’s high level of visual-spatial targeting ability, for one. 2. The large difference in preferences between men and women: http://goo.gl/ccKyj A study by Lubinski and Benbow followed the careers of mathematically precocious youth from age 13 to 23. All were in the top 1% of mathematical ability. At age 23 less than 1% of the girls were pursuing doctorates in mathematics, engineering, or physical science, while almost 8% of the boys were. Equal aptitude not withstanding, girls pursued doctorates in biology at more than twice the rate of boys, and in the humanities at almost three times the rate of boys. The asymmetric part of this whole debate is that someone who voices the above counterarguments in public runs the risk of being browbeaten like Larry Summers or Michael Arrington. [1] This is of course assuming that distributions remain Gaussian, though it is well known that correspondence to Gaussianity drops off considerably as you move into the tails.

DaniFong 15y ago
Mathematical achievement doesn't fit a gaussian, and neither do the gendered groups of your conception. And if mathematical ability were distributed as a Gaussian, and genetic, women couldn't be ascending so rapidly. See for example Lisa Sauermann, the all time best performer in the international math olympiad: http://en.wikipedia.org/wiki/Lisa_Sauermann http://en.wikipedia.org/wiki/Lisa_Sauermann As I wrote four years ago: http://news.ycombinator.com/item?id=65494 http://news.ycombinator.com/item?id=65494 The thing is that intelligence isn't some kind of nice, statistically normed quantity. There's more to most variables than a mean and a standard deviation -- so I don't know why people seem to always think that you can restrict a discussion of intelligence to such concepts. ... But intelligence isn't a gene. Researchers have, since the time of Galton, tried to find a simple, biological basis for genius. You know, memory capacity, reaction times, brain size, brain structure convolution, etc. They haven't found anything -- literally everything has turned out to be a false start, even brain size, which, has been shown, within families does not even predict g. In the mid ranges, there are greater standard deviations, yes. But every single normed test is normed on a sample on the order of 1000. They're designed for regular people. The designer of the Weschler has adamantly opposed the use of IQ tests for anything other than clinical settings, for this reason. It's just no good at drawing conclusions on the extremes of ability. A better guide might be actual performance. The IOI this year had more girls than ever before -- 11. That's nearly 300% more than last year, where they had 4, and one medal. They are: Emina Bukva (Bosnia and Herzegovina) Constanza Contreras (Chile) Anna Currel (Spain) Romina Huenchunao (Chile) Vaiva Imbrasaite (Lithuania) Taksapaun Kittiakrastien (Thailand) [Silver] Sepideh Mahabadi (Iran) [Gold!] Radwa Metwali (Egypt) Katie O'Mahony (Ireland) Phitchaya Phothilimthana (Thailand) [Silver] Ye Wang (USA) [Silver] Sepideh Mahabadi had one of the best performances of anyone. If you're familiar with IOI scoring, only the top 1/12 are to get golds, and 2/12 to get silvers, thus 1 gold and 3 silvers out of 11 implies that they did at least as good as the boys, and in fact somewhat better. Were the 'standard deviation' explanation correct they should have, instead, had 0.4 girls earning maybe 0.01 medals. It just doesn't work. And three years ago: http://news.ycombinator.com/item?id=244449 http://news.ycombinator.com/item?id=244449 Why is it sexist to say we show up more frequently in science departments because we have also been designed by evolution to be better at math? Because compared with bench-pressing, claims of mathematically ability being better in men (and partially ordered, to boot) is seriously jumping the gun. We know what's involved in a bench press. We understand how testosterone stimulates the production of muscle. We are nowhere close with mathematical ability. We have no theory of mathematically ability -- we really don't know what it means, or if the simplest metrics are even useful for higher level math. We have no experimental results, because we have no controlled variables. We have few pieces of data, none of which are conclusively disentangled from cultural and historical influence. In the past two decades, the number of women scoring highly on the IMO, the IOI, the Putnam, and SMPY has gone up by roughly a factor of six. Doubtful that the number of girls with 'math talent genes' have sextupled that quickly. Isn't this evidence that we should hold off on our conclusions? And four years ago: http://news.ycombinator.com/item?id=65524 http://news.ycombinator.com/item?id=65524 "Brain size does not predict general cognitive ability within families" http://www.pnas.org/cgi/content/abstract/97/9/4932 http://www.pnas.org/cgi/content/abstract/97/9/4932 You can't discount that IOI statistic becuase it's an outlier. Every single participant at the IOI is an outlier in cognitive ability. Do you know about the theory of outliers? There's this thing called the central limit theorem. It says that if you have a lot of small independent variables, randomly assigned some value, then the mean of all these variables (or, by the same token, the sum of the variables) is distributed approximately normally. But suppose the variables are not small, or they're not independent. Then the central limit theorem doesn't hold, and what you have, almost all of the time, is an outlier -- that's why there are often many more outliers than you'd predict in a given population, using a small sample. Now, I'm not saying that g is zero. I said that