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Meritocracy: Dangerous Cancer Statistics

About the only detailed public criticism of my Meritocracy [1] article by an academic has come from Prof. Janet Mertz, a Wisconsin cancer researcher.  Since her analysis draws so heavily upon her own 2008 academic paper on top performing math students [2], I decided that paper warranted a close examination.

The primary focus of her article was a worldwide gender analysis of top performing math students aimed at refuting the controversial speculations of former Harvard President Larry Summers [3], who had suggested that men might be better at math than women, at least at the very high end of math ability.  She and her co-authors therefore examined the previous twenty years of the International Math Olympiad, determining the exact number of male and female participants from all the leading countries.  They provided their findings in Table 6 (p. 1252), which I am summarizing below in terms of the male percentages for the aggregate years 1988-2008:

ASIA:
China, 96% male
India, 97% male
Iran, 98% male
Israel, 98% male
Japan, 98% male
Kazakhstan, 99% male
South Korea, 93% male
Taiwan, 95% male
Turkey, 96% male
Vietnam, 97% male

EUROPE:
Belarus, 94% male
Bulgaria, 91% male
Czech Republic, 96% male
Slovakia, 88% male
France 97% male
Germany, 94% male
Hungary, 94% male
Poland, 99% male
Romania, 94% male
Russia/USSR, 88% male
Serbia and Montenegro, 80% male
Ukraine, 93% male
United Kingdom, 93% male

OTHER
Australia, 94% male
Brazil, 96% male
Canada, 90% male
USA, 96% male

INTERNATIONAL AVERAGE, 94.4% male

Now to an untutored eye such as my own, Mertz’s discovery that the top math students of virtually every country have been around 95% male for decades might seem to somewhat confirm rather than refute the distasteful speculations of President Summers; but Mertz had a very different perspective.  Surrounding these basic quantitative facts by 10,000 words of often complex verbiage, she concluded that math performance differences between males and females were overwhelmingly due to culture rather biology, and that at the very high end, women had just as much math ability as men.

She later cited these same research results to support her equal-ability gender claims in subsequent published papers, with her most recent 2012 paper bearing the descriptive title “Debunking Myths about Gender and Mathematics Performance.” [4]  Most importantly, she claimed in her media interviews [5] that her research had demonstrated that men and women had equal innate ability in mathematics, and that any current differences in performance were due to culture or bias.  Therefore, the press reported that Mertz and her allies had proven Summers wrong, and women had just as much talent in math as men.

 

One obvious possibility was that I was missing something in Mertz’s research, and somehow misunderstanding her apparent result that 95% of all top math students have always been male and just 5% female.   Perhaps a careful researcher such as Mertz was correct and I was just failing to comprehend her analysis.  Fortunately, there are others with far greater statistical expertise, much better able to judge such matters.

Consider, for example, Prof. Andrew Gelman, an award-winning Ivy League statistics professor.  Over the last month or so, Prof. Gelman has heavily promoted Prof. Mertz’s research on his blogsite [6], repeatedly pointing to her strong academic credentials in sharp contrast to what he describes as my own background as a “political activist” with “sloppy” research methods.

I therefore dropped Prof. Gelman a respectful note, asking him what he thought of the conclusions that Prof. Mertz drew from her 2008 paper, and whether they seemed warranted by her underlying data.  He replied that he had merely “skimmed” her paper and had no particular opinion on whether she was right or wrong.  With his permission, I am publishing our brief exchange [7].

Although I am certainly pleased that Gelman now seems to be backpedaling from his criticism of my work—he argues that “sloppy” was never meant to be an insulting adjective—I really wonder what this indicates about his own scholarly methods.  After all, not only had he written four or five separate columns and numerous comments—probably totaling over 15,000 words—promoting Mertz, but he had also repeatedly cited or linked to her 2008 paper.  Shouldn’t he have actually *read* rather than merely “skimmed” her paper and even investigated her use of statistics before he repeatedly used it to denounce my own research?  Perhaps this raises questions about whether he bothered reading my own article before criticizing it.  One suspects that something more than mere dispassionate scholarly interest explains the rapidity with which Gelman wholeheartedly endorsed Mertz’s accusations without apparently bothering to investigate them.

We must ask ourselves what it means for our society when an academic such as Mertz can determine that 95% of all top math students have always been male and then immediately announce that she has proven that men and women have equal mathematical ability at the high end, thereby producing headlines in Science Daily [8] and on popular websites [9].  Mertz may simply be an agitated ideologue, but those lazy or biased journalists who eagerly promote her absurd claims are just as guilty, and that goes double for seemingly-reputable academics such as Prof. Gelman who lend their names [10] to similar nonsense.

I suspect that Mertz’s tendency to wildly mischaracterize statistical data is confined to her ideological math-feminism and similar matters, but perhaps that I am mistaken.  Her field of professional expertise is cancer research, in which misuse of statistics may have life-or-death consequences.

Suppose Mertz had conducted a study of two different cancer treatments, tested in trials across two dozen countries around the world.  Suppose also the patient death rate for one of those treatments averaged twenty times greater than the other, with the death ratio for nearly all the countries falling in the range between 15-to-1 and 50-to-1.  If Mertz then summarized her results by reporting that the two cancer treatments seemed very similar in effectiveness, there might be very serious consequences for human health.  I do hope that someone of Prof. Gelman’s statistical expertise is keeping close watch to ensure that Mertz’s statistical misfortunes are confined solely to ideological matters and do not contaminate her life-determining medical research.

