Geoff's Blog

Big news in the papers these days, about the “math gap” between the sexes. Via Newsweek’s Sharon Begley:

Even the most hidebound male chauvinists have been forced to admit that girls are as good at math as boys, on average. Boys no longer start outperforming girls at age 12 or 13, as they did as late as the 1970s … tests mandated by No Child Left Behind [NCLB] show that girls have reached parity with boys in math achievement through high school….

[T]he stereotype that females lack the innate ability to match males at the highest levels of math lives on. A new study comes as close to burying it as anything yet.

In a paper posted this evening in the Proceedings of the National Academy of Sciences, researchers describe analyzing data on the highest level of math achievement….

In the U.S., tests typically show that, among students scoring in the 99th percentile for math achievement, boys outnumber girls 2-to-1. But that’s only among white students. Among Asians in the U.S., girls outnumber boys [in math achievement] very slightly, as they do in Britain, Iceland and Thailand. That suggests that males’ superior math ability does not hold true across the world, which is always a strong clue that social and cultural forces are involved….

“We concluded that the main reason many fewer females than males excel in math in most countries is not lack of innate ability or ‘intrinsic aptitude’ but gender inequality,” says [Janet] Mertz. “Nations with greater gender equality typically have a smaller math gender gap“…. That suggests that the root of gender disparity in math is sociocultural factors, not anything unchangeable that girls are born with. Society either sends a message that girls can excel at math, that they will be rewarded for doing so—or it doesn’t….

Mertz and [also Janet] Hyde looked for evidence of [the "greater male variability hypothesis"] imbalance—more boys than girls at the extremes of math ability—in international data, too. Again, they found that in some countries as many girls as boys score above the 99th percentile, and in others more girls than boys are extreme math dunces or math geniuses. In both cases, countries with as many or more girls at the upper extreme tend to be those with the greatest gender equality, such as Germany and the Netherlands. If the greater male variability in math performance that Summers cited as an explanation for the low numbers of women among math geniuses is not ubiquitous across the world, then “the occurrence of greater male variability and scarcity of top-scoring females in many, but not all countries .. . must be largely due to changeable sociocultural factors,” the scientists write, “not immutable, innate biological differences between the sexes.” If the differences were innate, they should show up in every culture.

For anyone who still believes that innate factors explain the math gender gap, as I wrote last year, look at countries with a common gene pool. East Germany regularly sent many more girls than West Germany to the International Mathematics Olympiad by margins of 5-to-0; Slovakia sent more girls by a margin of 3-to-1; Korea topped Japan by 6 to 0. As I wrote then, “It’s hard to see that as anything but the result of the starkly different social and other environmental forces in each country, not intrinsic biology.”

Convincing arguments, eh?

And even more convincing when you read Hyde’s recent paper itself:

In one recent study [done by Hyde herself; the reference points to her July 2008 paper], researchers obtained useable [NCLB] data from 10 states representing the testing of >7 million youth. Averaged across these 10 states, gender differences in performance were close to zero in all grades, including high school…. When analyzed by ethnicity, the same pattern of gender similarities was found for all ethnic groups studied, that is, African Americans, Latinos, Asian Americans, American Indians, and Whites. Thus, girls have now reached parity with boys in mathematics performance in the U.S., even in high school where a gap existed in earlier decades.

However, coding of the test items on these [NCLB] examinations for cognitive level indicated that none of them tapped complex problem solving at most grade levels for most states. Thus, it was impossible with these NCLB datasets to investigate whether a gender gap existed in complex problem solving. Therefore, the researchers also examined data from the National Assessment of Educational Progress (NAEP), a federally managed program that tests a random sample of U.S. students each year. Items from 12th grade data categorized by NAEP as hard and by the researchers as requiring complex problem solving were analyzed for gender differences; effect sizes were found to average … a trivial difference. These findings provide further evidence that U.S. girls have now reached parity with boys, even in high school, and even for measures requiring complex problem solving.