psychometrics is a non-science, in the same sense that a lot of the social sciences are non-sciences (you can find papers which try to show a causal effect of insurance regulation on premium prices, ignoring profits entirely, for example). The fact that g is non-zero can be readily explained by the following simple observation -- most academic subtests, including IQ's, rely on skills that are either practiced as a group, or on skills that are shared between subtests. One example is focus, in general. Another is visualisation. Another is working memory. And so on and so on. Many of these skills are also practiced in situations, like school, where if one does well in one area, they do well in another. If you're the teacher's pet, you get more attention. If you're known as the bad kid, you're immediately discounted (and I've been on both sides). If you're poisoned against a learning environment, you just won't put any effort in. So it's no mystery to me that g is non-zero. The point is that the field of psychometrics is totally absent of content. There's no objective test for the validity of a test, for example -- the best they have is g-loading. Over the years, this means that tests have become higher and higher g-loaded. Now this could mean that the tests are getting better, or it could be that the subtests only look different, they are becoming more similar in content. I've been studying these tests, the actual tests, since I was twelve. It didn't take long before I figured out how poor they were at answering research questions, or questions of individual ability. If you get the chance, try to look up the history of the Stanford-Binet, or Terman's kids, or actually take a look at the scoring method behind most of these things. They're totally full of crap...
- evolve2k 15y ago
  Woah EPIC post, would be great if you added a TLDR comment upfront for skimming.
  - DaniFong 15y ago
    tl;dr, people often claim that greater variance in mathematical ability accounts for lower numbers of women in high level scientific positions. this is doesn't match the data: one can't mathematically fit a gaussian curve to explain the distributions. thus the supposed scientific explanation for why women are underrepresented is actually faulty science. likewise, genetic explanations cannot account for the recent and rapid ascendancy of woman in such technical areas (though we have a long way to go). participation at the highest levels of academic competition has increased dramatically. given the holes in these, and other, explanations, it is both scientifically and morally irresponsible to posit innate differences as the governing factors. yet despite these arguments, many people still feel they have the station to proclaim some scientific basis for what would otherwise be evidence of continued unequal opportunity. the scientific claims of a human group's inferiority must withstand scientific scrutiny far beyond that expected in physics for, say, proving faster than light neutrinos. yet the scientific rigor of studies of human inferiority is actually far below that of physics. i ascribe the difference to politics. an actual big problem preventing women from advancing: being successful, as a woman, is anticorrelated with being liked. this is far from the fault of men alone -- it is a pervasive cultural bias. see Sheryl Sandberg's TED Talk: why we have too few women leaders. http://blog.ted.com/2010/12/21/why-we-have-too-few-women-leaders-sheryl-sandberg-on-ted-com/ http://blog.ted.com/2010/12/21/why-we-have-too-few-women-lea... likewise, academic success among some african american communities is occasionally dismissed as 'acting white.' social pressure is a powerful, powerful thing.
- yummyfajitas 15y ago
  "And if mathematical ability were distributed as a Gaussian, and genetic, women couldn't be ascending so rapidly." This is false. It could be that mathematical ability is genetic and normally distributed, but some component of women's underrepresentation is caused by factors other than this (e.g., discrimination, personal preferences). "It's just no good at drawing conclusions on the extremes of ability. A better guide might be actual performance. The IOI this year had more girls than ever before -- 11... Were the 'standard deviation' explanation correct they should have, instead, had 0.4 girls earning maybe 0.01 medals." Come on. I know you know better than to draw statistical conclusions from a single event with a sample size of 11. So why do it? "The fact that g is non-zero can be readily explained by the following simple observation -- most academic subtests, including IQ's, rely on skills that are either practiced as a group, or on skills that are shared between subtests. One example is focus, in general. Another is visualisation. Another is working memory. And so on and so on." You've come up with a plausible theory of what g is. It might be f(focus, visualization, working memory). This does not make the theory of psychometrics "totally absent of content", it just means they don't understand everything yet. The fact that pressure is non-zero can be readily explained by the following simple observation -- air is made of particles obeying Newtonian mechanics which impart a force upon a vessel when they collide with it. Does this make thermodynamics "totally absent of content"? The fact of the matter is that a variety of seemingly unrelated tests are correlated with each other. They are also strongly correlated with various life outcomes in a manner which more or less corresponds to our intuitive intuition about the idea of "intelligence". Stuff like this rarely happens by chance, and it is highly likely there is something behind it.