 

Finally, on a different matter, NYT columnist David Brooks had been so surprised and impressed with some of my findings that he gave my article a “Sidney award” as among the best of the year [11]. One of my findings had been the collapse of Jewish academic achievement in recent decades, and I had speculated that the exponential growth of the academically unimpressive ultra-Orthodox community might be a major reason. Brooks has now investigated this “Orthodox Surge” [12] in greater detail, and written a column about it.

I also yesterday participated in a well-attended DC Aspen Institute panel on raising the minimum wage.  More about that in a future column.

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#1 Comment By oval On March 16, 2013 @ 11:19 am

Again you fail to adress the issue which gelman and mertz raised, which is your faulty stats on jewish acedemic performance and overrepresentation. you weazel away from the main point by critisizing mertz based on something unrelated to the issue of your faulty stats.

#2 Comment By Johann On March 16, 2013 @ 12:03 pm

When I attended University many years ago, the left of center slant on reality mostly resided in the non-science, non-engineering departments. Its disturbing that we are now seeing science distorted by ideology.

#3 Comment By William Dalton On March 16, 2013 @ 2:58 pm

It is certainly possible that a 95-5 ratio of men to women in the top echelons of Math may be the consequence of cultural attitudes that transcend all world cultures, rather than any inherent differences between women and men, but what evidence did Prof. Mertz offer that this is the case? Can you construct a test that would rule out the factor of cultural bias and all parties to the debate be bound to recognize only one conclusion can then be derived from the results, depending on its outcome?

#4 Comment By Gaeranee On March 16, 2013 @ 3:14 pm

Ditto William Dalton. I would guess that not just in the area of mathematics, there is a higher ratio of men to women at the very top of many other fields as well – science, social sciences, culinary, fashion…. Show me one society were women are the dominant ones in the society – economically, politcally, socially, culturally. I can’t think of any. That is because until recently, physical brawn mattered socio-economically. Even now, when it counts less, gender discrimination has been institutionalized so women still aren’t considered equal. But give it maybe a thousand years.

That being said, I agree with Unz that Mertz’ conclusion appears unsupported. And while we’re on this subject, why did Mertz not count in the Asian-American category a biracial Math Olympiad student with an Asian-American surname? Does half Asian mean that one isn’t Asian-American? And if that’s the case, did she similarly exclude from the Jewish category half Jews with Jewish surnames?

#5 Comment By RH On March 16, 2013 @ 3:41 pm

“It is certainly possible that a 95-5 ratio of men to women in the top echelons of Math may be the consequence of cultural attitudes that transcend all world cultures,”

If there were cultural attitudes that transcend all the world’s cultures, where besides human nature would they come from?

#6 Comment By Jolly Ole On March 16, 2013 @ 4:14 pm

Its disturbing that we are now seeing science distorted by ideology.

Would that it were only “now”. Science has always been subject to ideological drivers. It’s dangerous to think otherwise. And phrenology, Nazi genetic theory and Lysenkoist biology are not the sum total of ideologically driven science.

#7 Comment By NB On March 16, 2013 @ 4:34 pm

You continue to claim that there has been a collapse of Jewish academic achievement in recent decades. Now that it’s been established that Jews represent at least 13% of US IMO team members from 2000-12, where is this evidence of a collapse of Jewish academic achievement?

The ratio of Jews to non-Jewish whites among US IMO participants (1:2-3) has scarcely changed over the decades, despite that Jews represent a declining %age of the US population. What has changed is the massive overrepresentation of Asian-Americans at the highest levels of HS math and science academic achievement, so what we’re actually seeing is a decline of white academic achievement in HS math and science competitions vs Asian-Americans.

I’d also like to note that you seem happy to engage in polemics with Prof. Gelman via email but ignore my dry inquiries asking for clarification as to how you performed Weyl Analysis.

#8 Comment By NB On March 16, 2013 @ 5:24 pm

I’d like to separately address Prof. Mertz’s academic work on the representation of women in mathematics. Once again, Unz is misrepresenting Prof. Mertz’s work. In particular, I highly recommend that readers look at Table 5 (p. 1252):
[2]
From 1977 to 1990, the East German IMO team had 5 girls (at least one of whom was a gold medalist), while the West German IMO team had none. This represents a significant disparity between two nations that were comprised of the same ethnicity and suggests the significance of sociocultural factors in the absence of girls on the West German IMO team.

The US IMO team did not have a female member until 1998. i.e. for over 2 decades, there were zero girls on the US IMO team, even though the USSR had had female gold medalists at the IMO in 1962, 1976, 1985, etc. The UK first had a female IMO team member in 1983, 15 years before the US. The US did not have a female gold medalist until 2004, while the UK had had 2 female gold medalists at least 10 years prior. From 1998 to present, girls have represented 6% of US IMO participants. Clearly, this change is not due to genetics but rather sociocultural factors. Prof. Mertz is simply demonstrating the importance of sociocultural factors in assessing the under-representation of women at the highest levels of mathematics.

#9 Comment By Janet Mertz On March 16, 2013 @ 6:16 pm

William Dalton says:
“It is certainly possible that a 95-5 ratio of men to women in the top echelons of Math may be the consequence of cultural attitudes that transcend all world cultures, rather than any inherent differences between women and men, but what evidence did Prof. Mertz offer that this is the case?”

Unz is, yet again, in his March 16th post pre-selecting the data that agree with the claims he desires to draw, while ignoring all of the other data that disprove his claims. He did this with his “Meritocracy” article, and he is doing it again with my 2008 and 2012 Notices articles. This is not the way proper science is done.