Per Hyde’s references, the NAEP data she is using came from the National Assessment of Educational Progress (NAEP) (2008) The Nation’s Report Card. Available at http://nces.ed.gov/nationsreportcard/itmrls/startsearch.asp.

The interesting thing is that Hyde’s earlier work on exactly these issues was convincingly debunked by the statistician La Griffe du Lion back in December of last year:

Hyde et al. analyzed a huge database of standardized test data from state assessments mandated by the No Child Left Behind initiative (NCLB). Records from 10 states and 7 million students in grades 2 through 11 yielded a math gender gap of 0.0065 SD in favor of boys—trivial by any yardstick. For all intents and purposes there was no gender gap. “Our analysis shows that, for grades 2 to 11, the general population no longer shows a gender difference in math skills,” concluded the authors.

The problem here is one of sophism rather than error. Sex gaps favoring boys are not fully developed until the onset of puberty. In lower grades, math gaps are often non-existent or favor girls. By including data from the lower grades, Hyde’s estimate of the gap was much too low. The average gap in grades 2 through 8 was 0.0054 SD. Data from post-pubescent students in grades 9, 10 and 11 were an order of magnitude greater….

NCLB assessments, for example, are ill suited to the job of assessing the math gender gap. Rather, they are designed to assess whether a student has reached some minimum level of proficiency. None of the questions require complex problem solving skills—the domain where sex differences are most apparent. As a result, NCLB tests underestimate sex gaps. Hyde et al. addressed this issue by turning to the somewhat more difficult National Assessment of Educational Progress (NAEP) tests. There too, however, they could find no complex problems. They did manage to harvest some moderately difficult questions from the NAEP set, from which they obtained gender gaps of 0.07 SD and 0.05 SD in grades 12 and 8, respectively—both in favor of boys—and also an order of magnitude greater than the NCLB gaps reported for grades 2 through 11. None of this appeared in the paper’s conclusion or in post-publication publicity.

Uh, so these “moderately difficult questions” are what Begley characterizes as being “not multiplication calculations, not even second derivatives; they’re more like calculating the necessary relationship between N and epsilon for a uniform continuity proof”? Surely the questions haven’t changed that much in a year, to become so much more difficult, even accounting for the differences in perception of difficulty between La Griffe and Begley?

The only thing you can do in a situation like this is bite the bullet and purchase the original (2008) paper by Hyde, et al. (Two pages, $15, Highway Robbery.)
From which:

In all cases, the [NCLB] data represent the testing of all students attending school in that grade. These [ten] states are geographically diverse and appear to be representative of all 50 states insofar as their average scores on the National Assessment of Educational Progress (NAEP, a federal assessment that carefully samples students nationwide) match the average for all 50 states quite closely. For 8th-graders, the average NAEP mathematics score was 280.22 for our 10 states and 280.17 for all 50 states….

Greater male variance [in NCLB results] is indicated by VR > 1.0. All VRs, by state and grade, are > 1.0 [range 1.11 to 1.21....]. Thus, our analyses show greater male variability, although the discrepancy in variances is not large. Analyses by ethnicity show a similar pattern….

Hyde essentially repeats that (VR) paragraph in the 2009 paper.

For whites, the ratios of boys:girls scoring above the 95th percentile and 99th percentile are 1.45 and 2.06, respectively, and are similar to predictions from theoretical models. For Asian Americans, ratios are 1.09 and 0.91, respectively. Even at the 99th percentile, the gender ratio favoring males is small for whites and is reversed for Asian Americans. If a particular specialty required mathematical skills at the 99th percentile, and the gender ratio is 2.0, we would expect 67% men in the occupation and 33% women. Yet today, for example, Ph.D. programs in engineering average only about 15% women….

That paragraph, too, is essentially just repeated in the 2009 paper.