by temphn 15y ago

DaniFong 15y ago

Mathematical achievement doesn't fit a gaussian, and neither do the gendered groups of your conception. And if mathematical ability were distributed as a Gaussian, and genetic, women couldn't be ascending so rapidly. See for example Lisa Sauermann, the all time best performer in the international math olympiad: http://en.wikipedia.org/wiki/Lisa_Sauermann http://en.wikipedia.org/wiki/Lisa_Sauermann As I wrote four years ago: http://news.ycombinator.com/item?id=65494 http://news.ycombinator.com/item?id=65494 The thing is that intelligence isn't some kind of nice, statistically normed quantity. There's more to most variables than a mean and a standard deviation -- so I don't know why people seem to always think that you can restrict a discussion of intelligence to such concepts. ... But intelligence isn't a gene. Researchers have, since the time of Galton, tried to find a simple, biological basis for genius. You know, memory capacity, reaction times, brain size, brain structure convolution, etc. They haven't found anything -- literally everything has turned out to be a false start, even brain size, which, has been shown, within families does not even predict g. In the mid ranges, there are greater standard deviations, yes. But every single normed test is normed on a sample on the order of 1000. They're designed for regular people. The designer of the Weschler has adamantly opposed the use of IQ tests for anything other than clinical settings, for this reason. It's just no good at drawing conclusions on the extremes of ability. A better guide might be actual performance. The IOI this year had more girls than ever before -- 11. That's nearly 300% more than last year, where they had 4, and one medal. They are: Emina Bukva (Bosnia and Herzegovina) Constanza Contreras (Chile) Anna Currel (Spain) Romina Huenchunao (Chile) Vaiva Imbrasaite (Lithuania) Taksapaun Kittiakrastien (Thailand) [Silver] Sepideh Mahabadi (Iran) [Gold!] Radwa Metwali (Egypt) Katie O'Mahony (Ireland) Phitchaya Phothilimthana (Thailand) [Silver] Ye Wang (USA) [Silver] Sepideh Mahabadi had one of the best performances of anyone. If you're familiar with IOI scoring, only the top 1/12 are to get golds, and 2/12 to get silvers, thus 1 gold and 3 silvers out of 11 implies that they did at least as good as the boys, and in fact somewhat better. Were the 'standard deviation' explanation correct they should have, instead, had 0.4 girls earning maybe 0.01 medals. It just doesn't work. And three years ago: http://news.ycombinator.com/item?id=244449 http://news.ycombinator.com/item?id=244449 Why is it sexist to say we show up more frequently in science departments because we have also been designed by evolution to be better at math? Because compared with bench-pressing, claims of mathematically ability being better in men (and partially ordered, to boot) is seriously jumping the gun. We know what's involved in a bench press. We understand how testosterone stimulates the production of muscle. We are nowhere close with mathematical ability. We have no theory of mathematically ability -- we really don't know what it means, or if the simplest metrics are even useful for higher level math. We have no experimental results, because we have no controlled variables. We have few pieces of data, none of which are conclusively disentangled from cultural and historical influence. In the past two decades, the number of women scoring highly on the IMO, the IOI, the Putnam, and SMPY has gone up by roughly a factor of six. Doubtful that the number of girls with 'math talent genes' have sextupled that quickly. Isn't this evidence that we should hold off on our conclusions? And four years ago: http://news.ycombinator.com/item?id=65524 http://news.ycombinator.com/item?id=65524 "Brain size does not predict general cognitive ability within families" http://www.pnas.org/cgi/content/abstract/97/9/4932 http://www.pnas.org/cgi/content/abstract/97/9/4932 You can't discount that IOI statistic becuase it's an outlier. Every single participant at the IOI is an outlier in cognitive ability. Do you know about the theory of outliers? There's this thing called the central limit theorem. It says that if you have a lot of small independent variables, randomly assigned some value, then the mean of all these variables (or, by the same token, the sum of the variables) is distributed approximately normally. But suppose the variables are not small, or they're not independent. Then the central limit theorem doesn't hold, and what you have, almost all of the time, is an outlier -- that's why there are often many more outliers than you'd predict in a given population, using a small sample. Now, I'm not saying that g is zero. I said that psychometrics is a non-science, in the same sense that a lot of the social sciences are non-sciences (you can find papers which try to show a causal effect of insurance regulation on premium prices, ignoring profits entirely, for example). The fact that g is non-zero can be readily explained by the following simple observation -- most academic subtests, including IQ's, rely on skills that are either practiced as a group, or on skills that are shared between subtests. One