In my 2008 article, I show quite clearly that large differences exist among countries in the frequency with which girls qualify for membership on their country’s IMO team. For example, prior to reunification, West Germany had NEVER had a female on their IMO team. On the other hand, East Germany had numerous girls, with their names listed in one of my tables in this article. Both countries had an average rank of ~7th in the IMO in the 1980s. East and West Germans were genetically essentially identical. Thus, the most likely explanation for the failure of West Germany to have identified outstanding female mathematicians is sociocultural factors that differed between it and East Germany. One plausible difference was accessibility of child care, plentiful in East Germany when it was a communist country yet almost non-existent in West Germany; East German women were expected to work full-time while West German women were expected to stay home to care for their children once they became mothers. Thus, East German girls grew up with different career dreams and expectations than their West German counterpoints. West Germany had 2% of their tenured math professors at universities being female in the 1980s. Communist Eastern European countries averaged ~25% of their tenured math professors being female in the late 20th century. Harvard University had zero female tenured math research professors from 1636 until 2006! This is one example of how sociocultural factors can strongly influence the identification of females who excel in mathematics.

In my 2012 article, I go on to show that a strong correlation exists between % girls on a country’s IMO teams and its gender equity index. It’s NOT true that all countries have ~5% girls on their teams. The US had ZERO girls on its teams until 1998, while some countries have had girls on their teams throughout the past 1/2 century. In the 1950s and 1960s, only 5% of math Ph.D.s awarded to US citizens went to women; in the 2000s, ~30% did. Humans don’t evolve this quickly. These large differences and fairly rapid changes must be largely due to sociocultural differences and changes.

I also show in this latter article that some countries do not show greater male variance in their distribution of scores in math performance; in some countries, the boys and girls distributions are essentially coincident. If greater male variance in math performance were primarily due to an innate biologically determined difference between the sexes as suggested by Larry Summers, such countries should not exist.

Lastly, I have NEVER claimed that innate differences between male and females in math ability at the very high end don’t exist. Rather, what I have claimed based upon my data is that much of the difference in math performance, where it exists, is due to a variety of sociocultural factors that vary among countries. As long as these sociocultural factors remain, one can’t measure the size, if any, of the remaining difference that could be due to differences in “intrinsic aptitude” between the sexes.

I have published ~80 peer-reviewed primary scientific articles over my 4-decade career as a research scientist. NOBODY, including Unz, has ever claimed ANY of the data I have reported in these dozens in articles was in error. It is fine to agree to disagree on how to interpret data. However, it is crucial for the progress of science that published data are error-free. When errors are identified, the onus is on the author to publish a “correction” so wrong data do not contaminate the literature. In his “Meritocracy” article, Unz clearly published data that contain significant errors due to his direct inspection method being highly inaccurate and imprecise. It is long past due for him to acknowledge this methodological problem with this study and to correct his erroneous data. I look forward to his doing so soon and requesting that David Brooks do likewise.

p.s. If Unz has Googled me, he would know I am a basic research scientist, not a clinician. The only vertebrates on which I have ever performed experiments (in very small numbers) are frogs, mice, and rabbits. As a Ph.D. biochemist, most of my work in cancer research involves test tubes and petri dishes. Why would Unz “Suppose Mertz had conducted a study of two different cancer treatments, tested in trials across two dozen countries around the world”? I’m not going to bother responding to such irrelevant suppositions given nobody has ever questioned the quality of any of my published data or statistics.

#10 Comment By Janet Mertz On March 16, 2013 @ 6:27 pm

Gaeranee says:
” Why did Mertz not count in the Asian-American category a biracial Math Olympiad student with an Asian-American surname? Does half Asian mean that one isn’t Asian-American? And if that’s the case, did she similarly exclude from the Jewish category half Jews with Jewish surnames?”

If one reads my articles very carefully, you will see that I always clearly indicate when I am counting bi-racial and bi-ethnic students as the minority race/ethnicity and when I am counting them proportionally for each of these races/ethnicities. Yes, there are biracial Asian-whites in my data just like there are bi-ethic Jews-Gentiles. I have never knowingly mis-counted a bi-racial Asian-white as solely white, regardless of whether their surname is Asian or not.

#11 Comment By KatherineW On March 16, 2013 @ 7:44 pm

Mr. Unz,

You compare statistics on participants in a math contest to tests of anti-cancer drugs. However, the nature of drug testing is that it requires controlled trials in which one group is given the drug and the other is not (or is given a placebo), with the purpose of ensuring that factors other than the drug do not confuse the results of the trial.

The absolute absence of that in everyday life is why we cannot look at statistics showing that people of a given gender (or other group) tend to do better or worse than another in some area, and immediately attribute that to inherent biological differences. Being a woman doesn’t solely mean that you’re biologically female; it means there are all kinds of social expectations and presumptions that influence you. There have been multiple scientific studies showing that people perform worse when they are expected to perform worse. If girls hear that girls are bad at math, they are not only less likely to pursue math as an area of interest, but less likely to perform well in it.

Moreover, referring to statistics on participation in an international event is even less reliable as a measure of sex-based ability in math, because it is also influenced by things like who gets financing to go to such conferences, which is also likely to not be gender-neutral.

In short – being a woman or a man is a social as well as a biological quality, so differences between women’s and men’s achievements in some area cannot automatically be attributed to sex. (It is, incidentally, even more egregious when people draw similar conclusions about ‘innate ability’ on racial lines, since race is not a genetic quality to any meaningful degree.)

I am interested in whether there are biological factors affecting male and female academic performance, but in order for someone to prove that – or even make any scientific argument relating to it – they have to actually look at biological factors. If someone can find a gene on the X or Y chromosome which produces a protein that causes a demonstrable effect on academic ability in some way, then I will be very interested in that finding. But shallow examination of statistics cannot prove any difference between the innate capacities of men and women in any subject.