Today, with the gender gap erased in taking advanced math courses, does the gender gap remain in complex problem-solving? To answer this question, we coded test items from all states [on the NCLB data] where tests were available, using a four-level depth of knowledge framework. Level 1 (recall) includes recall of facts and performing simple algorithms. Level 2 (skill/concept) items require students to make decisions about how to approach a problem and typically ask students to estimate or compare information. Level 3 (strategic thinking) includes complex cognitive demands that require students to reason, plan, and use evidence. [Lofty goals, indeed, in a country that self-identifies as majority [78%] Christian, and 84% religious.] Level 4 (extended thinking) items require complex reasoning over an extended period of time and require students to connect ideas within or across content areas as they develop one among alternate approaches. We computed the percentage of items at levels 3 or 4 for each state for each grade, as an index of the extent to which the test tapped complex problem-solving. The results were disappointing. For most states and most grade levels, none of the items were at levels 3 or 4. Therefore, it was impossible to determine whether there was a gender difference in performance at levels 3 and 4….

To address this limitation in the state assessments, we returned to the NAEP data. [Reference: National Assessment of Educational Progress, http://nces.ed.gov/nationsreportcard/itmrls/startsearch.asp (2008).] NAEP categorizes items as easy, medium, or hard. We coded hard sample items for depth of knowledge. No items were at level 4 but many were at level 3.

Recall: Level 3 “includes complex cognitive demands that require students to reason, plan, and use evidence.” But there were no “Level 4″ questions, i.e., ones which required “complex reasoning over an extended period of time and require students to connect ideas within or across content areas as they develop one among alternate approaches.” So Hyde’s “complex problem solving” is not the same thing as the “complex reasoning” which would qualify a question as being level 4, even though they’ve confusingly/obfuscatingly decided to use “complex” in both of those categorizations. (Outside of the paper’s context, doesn’t “complex reasoning” sound like something you’d use in doing “complex problem solving”?)

Ach…. I weep for our children, when I reflect that this is what the American educational system is doing to them.

Of course, I’m Canadian, so they’re not actually screwing up my children (of which there are, thankfully, none anyway). But you know what? When I was in grade 12, we (i.e., the rural Hanover school division south of Winnipeg) were so poor (“How poor were we?”) we were so poor that we couldn’t even afford up-to-date textbooks. So the math text I used in my graduating year was published in 1964, a couple of years before I was even born.

Those of you who understand what it means to have learned from a curriculum that was created before all the dumbing-down of the educational system occurred, even (to a lesser degree) here in the Great White North, are now turning green with envy. Don’t you wish your kids could learn in that kind of environment? Alas, you’ve thrown it all away, as part of the “long march through the institutions,” guaranteed to make everything “fair” for every blank-slate person of color, creed, language, and gender. You damned fools.

We computed the magnitude of gender differences on the hard items that were at level 3 depth of knowledge. At grade 12, effect sizes for these items ranged between 0 and 0.15 (average d = 0.07). At grade 8, effect sizes for these items ranged between 0 and 0.08 (average d = 0.05). Thus, even for difficult items requiring substantial depth of knowledge [but no actual "complex reasoning over an extended period of time" or "connect[ing of] ideas within or across content areas”], gender differences were still quite small.

So yes, it’s NAEP there too, with no level-4 questions at all to truly “separate the men from the boys” … and from the girls.

In fact, a closer inspection shows that the 2009 paper includes no new research in the area of the “math gap,” but is instead simply quoting the 2008 study’s results! (That is, the 2008 study done by the same lead author.) And it gets served up as “news,” for closing the gap, by the “useful idiot” Sharon Begley at Newsweek!

I had originally figured that they’d at least be using different (annual) data sets. In that case, the grade 12 girls of 2009 would have been the grade 11 girls of 2008, etc., … and had equally figured that the latter were behind the grade 11 boys in math skills, even on the NAEP tests, by somewhere between the 0.07 and 0.05 standard deviations (for that year’s grade 12 and 8, respectively), as measured by Hyde herself. And now (I thought to myself, incredulously) the very same girls have caught up, in the year since then?

But, of course, it wasn’t even that “complex.” It was just Hyde and Begley re-heating old (invalid) results, and presenting them as something new.

As long as there’s a math-sex gap in the SATs for people scoring above 750 on the math portion, there is a gap at the high-proficiency end in grade 12, too. When that (SAT) gap vanishes, without dumbing the test down further, you’ll have a reason to get excited. Until then, not so much. (Note: The odds of that actually happening are near-zero.)