example is focus, in general. Another is visualisation. Another is working memory. And so on and so on. Many of these skills are also practiced in situations, like school, where if one does well in one area, they do well in another. If you're the teacher's pet, you get more attention. If you're known as the bad kid, you're immediately discounted (and I've been on both sides). If you're poisoned against a learning environment, you just won't put any effort in. So it's no mystery to me that g is non-zero. The point is that the field of psychometrics is totally absent of content. There's no objective test for the validity of a test, for example -- the best they have is g-loading. Over the years, this means that tests have become higher and higher g-loaded. Now this could mean that the tests are getting better, or it could be that the subtests only look different, they are becoming more similar in content. I've been studying these tests, the actual tests, since I was twelve. It didn't take long before I figured out how poor they were at answering research questions, or questions of individual ability. If you get the chance, try to look up the history of the Stanford-Binet, or Terman's kids, or actually take a look at the scoring method behind most of these things. They're totally full of crap...

evolve2k 15y ago
Woah EPIC post, would be great if you added a TLDR comment upfront for skimming.
- DaniFong 15y ago
  tl;dr, people often claim that greater variance in mathematical ability accounts for lower numbers of women in high level scientific positions. this is doesn't match the data: one can't mathematically fit a gaussian curve to explain the distributions. thus the supposed scientific explanation for why women are underrepresented is actually faulty science. likewise, genetic explanations cannot account for the recent and rapid ascendancy of woman in such technical areas (though we have a long way to go). participation at the highest levels of academic competition has increased dramatically. given the holes in these, and other, explanations, it is both scientifically and morally irresponsible to posit innate differences as the governing factors. yet despite these arguments, many people still feel they have the station to proclaim some scientific basis for what would otherwise be evidence of continued unequal opportunity. the scientific claims of a human group's inferiority must withstand scientific scrutiny far beyond that expected in physics for, say, proving faster than light neutrinos. yet the scientific rigor of studies of human inferiority is actually far below that of physics. i ascribe the difference to politics. an actual big problem preventing women from advancing: being successful, as a woman, is anticorrelated with being liked. this is far from the fault of men alone -- it is a pervasive cultural bias. see Sheryl Sandberg's TED Talk: why we have too few women leaders. http://blog.ted.com/2010/12/21/why-we-have-too-few-women-leaders-sheryl-sandberg-on-ted-com/ http://blog.ted.com/2010/12/21/why-we-have-too-few-women-lea... likewise, academic success among some african american communities is occasionally dismissed as 'acting white.' social pressure is a powerful, powerful thing.
yummyfajitas 15y ago
"And if mathematical ability were distributed as a Gaussian, and genetic, women couldn't be ascending so rapidly." This is false. It could be that mathematical ability is genetic and normally distributed, but some component of women's underrepresentation is caused by factors other than this (e.g., discrimination, personal preferences). "It's just no good at drawing conclusions on the extremes of ability. A better guide might be actual performance. The IOI this year had more girls than ever before -- 11... Were the 'standard deviation' explanation correct they should have, instead, had 0.4 girls earning maybe 0.01 medals." Come on. I know you know better than to draw statistical conclusions from a single event with a sample size of 11. So why do it? "The fact that g is non-zero can be readily explained by the following simple observation -- most academic subtests, including IQ's, rely on skills that are either practiced as a group, or on skills that are shared between subtests. One example is focus, in general. Another is visualisation. Another is working memory. And so on and so on." You've come up with a plausible theory of what g is. It might be f(focus, visualization, working memory). This does not make the theory of psychometrics "totally absent of content", it just means they don't understand everything yet. The fact that pressure is non-zero can be readily explained by the following simple observation -- air is made of particles obeying Newtonian mechanics which impart a force upon a vessel when they collide with it. Does this make thermodynamics "totally absent of content"? The fact of the matter is that a variety of seemingly unrelated tests are correlated with each other. They are also strongly correlated with various life outcomes in a manner which more or less corresponds to our intuitive intuition about the idea of "intelligence". Stuff like this rarely happens by chance, and it is highly likely there is something behind it.