This seems very simple and obvious to me, from a scientific background, so I am surprised that anyone could fail to grasp such a basic point and still regard themselves as having something valuable to say on issues of scientific methodology.

#12 Comment By MathGuy On March 16, 2013 @ 9:14 pm

What I find frustrating about this post is Ron Unz’s refusal to present Mertz’s arctual arguments. Unz reproduced one table and claimed that it was surrounded by “10,000 works of often complex verbiage”. In fact, much of the paper summarized the variation in participation by women and ethnic groups in various contest. Towards the end, the Discussion section begins:

One commonly held belief to explain the extreme scarcity of females who excel at the highest level in mathematics is that women simply lack sufficient aptitude for the field (for examples, see [25], [31], [36]). The data presented here neither prove nor disprove whether the frequency of occurrence of people with profound intrinsic aptitude for mathematics differs between women and men. What they do indicate, however, is that this scarcity is
due, in significant part, to changeable factors that
vary with time, country, and ethnic group.

This seems a long way from Unz’s description of the article’s conclusions as attributing differences between men and women in high-end math as being “overwhelmingly due to culture rather biology”. In fact, the Conclusions section of the article begins with the following:

In summary, some Eastern European and Asian countries frequently produce girls with profound ability in mathematical problem solving; most other countries, including the USA, do not. Children, including girls, of immigrants to the USA and Canada from some of the countries that excel in the IMO are overrepresented among students identified as profoundly gifted in mathematics; USA-born girls from all other ethnic/racial backgrounds, including white, are very highly underrepresented. There exist many girls with profound intrinsic aptitude for mathematics; however, they are rarely identified due to socio-cultural, educational, or other environmental factors.

These two passages do not seem very complex. I think it is clear that the article, rather than drawing strong conclusions, seems rather to draw much milder conclusions. I wish Unz’s “closer examination” dealt with those conclusions.

#13 Comment By minty On March 16, 2013 @ 9:17 pm

In fairness to Professor Mertz, her comments to Unz’s previous blog were perfectly reasonable:

“I’m not saying that innate gender differences can’t play any role in there being fewer women than men among top mathematicians. I’m simply saying that the US could be producing lots more female (AND male) outstanding mathematicians given there are some European and Asian countries that produce many more than we do. ”

On the other hand, the headlines about her research, from Jezebel and Science Daily, were astonishingly dishonest. “Sorry, Larry Summers: Math Gender Gap Caused By Culture, Not Biology”!

Some things can just not be talked about in polite society, the costs are too high.

#14 Comment By gcochran On March 16, 2013 @ 9:23 pm

You’re ALL nuts. Ron hasn’t made his case about favoritism towards Jews at Harvard. Pointing that Mertz is wrong on another subject – which she certainly is – hardly proves that her objections to Ron’s argument are incorrect.

As for top-level math ability, the evidence strongly supports greater male ability. Mertz is full of it. To Katherine W: if you think that race is ‘not a genetic quality to any meaningful degree’, you win the crazy award.

#15 Comment By Gaeranee On March 16, 2013 @ 11:10 pm

Ms. Mertz,

I am referring to your comment on the Larry Summers articles Unz published earlier. You wrote that you had 42 Asian Ams to Unz’s 44 because you knew at least one Asian surname to be for a biracial kid (meaning, you didn’t count him or her as an Asian-Am for the purpose of this exercise.) Yet you point out that your 26 Jews to Unz’s 23 Jews could be the result of him not counting names like Miller, Mildorf and Lawrence as Jewish names. And yet, these three students were biracial – Jewish/White. So, your method of racial identification seems inconsistent.

So, yours and Professor Gelman’s point is that the percentage of high achieving Jews have been consistent in the past 25 years and their Ivy Leagues’ admissions rates have remained the same? So the rise in high achieving Asian-Americans during this time (and the Ivy League’s failure to admit them correspondingly) can be entirely attributed to their preference for everyone except the Jews?

#16 Comment By DT On March 16, 2013 @ 11:10 pm

KatherineW wrote:

“But shallow examination of statistics cannot prove any difference between the innate capacities of men and women in any subject.”

It seems you are ignoring the function statistics plays in research. Random sampling error must be calculated in random sampled trials with controls. If you accept the results of such trials, then you can’t reject the fundamental importance of statistical inference that underlies almost all research.

Larry Summers argued that it was the difference in variance that leads to the disparity in mathematical ability. While men and women do not differ in mean intelligence, Summers pointed out that the higher variance means that at the tails of the distribution there would be large disparities in the numbers of high IQ men relative to women. This also means that there are many more men with lower g as well. However we don’t see anybody rushing to uphold women’s right to be equally stupid. Men also have higher rates of ADHD, and autism, and commit far many more crimes. But, alas we are not striving to see that women commit there fair share of rape and murder. It seems as a society we are willing to accept averages if they follow our prior established bias, at the same token we ignore differences in variation unless they show a disparity in “beneficial” traits.

Mertz argues that there are not any innate differences. Mertz in correct. However, that isn’t Summer’s argument. The argument is whether there are many more men at +3, +4 standard deviation, and whether this translates to many more men in math and the hard sciences. The argument should be whether the disparity is close to 10 to 1 average demonstrated by the data, or closer to the 5 to 1 ratio demonstrated by Serbia and Montenegro. Perhaps social factors account for THAT gap, and on this I agree that there should be many more women in the hard sciences. Even if these social and cultural issues were controlled for we would still see a disparity.

#17 Comment By S Peter Cordner On March 16, 2013 @ 11:14 pm

There are a lot of very uncomfortable things to see in statistics, if one is willing to discount culture.