And the thing is, if they have to fudge around like this to get the answers they want/need to hear—with Begley disingenuously claiming that Hyde’s regurgitated study data relate to “the highest level of math achievement,” for example—you know (yes, you do) that the real answers in the objective universe are exactly the opposite of what they want and need to hear. ‘Cause they wouldn’t have to fake it, if it was real.

Hyde, 2009:

Some studies have focused specifically on the mathematically talented. The best known example is the Study of Mathematically Precocious Youth (SMPY) or Study of Exceptional Talent (SET), an ongoing study originally begun at The Johns Hopkins University in the 1970s. These researchers administer the SAT to children <13 years of age who have been identified as mathematically advanced. Their sample is voluntary, and the sampling frame is not well defined. It has also changed over time with respect to sample size and ethnicity, including large numbers of children of immigrants from Eastern Europe and Asia in recent years. In 1980–1982, they reported a very lopsided M:F ratio of 13:1 among students scoring >= 700 on the quantitative section of the examination. However, here too, the gender gap has dramatically narrowed with time. The M:F ratio was down to 2.8:1 by 2005. Thus, females now represent at least 1/4 of the mathematically precocious youth being identified in this U.S. talent search. This fairly rapid and dramatic change occurred coincident with enactment of Title IX [in 1972], the second wave of the women’s
movement, and greatly increased immigration of Eastern Europeans and Asians to the U.S….

Yes, and what else has changed, in that area, since the early ’80s? That’s right: The SATs have been repeatedly dumbed-down, even in the “quantitative section.” Observe:

Anecdotally, I can tell you that the test has definitely and drastically been dumbed-down over the last 30 years…. my brother is 13 years older than I am and took the test in 1975, scoring about 1200. I have a cousin who is a senior in high school and recently scored a 1440 on the math/verbal component (not including the essay). I had occasion to look at my brother’s old SAT prep book and compare it to my cousin’s current edition. Long story short… the two tests are not even in the same ballpark. It’s as if the new version is designed for people who are 3 or 4 years younger (junior high). This is particularly noticeable in the math section which on the current test seldom rises above intermediate level Algebra and Geometry. The older tests made numerous forays into Differential Calculus, vector analysis, sophisticated Trigonometry, etc.

It’s just as bad in the non-math sections:

First, after three decades of falling SAT scores (i.e., of the American public getting dumber and fatter, not necessarily in that order), in 1994 the test was “re-normalized” to an average score of 500.

In recent years, SAT scores have again been rising. Why? In 2005, verbal analogies were scaled back significantly so as not to discriminate against ESL minorities, and quantitative comparisons were removed from the math section. The same year, an Essay component was introduced, in which there was no penalty for factual errors, and where the grade awarded was basically proportional to the length of the essay delivered!

So a 700 (math) now doesn’t mean what it did in the early ’80s. That is, Hyde is comparing apples and oranges. Because:

[T]here has been a deterioration in the quality of education. This deterioration precludes any comparison because if one dumbs down math beyond a certain point, eventually the innate differential advantage of boys will be untapped and thus invisible. [That is why the ratio of high-scoring boys to girls on the SATs has dropped markedly since the early '80s: It's a simple artifact of the test being drastically dumbed down.] It is probable that what are considered grade [i.e., level] 3 and 4 questions today are really the grade 2 questions of 20 years ago…..

And yes, it is no coincidence that Title IX has been a major force in that “improvement” of girls’ scores, simply because the only way to get women and non-Asian minorities to score comparable to white men in the upper end of the distribution on tests of real math/science ability is to dumb the tests down to the point where there’s “no room left to excel.” If you did a similar thing to English/Reading tests, you could equally “improve” the performance of boys relative to girls, there, and thus reduce the “English gap,” which has always favored girls (and will continue to do so).