East African descendants win long-distance running Olympic events. West Africans descendants win short-distance running Olympic events. Slavs dominate wrestling. Males win Fields Medals.

The truth of the matter is much more complex than just birth. Mertz’s paper spends some time illustrating how gender inequality in a society is mirrored in female performance at the high end of adolescent mathematics, and the paper’s conclusions merely point this out, posit that there is more research to perform, and that the question cannot be said to be purely biological or purely cultural.

Jamaican culture, by the way, extols sprinting.

#18 Comment By Fran Macadam On March 17, 2013 @ 1:14 am

The striking thing to me is that 5% statistic. Apparently those women are not inferior in mathematical ability to men. So saying “women” are inferior doesn’t tell us anything about their abilities, does it? Any yet, they are women, so they must be inferior.

The problem with interpreting these statistics to say that anyone is inferior or superior doesn’t predict the outcome for any particular individual at all, but it will be taken to predict individual achievement by a group statistic.

For instance, I am a “man” or a “woman; I an not a “men” or a “women.”

Any use of group statistics to predict any individual’s actual performance is useless; and yet individuals, not groups, perform.

The only way that it could be said there is not equal ability possible, is for there to be 0% performance by any member assessed as an individual but who is also being classified as a member of a group (but which actually says nothing about performance which will always be by the individual.)

Which point was Summers making? I infer, I hope not unfairly, from his own obvious sense of dominating entitlement that he was likely self-referentially pondering that few measure up to him of any sex but certainly that no one of the female sex could.

#19 Comment By Alphysicist On March 17, 2013 @ 1:23 am

The philosopher John Searle has written an article in the 90s about how political correctness is undermining rational discourse in academia (back then this was true mainly for the humanities), because objective reality becomes irrelevant. Here is a link to this early warning, whose title is “The mission of the university: Intellectual discovery or social transformation”:

[13]

I think the question Searle raises goes further. If universities are institutions of social transformation, then they are not moreally entitled to tax money or public funds, since social transformations are based on ideological bias, and some taxpayers may not agree with that bias. Thus universities should be financed with those who agree with the particular ideological slants. A better option would be, of course, to restore the university as an institution of intellectual discovery.

#20 Comment By namae nanka On March 17, 2013 @ 1:32 am

Replying to Ms. Mertz’s points from the older thread:

“A third major point I make in my 2012 article relates directly to Summers’ argument of greater male variance in math performance being the primary reason for the scarcity of top female mathematicians. I show that while the US and most other countries have greater male variance in math, there are some countries that do not. In fact, there exist some countries where the entire distribution of math scores are essentially identical. If greater male variance is a biologically determined difference between the sexes, such countries should not exist!”

Countries like Tunisia are basket-cases. From 2003 PISA data, 49% of girls and 46% of boys scored below Level 1, the lowest level that there was. Their anomalous variance ratios exist not because boys don’t outnumber girls at the higher end, they do, but because their whole bell curve is smashed at one end.

“If greater male variance is a biologically determined difference between the sexes, such countries should not exist!”

Why not? Once you have biologically determined gender differences, it’s surely a smaller step to biologically determined racial differences, the racial differences are far larger than gender differences after all.
Everything’s fair game after that.

“I further show that there is a very strong, statistically significant correlation between gender gap in mean math performance ”

Comically the east asian data points are removed as outliers for regression with the gender equity index.
Secret formula, makes you berry strong!

“The tiny country of Romania has produced more female Putnam Fellows than the US. How can this be?”

That your “study” was published in the American Mathematical Society? Tunisia doesn’t look far.

#21 Comment By Reader On March 17, 2013 @ 6:06 am

gcochran,

What’s your story for the tremendous and more sex-equal performance of Bulgaria, Romania, and so on in the IMO? And more generally, the success of the Soviet bloc in getting women to study math, get PhDs, and do well on the IMO decades ahead of the curve for whites in the US?

Isn’t she right then that countries vary in the rate at which they get mathematically skilled people to train for extracurricular math contests, and take up careers in math academia?

#22 Comment By Reader On March 17, 2013 @ 6:10 am

As others have shown in the comments, Unz is badly misrepresenting Mertz’s article, and not even mentioning the key points about East European performance, increasing representation of women over time, and sustained differences in variance ratios and variance across countries.

#23 Comment By TomB On March 17, 2013 @ 10:13 am

What I find ridiculous is the basic assumption that can be seen on both sides of this issue to the essential effect that it’s the end of the world (or at least very important) if there are some genetic differences between the sexes or races.

In the first place, there obviously are, so creating sexes and races.

In the second, it would be rather remarkable given what we know of genetics and natural selection and human history if there *weren’t* any further genetic differences. Or, to put it another way, who really disbelieves that many physical features of the Innuit people derives from them living and evolving in their cold climes? (E.g., being shorter/smaller in general, which is better at fighting off the cold, and etc. and so forth.)

And in the third, so bloody what? As a male I have no doubt whatsoever that not only in general but in particular vis a vis me personally that women far exceed my abilities in any number of different ways. And that includes in some intellectual ways too: Again, does anyone really doubt that in general—but still rather overwhelmingly—females far outstrip males in terms of reading social situations and dynamics? Amazingly complex, tough, confusing, subtle thing, and yet I suspect most men would admit that women are just far far smarter at reading same than they are.

And that ain’t an *unimportant* thing either given that much of one’s ability to get ahead in society depends upon reading social situations and other people.

But, speaking about individuals, it means nothing at all since there are always outliers, and, morally, it means *absolutely* nothing at all.