Hyde can’t admit any of that, of course. But regardless, if she’s doing research in this area and doesn’t already know about the SAT re-normalization and dumbing-down, she’s not academically, er, “fit” to be publishing, much less as a lead author; if she knows about it and is deliberately leaving it un-mentioned to further her thesis, she’s academically dishonest; if she just forgot, she’s garden-variety bumbling. Take your pick. Either way, what the hell were the referees for the 2009 paper thinking, to let that slide?

Back to La Griffe:

A persistent sex gap favoring boys in the math SAT is a gap buster’s nightmare. At odds with the claim of a nonexistent math gap, Hyde et al. needed to address this matter [concluding that "The gender gap is likely in large part a sampling artifact"]….

By making use of the Colorado and Illinois ACT data we can estimate the effect of sampling error. In 2007, the gender gap nationally on the math ACT was 0.21 SD. The same year in Colorado and Illinois, absent sampling error, the gaps were 0.13 SD and 0.16 SD, respectively. The difference between the national and full-cohort gaps is the contribution of sampling error to the math gap. Thus, “largely an artifact of sampling” means that sampling errors caused the gender gap to be overestimated by approximately 0.05 to 0.08 SD, leaving behind a generous gap of between 0.13 and 0.16 SD, remarkably close to those we shall presently reveal. Sampling error not withstanding, the math gap proves durable….

Luigi Guiso, Ferdinando Monte, Paola Sapienza and Luigi Zingales concluded that the sex gap in mathematics is cultural in origin and therefore erasable. In fact, they maintain, it has already been erased in a few gender-neutral countries. These conclusions were drawn from correlations between gap sizes and measures of women’s emancipation, or, as they put it, gender neutrality. Guiso et al. also looked at the effect of gender neutrality on the reading-comprehension gap where women enjoy a substantial advantage. They summarized their findings writing: “In more gender-equal cultures the math gender gap disappears and the reading gender gap becomes larger”….

In the three years between PISA [Program for International Student Assessment] 2003 and PISA 2006, Iceland, Korea, Macao-China and the Netherlands, outliers in 2003, migrated sharply back into the mainstream of performance…. The Czech Republic moved in the other direction away from prediction. None of the swings was accompanied by a corresponding change in gender neutrality. They are statistical fluctuations whose size warns against overinterpreting data from a single PISA year….

Each country that took part in both PISA years, 2003 and 2006, contributed a single point to the plot giving its gender math gap in both years. Not only do the points not lie on a straight line of unit slope, but excluding the outlier Iceland, there is no relation whatsoever between the gaps observed in 2003 and 2006 (r = 0.0006). The graph is nothing more than a plot of statistical noise….

[footnote: Icelandic girls performed anomalously well in both PISA 2003 and 2006. A more detailed look at Icelandic data, however, reveals that only in rural Iceland were girls' mean scores higher than boys'. In the Reykjavik metropolitan area the math performance of girls and boys was much like that found in other countries. No satisfactory explanation of the Icelandic anomaly has yet been put forth.]

Both tests confirm a single math-ability gender gap independent of country, and by implication of race and culture….

National mathematical ability and national ability of men correlate at r = 1.00. Both are excellent proxies for national intelligence. PISA math means correlate at r = 0.85 with the Lynn and Vanhanen compilation of national IQ, while PISA means of males correlate even higher at r = 0.87. One could even argue that PISA means, whether national or male, better assess national intelligence than do the IQs derived by Lynn and Vanhanen from often sketchy data and dubious assumptions based on the Flynn effect. (Alternatively, one could take these correlations as evidence in support of the L and V compilation.)….

In brief, we have seen … that the gender gap in mathematics has been stable for at least half a century; that sex differences in ability-distribution means and variance ratio are independent of race, culture and geography; that female math performance is closest to that of males in high-IQ countries; [and] that culture plays a role in math performance, albeit small….

I have no vested interested in boys being better at math than girls, at any level; on the contrary, smart girls are sexy. But I also can’t stand being lied to by the “PC Police” and their enablers … or by anyone else (including idiots who won’t accept that a vegetarian/vegan diet can be perfectly healthy—even for world-class athletes—regardless of how much you debunk their cherished, carnivorous, magical-thinking notions).