When we talk genetics we’re talking nature, and nature’s fundamental unit is the species, and show me a species that’s genetically homogeneous and you’re almost certainly talking either of a species that’s extinct, or living on the very edge of extinction because their lack diversity puts them on that edge. One new microbe deadly to one is deadly to all. One new change in environment deadly to one is deadly to all. And etc., and so forth.

We vary, and no doubt we have not just thrived but have enjoyed our successes due to our genetic diversity. Being concerned with our *individual* genetic makeup, while of course only natural to some degree, is not only entirely pretending ourselves to be outside of nature, but can also become nothing less than foolish vanity.

#24 Comment By namae nanka On March 17, 2013 @ 10:42 am

“and not even mentioning the key points about East European performance”

“For example, prior to reunification, West Germany had NEVER had a female on their IMO team. On the other hand, East Germany had numerous girls, with their names listed in one of my tables in this article. ”

wikipedia:

“It was initially founded for eastern European countries participating in the Warsaw Pact, under the Soviet bloc of influence, but eventually other countries participated as well”

Teaching to the test? A difference in curriculums that still exists in former soviet countries? Didn’t them East German scientists do some nasty things with their sportswomen, perhaps with their mathletes as well? 🙂
And did women have a free choice in those jobs?

“the success of the Soviet bloc in getting women to study math”

The studies will continue until gender-equality improves.

“Sustained differences in variance ratios and variance across countries.”

Their assumptions seem to be:
1)Gender differences should remain exactly the same across different countries
2)The above exact gender differences should be time invariant.

Both are arbitrary. And country is country.

From a cursory look at her 2012 paper, China was absent in TIMSS07, Shanghai was not.

“Noteworthy is the
fact that 26 and 27 percent of the girls and boys,
respectively, from Shanghai, China, scored above
669 on the 2009 PISA; the corresponding numbers
for the U.S. girls and boys were 1.2 and 2.5 percent, below the 2.8 percent overall for OECD countries.”

Sampling differences. Sieve out the asians from the US numbers, and the gender ratio should go even more lop-sided, and shanghai to US ratio even higher.
Sieve out the NAMs and low performing asians and you have the opposite effect for the latter.

In another paper she mentions that 2003 PISA data:

“indicated that as many, if not more girls than boys scored above the 99th percentile in Iceland, Thailand, and the United Kingdom ”

Now what sort of socio-cultural factors explain Thailand and Iceland being in the same category? Not to mention the 300,000 something odd population of the latter.

Then there’s the SMPY factoid where the ratio of boys to girls, age700 on SAT-M, went from ’13 to 1′ in 80s to ‘3 to 1’ or ‘4 to 1’ in 2000s according to Wai 2010.
Asians are now the majority of those selected. Asian girls have been the majority of girls since the 80s. Must be the Tiger moms and the gender-egalitarian culture of formerly foot-binding women which is continued today by the heels-wearing frau?

In another gender-equality paper, more gender equality means girls do almost as good at maths as boys, and even better in reading. Apparently the gender-equality index is not what I think it says it is.
It is amusing when these studies are tooted as showing Summers wrong, often by mischaracterizing what he said, when they keep validating what he said.

#25 Comment By Gaeranee On March 17, 2013 @ 11:11 am

Interestingly, countries with a Communist history have more women mathematicians at the top level/competitions. China, former Soviet countries, East Germany…. Perhaps the concept of ideological equality has promoted gender equality in those countries. I am in no way advocating communism. I just think this should be studied if it hasn’t been already.

#26 Comment By Do Tyrants Need Excuses On March 17, 2013 @ 11:53 am

People want to refer to woman of exception as proving the general rule is invalid. But perhaps the rarity of such women are the exception that proves the general rule. If the odds of a male child having exception math skills is 1 in 10but a female child is 1 in 20, would anyone say in good faith men and women, in general, are the same? I doubt it.

In any event, I really could not care about this, except to the extent anyone wants to use these statistics as a pretext to limit my ability to organize my affairs in a way that does not rely on the initiation of force or the use of fraud.

#27 Comment By Alphysicist On March 17, 2013 @ 3:27 pm

Actually, on this point Unz’s statements may be questionable. But it seems to me that he is just saying that the conclusion of Mertz certainly does not follow from the data, and arriving at the conclusions depends on whether one accepts what in the end are only hypotheses. Moreover, the press who used Mertz’s study as “proof” was wrong and ideologically biased. It also should not have been a sufficient reason to dismiss Summers from his position. Especially because there were much better reasons for that.

But the original article dealt with another problem….

#28 Comment By NB On March 17, 2013 @ 4:02 pm

Gaeranee, Prof. Mertz counted half-Asians as half-white and half-Asian in her data, just as she counted half-Jews as half-Jewish and half-non-Jewish white. There is no inconsistency.

You have misinterpreted several of Prof. Mertz’s remarks. Unz stated that he counted East European and Germanic names as Jewish, which is how he arrived at a gross overestimate for the % of Jews on the 1970s US IMO teams. Yet, Unz ceased to count ethnic German names (e.g. Mildorf) as Jewish in the post-2000 data, i.e. Unz used an inconsistent methodology to identify Jews. By overestimating the % of Jews in older data and underestimating the % of Jews in recent data, Unz exhibited a spurious collapse in Jewish academic achievement.

Prof. Mertz counted both Miller and Lawrence as half-Jewish/half-non-Jewish white in her data. She counted Mildorf as non-Jewish white, as she did for all white people on whom we have no info.