Further, as far as how many girls East Germany vs. West Germany were “regularly sen[ding]” to the International Mathematical Olympiad, etc., it turns out that Begley got those numbers from pages 4-5 of Hyde’s 2009 paper, as follows:

[T]he U.S. had zero females on its teams throughout the first 23 IMOs in which it participated, finally having 3 females on 5 of its teams during the past 11 years. Likewise, the United Kingdom fielded only 1 female on its teams from 1967 to 1988, yet has had 10 different females on its teams during the past 2 decades, with several participating more than once. During the 13-year period immediately before reunification, the German Democratic Republic had 5 females on its teams, whereas West Germany had zero. Since partitioning, Slovakia has fielded 3 times as many females on its teams as has the Czech Republic. During the past decade, the Republic of Korea has had 6 female participants versus Japan’s zero. Such large differences among genetically related populations and rapid changes over time within countries in the frequency of identification of females with extreme talent in mathematical problem solving cannot be primarily due to biological factors.

The thing about “common gene pools,” however, is all Begley’s.

So then consider this: “Korea topped Japan by 6 to 0.” But while both of those are in the “top 12″ of PISA-scoring countries, Korea actually has a slightly lower World Economic Forum Gender Gap Index (0.6157 vs. 0.6447) than does Japan. (Higher is better, in terms of female emancipation, etc.; Sweden, for example, is 0.81, while Yemen is 0.45.) So the 6-to-0 ratio between countries with a “common gene pool” is exactly in the opposite direction of what it should be if the greater number of girls sent by Korea was the product of negative “social and other environmental forces” directed toward young females, and rather wildly so. (In terms of the disparity, not the girls-gone-wild. Anyway….)

So that ratio is either a statistical fluctuation, or it’s one data-point of disproof for Begley’s ideas; either way, it doesn’t support her thesis, so she was dumb to quote it. And it quite probably encapsulates the depth of thinking and research she’s even capable of doing.

La Griffe du Lion:

Of the 26 percent [of college graduates] that proceeded to the doctoral level, men entered math-intensive fields at five times the rate of women. Women frequently chose careers in the life sciences and medicine, as well as in the social sciences, arts and humanities. If we incorporate this proclivity factor of 5 into the rank-order calculation, the ceiling on tenured women faculty in math-intensive fields at research institutions drops to between 4% and 6%. In elite departments, say the top five, the ceiling will be lower still….

Or, like “mathgirl” says:

Results in science are not only about abilities. You can be very good at something, but just not that interested (and choose biology or medicine over math, for example). Scientific achievement at 40 is not perfectly correlated with grades at the graduate or undergraduate level at all. And the “extremes of math ability” as manifested by the number of math professors is not 1% of population, it is much much less, so drawing conclusions on the basis of school results is similar to describing the properties of 10 karat blue diamonds by looking at large pool of standard 1-karat ones.

Oddly enough, that’s a point Larry Summers brought up, too:

[I]f one is talking about physicists at a top twenty-five research university, one is not talking about people who are two standard deviations above the mean…. [I]t’s talking about people who are three and a half, four standard deviations above the mean in the one in 5,000, one in 10,000 class. Even small differences in the standard deviation will translate into very large differences in the available pool substantially out.

Hyde actually quoted exactly those figures, in her current paper (p. 2 of the 7-page PDF), while otherwise focusing on 99th percentile values for boy:girl comparison. The gloss that the 99th percentile has any relation to “math geniuses” is thus much more the product of Begley’s mangling of the study and garbled writing (and thinking, one assumes) style, than it is Hyde’s error. (I am serious about “garbled”: When Begley writes that “Slovakia sent more girls by a margin of 3-to-1,” Hyde’s paper itself is clear that the implied “than” relates to the Czech Republic; Begley’s isn’t, and instead leaves one wondering whether it’s a 3:1 ratio of girls to boys.)

There’s also this debunking of Hyde’s earlier paper:

Hyde herself offers a conceivable but not straightforward interpretation of [the SAT math-sex gap]—one that she chose not to apply in other cases….

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….

[T]heir 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)…. But Hyde et al. were very careful that this particular result didn’t get into the media….

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….

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….

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 [in two years] 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….

[T]he 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% [of girls] 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….

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!). [Plus, her second Nobel prize was actually just given in sympathy for the same work as the first but in a different field, over the fact that her name was getting dragged through the mud/newspapers for having an affair with a married Frenchman. You see, chivalry isn't dead, it's alive and living in Stockholm.] 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.

The asserted “30% of girls” on losing teams may be contrasted with Hyde’s 2009 paper, regarding the composition of the International Mathematical Olympiad teams:

Table 4 indicates the percentages of students on IMO teams who were female during the past 3 decades for countries whose teams achieved a median rank among the top 30 in recent years. Some of these high-ranked countries (e.g., Russia, Serbia) had >20% female team members during some decades, a number that should be considered a lower bound on the percentage of the population with profound intrinsic aptitude for mathematics who are female.

I don’t think that last sentence makes sense: In no way does 20% of the female (or male) population have “profound intrinsic aptitude for mathematics,” at a 99th-percentile-plus level. By friggin’ definition, the top 20% of the population is at or above 80th percentile, and there’s nothing “profound” about that. But regardless, the only teams with greater than 20% girls on their above-median iterations were: USSR/Russian Fed. (1989-1998), and Yugoslavia/Serbia (1999-2008). Rep. of Moldova (1989-1998), Hong King (1978-1988), and People’s Rep. of China (1978-1988) were above 15%; the rest of the 30 countries by three periods were below that, usually well below 10%.

To know exactly what Hyde’s “Table 4″ implies, you’d need to know whether the percentage of girls on teams below the median rank was lower or (as is more likely) higher than the figures she’s presented. That is, are the girls raising the game of the teams they’re on, or is ~22% females (i.e., one or [rarely] two per six-person team) the maximum that a team can carry, and still be competitive? As usual, Hyde’s obfuscating “damned lies and tables” give no indication.

No one with even half a clue would dispute that there are indeed women who can do mathematics at the highest level. But that’s very different from the “equal outcomes for women as for men” that people like Hyde and Begley are insisting on. As a sobering thought, La Griffe du Lion calculated, based on the differences in variability between men and women, that one should expect a female Fields Medal winner to surface once every 103 years.

Hyde again, from 2009:

Guiso and colleagues, using 2003 PISA data testing 15-year-olds from 40 countries, found that gender inequality as measured by the World Economic Forum’s Gender Gap Index (GGI) significantly correlated with the magnitude of the mean math gender gap.

Of course, La Griffe already debunked that study … back in December of 2008. Quite presciently, seeing as it wasn’t even mentioned in Hyde’s 2008 paper!

There’s also this for additional thoughts, debunking Hyde’s year-old work:

[T]hey cannot make any conclusions regarding the alleged “improvement” in girls vs. boys because the level of deterioration has affected boys MUCH more than girls….

They completely gloss over the sample size of Asians which is only 219 (compared to 3473 for whites) and also the fact that they have cherry-picked Minnesota to represent the whole U.S.

Finally, there’s this from Hyde’s 2009 study:

Penner has performed a detailed analysis of the distributions of math scores obtained by boys compared with girls in each country that participated in the 1995 TIMSS. [Reference: Penner AM (2008) Gender differences in extreme mathematical achievement: An international perspective on biological and social factors. Am J Sociology 114:S138–S170.] Striking was his finding of considerable country-to-country variation, not only in the magnitude of the difference between mean male and female scores, but also in the shapes of the distributions, ratios of males-to-females scoring in the right and left tails of the distributions, and difference in standard deviation (SD) between males and females. We have normalized these latter differences to overall within SD for each country…. Notable is the fact that numerous countries had a normalized SD difference that was insignificantly different from zero [i.e., the same variability among girls as among boys], with 3 [Germany, Lithuania, and the Netherlands] even having a negative value, that is, greater female variability. Neither the 10th-grade 2003 PISA nor 12th-grade 1995 TIMSS data gave any indication of greater male variability in mathematics for either Denmark or the Netherlands. As Penner concluded, “The common assumption that males have greater variance in mathematics achievement is not universally true.” Given the absence of universality, the occurrence of greater male variability and scarcity of top-scoring females in many, but not all, countries and ethnic groups must be largely due to changeable sociocultural factors, not immutable, innate biological differences between the sexes.