We have not suggested that the admissions rates for Jews have remained the same in the past 25 years, and if you had read Prof. Mertz’s rebuttal of Unz, you’d see that Unz’s Harvard enrollment data includes the non-selective Harvard Extension School and does not account for the significant %age of students who are multiracial or whose race is unknown. Prof. Mertz also linked to a Harvard website stating that Harvard College’s Class of 2016 is 21% Asian-American, far higher than Unz’s claimed quota for Asian-Americans.

I find it curious that you chose to refer to Prof. Mertz as “Ms. Mertz,” while at the same time properly addressing Prof. Gelman as such.

#29 Comment By Thos. On March 17, 2013 @ 8:18 pm

@nb: “Unz’s Harvard enrollment data includes the non-selective Harvard Extension School “

It probably includes the selective part of Harvard Extension School, not the non-selective part. The selective part includes degree candidates who formally applied and were formally admitted. The program is notoriously rigorous, and relatively few (<150) Extension School bachelors degrees are conferred in any given year. These students are included in the University's overall count of undergraduates.

Unz probably did not include the non-selective (open enrollment) Extension students. If it had, there would have been thousands more.

#30 Comment By Thos. On March 17, 2013 @ 8:56 pm

Just to be clear: combining Harvard Extension School students with the College students is combining apples and oranges: the Extension students are typically older, many of them mid-career professionals. The selection process is different from the one for high school age applicants to the College.

#31 Comment By Glaivester On March 17, 2013 @ 9:39 pm

The striking thing to me is that 5% statistic. Apparently those women are not inferior in mathematical ability to men. So saying “women” are inferior doesn’t tell us anything about their abilities, does it? Any yet, they are women, so they must be inferior.

Anyone making a generalized statement that men are better than women at X is obviously referring to a statistical probability; in this case, in math the top x% of men tend to do better on average at math than the top x% of women. No one is saying that all women are worse than all men. Stop fighting straw men.

The problem with interpreting these statistics to say that anyone is inferior or superior doesn’t predict the outcome for any particular individual at all, but it will be taken to predict individual achievement by a group statistic.

No, it won’t. If as it turns out, in the top, say, .01% of people in terms of math, 80% are male and 20% female, that doesn’t mean that females should be discouraged from working on math, just that if a program aimed at the top .01% winds up 80% male, we shouldn’t be looking for discrimination or trying to find some way to equalize it.

For instance, I am a “man” or a “woman; I an not a “men” or a “women.”

I say 2000. We are discussing how many angels can dance on the head of a pin, aren’t we?

Any use of group statistics to predict any individual’s actual performance is useless; and yet individuals, not groups, perform.

There are plenty of places where the performance of groups is important. In particular, when gender/racial representation is used as evidence of discrimination, group statistics are very important.

Which point was Summers making?

I assume he was suggesting that the lopsided prevalence of males in the math department might not be due to discrimination and might not be in need of remedying. At the very least, it should not be taken as ipso facto proof of discrimination.

#32 Comment By KatherineW On March 17, 2013 @ 10:06 pm

It seems you are ignoring the function statistics plays in research. Random sampling error must be calculated in random sampled trials with controls. If you accept the results of such trials, then you can’t reject the fundamental importance of statistical inference that underlies almost all research….[Even if] social and cultural issues were controlled for we would still see a disparity.

I’m not ignoring statistics; I’m pointing out that their use is based on controlling for other factors and that social expectations around gender aren’t something you can control for when comparing men and women.

100% of women (or maybe 99.99% if we’re treating issues around gender identification as a thing) are both biologically female and socially treated as female. There is no society on earth where there are no expectations and preconceptions around what people of a given gender a like. So there’s no way for statistics to tell us whether differences between men and women in any skillset are based on biology, culture, or a mix of the two.

#33 Comment By Gaeranee On March 17, 2013 @ 10:18 pm

My apologies to Prof. Mertz for not addressing her as a professor. Just an oversight as I remembered “Prof. Gelman” as a statistics professor while remembering Prof. Mertz as not a professor but a cancer researcher, and I am just used to addressing people as Mr. or Ms.

NB,

Thanks for the clarification. While there is mention of fractional counting of Jewish biracial students, I didn’t see any mention of fractional counting of biracial Asian children in her refutation of Unz’ article (only her comment on the other post that her number was lower for Asian-Americans because there was one, which led me to believe she didn’t count biracial Asian children as Asian-American.)

I understand the point that you, Prof. Mertz, and Prof. Gelman are making about Unz not using consistent methodology. But if you are going to go through all the trouble of pointing out inconsistencies, you would be better served to conduct the entire analysis yourselves (three brilliant people, I gather) rather than simply arguing that Unz could have done better. If Hillel numbers are “implausible”, how should Unz have calculated the numbers, short of actually looking through each universities’ admissions list and combing through thousands and thousands of names for many years. If you think he should have done that, why can’t you?

Based on Prof. Mertz’ Putnam numbers, it appears that both Asian-Americans and Jew’s numbers have been collapsing since 2000 while the numbers of white Gentiles and foreign students have been going up. Do Ivy League universities’ admissions rates during this time reflect this? And it seems that based on your NMS numbers, the number of Jews have remained the same since 1987. Have Ivy League universities’ admissions numbers for Jewish students remained the same since 1987 or have they gone up?

I don’t think most people are interested in parsing over a couple of percentage points, which is what this debate has come down to. The more important questions are what Unz addressed in his article: (1) Are Asians discriminated against at these schools? (2) Are Gentile whites discriminated against at these schools? (3) Are Jews being favored at these schools? We won’t know until we look at the admissions numbers for these schools. And I think it would be worthwhile for both factions to agree on a list of names for each category of race and conduct a study that way. If tackling all the schools is too difficult, perhaps people should just start with Harvard, Yale and Princeton.