I don’t know what the “debunking” response to that might be. But you could get a greater female variability if you had a lot of really, really stupid girls, perhaps brought into the country by immigration. Say, girls from cultures where there already wasn’t a really high average IQ, but the boys were still encouraged to learn in school, while the girls are encouraged to just become baby machines, so their education won’t matter in the long run anyway.

Hmm, what are the Muslim immigration/population figures for Germany, Lithuania, and the Netherlands, then…? (Answer: 3.3 million Muslims in Germany, out of 82 million people; a mere 3000 in Lithuania, out of 3.4 million; and 950,000 out of 16.5 million in the Netherlands.)

Well, it’s gotta be something like that, where immigration and/or dysgenics are skewing the dumbfuck end of the girls’ distribution downward, more than they’re doing it for the boys.

Also, more boys drop out before completing high school than do girls, for any race (and probably for any religion, too). So that loss of the male “bottom-end,” too, increases the girls’ variability relative to the original boys’, as the high-school years pass: even utterly stupid and unmotivated people can complete grade 4, but less so for the higher years, where it’s increasingly a self-selected group, thus having potential selection biases.

When you consider that the 1995 TIMSS assessment included grades 4, 8, and the final year of high school, you begin to hope that Penner took all of that into account, eh? ‘Cause the dropout rate and attitude toward female education even for those girls who stay in school could seriously warp his calculated variabilities for the kids who are still attending classes, which is the only place they’d get tested, right?

Oddly, TIMMS was done in 40+ countries in both 1995 and 2007 … and also in 1999 and 2003 (data released December 14, 2004) … and Penner’s paper was published in 2008 … yet he uses the 1995 data. Why? The data is collected and available online every four years!

Something does not smell right, there: Why use 13-year-old data when you could just as easily use numbers that are only half a decade old?

So, “Even the most hidebound male chauvinists have been forced to admit that girls are as good at math as boys, on average”? Unfortunately not, Toots. If you were thinking clearly, rather than demanding that reality fit into what you’ve a priori decided it must be in order for it to be acceptable to you, you’d already know that.

And, “A new study comes as close to burying [the stereotype that females lack the innate ability to match males in math] as anything yet”? Well, in the words of Weird Al Yankovic, “Close, But No Cigar.”

P.S. Impressed by the Harlem Miracle, which purported to eliminate the achievement gap between white and black students? Don’t be: Teaching to the Test.

P.P.S. OMFG, Kaki King rocks out to “Pink Noise”.

See, there’s also a “guitar gap,” where it’s rare to find “guitar goddesses” among the “guitar gods.” But as Kaki and Marnie Stern demonstrate … OMFG!

I remember reading, years ago in Keyboard magazine, a letter to the editor in response to one of the contributors to the mag having basically attributed a greater appreciation for complex time-signatures, etc., to testosterone or XY chromosomes, in the context of guys liking art/prog rock more than girls typically do. The letter related the story of a very talented female drummer, who had quit Berklee just because of the harassment she had to deal with from the guys there.

So I realize it’s not just talent, and not just practice, and that there is value in things like girl-only music/band schools, where aspiring rock-ettes can do more than just make sandwiches for their boyfriends while the latter practice.

That doesn’t make stuff like those “band camps,” or Lilith Fair, any less sexist. (If you can’t admit that a school or festival that excludes male solo performers and male-majority bands is sexist, you’re an idiot: by definition they’re sexist. But then, we live in a world where criticizing Oprah for giving bad medical advice (e.g., anti-MMR) is probably “racist,” so what the hell do you expect?) But it does sort of explain and excuse why they exist. Sometimes.

‘Cause in my “perfect world,” every girl would be a math genius … and a guitar goddess.