#34 Comment By Withywindle On March 17, 2013 @ 11:05 pm

1) I do think the tone, the rhetoric, of Gelman, Mertz, et al., is off-putting: they make too much of “we are scientists, we seek the truth, you uncredentialed others are mere ignorant fools with no interest in the truth.” That last bit is not what they say explicitly, but the tone does lend itself to that summary. This can only irritate anyone who lacks their credentials, it seems incomplete as a description of reality, and it isn’t necessary. They can make identical points without reference to their doctorates, their peer-reviewed credentials, etc. Or if they must make reference to their professional character, as some sort of relevant authority, there must be some less annoying way to do so. I recommend that they make the effort to recast their mode of argument.

2) Mr. Unz is not perfect in his tone either. I think he could engage in a more charitable exploration of his opponents’ arguments–again, while making the same basic points. What I believe should be at issue both for Mr. Unz and his interlocutors is not so much their professionalism as their mutual charity.

3) I think the argument would benefit by disaggregation. I think one argument concerns the reliability of statistics used by pundits in general, another whether Mr. Unz should rely on Hillel statistics in particular. Mr. Unz points out that other pundits use the Hillel statistics, and that a great deal of public policy use of statistics is no less sloppy than he is in combining different statistical sources, and therefore it is something of a double-standard to criticize him as uniquely guilty in his approach to numbers. I think this argument is well-taken, and that it would not hurt Profs. Gelman and Mertz, and the mysterious NB, to acknowledge that Mr. Unz is entirely ordinary among public intellectuals in his practice–and even to say that whatever criticism they make of Mr. Unz ought to be leveled at all his peers, especially those who use such statistics to support those pieties of the day that Mr. Unz seeks to subvert. Mr. Unz, on the other hand, could also acknowledge that “others have sinned too” is an extenuation, but not a direct defense, and endorse (or fund?) a study on the same subject done to the preferred standards of his interlocutors.

4) I think one should also disaggregate the question of Jewish performance on Math Olympiads, etc., and Jewish admission into the Ivy Leagues. To say there are more Jews on current Math Olympiads, etc., is to say that the current level of Jewish admissions into the Ivies (whatever it is) argues against Mr. Unz’s contention that (to simplify) the Ivy League is more a Jewish country club than a Jewish meritocracy; it does not, however, argue against the contention that there is significant over-representation of Jews in Ivies as compared to their representation in the American population in general. The argument that the Hillel statistics of Jewish numbers in the Ivies are inflated does speak to this latter point–but these two arguments should be kept carefully delineated. I would also add that some of the Math Olympiad arguments presented here seem to say that the Jewish decline in numbers is proportionate to the general white decline, both reduced by the rise in Asian-descended participants. But this does not directly address Mr. Unz’s contention that, in essence, while both white gentiles and Jews should have seen their numbers reduced as a result of Asian meritocratic competition, Jews collectively preserved their numbers in the Ivies at the expense of white Gentiles. The Hillel numbers do speak to this last argument, but I do not believe the Math Olympiad, etc., numbers do. Of the various issues raised by Mr. Unz, I would favor further study of two closely focused, but separate, studies: one on whether there has been discrimination against Asians in Ivy League admissions by the various standards subject to quantification, and one on whether there is, in effect, discrimination in favor Jews at the expense of white gentiles in Ivy League admissions, by the various standards subject to quantification. I think it would be helpful if Profs. Gelman and Mertz joined Mr. Unz in urging the Ivy League admissions offices to release the information needed to make a study that meets the professional standards of Profs. Gelman and Mertz.

5) I think both sides need to address themselves explicitly and at greater length to how to define people of mixed heritage, whether part-Jewish, part-Asian, or what have you. What is being studied? Subjective identification as a Jew (Asian, etc.), or ancestral component? If the former, how precisely do we define people who are half-Jewish, but define themselves as Jewish, not-Jewish, or both, depending on person and context? How do we consider quarter-Jews, etc.? The subjective/objective definition–Who is a Jew, Who is an Asian?–should be considered before one gets to the methodology of counting.

6) On Prof. Mertz’s gender study: I believe one question underlying this debate is whether current culture skews or reflects the disparities you would expect from the great goddess Nature, in her current Mendelian dress. Or: if a country like Sweden, East Germany, or Romania has higher than the current world average of female performance on various mathematical tests, is this because their efforts have removed cultural constrictions on natural performance, or because their efforts themselves constitute a cultural, inflating skew on natural performance more in the nature of an outlier than a leading indicator. Whether or not these different presumptions can ever be settled by social science data, I would be skeptical that the current state of the field can yet allow a dispositive settlement of that question. Some mutual charity on this issue too might also be in order.

7) I would suggest that Mr. Unz not invest his time in defending the Weyl methodology as such. If it is accurate, then any reasonable alternate methodology will produce similar results; if it is not, then it won’t. The question is what to do given that Mr. Unz has come up with interesting results that don’t meet all the methodological results of the professional statisticians. Is the burden of proof on Mr. Unz to prove Ivy League discrimination by another method, or on the statisticians to disprove it? I would rather say the latter–but that and a buck fifty will get you a cup of coffee. I would suggest again that Mr. Unz continue his critique by funding some competent statistician to continue his inquiry into this subject matter, in hopes that the statistician will find a proof of discrimination that meets the standards of his interlocutors. (I am not a statistician, nor are any of my relatives.) I do not think it is a just world that requires this extra effort by Mr. Unz, and that it speaks badly of the statistical profession that they will not do this work themselves, but Mr. Unz must deal with the world as it is. Should such a result be produced, I trust in Mr. Unz’s ability to provide it sufficient publicity.

8) It would help the inquiry into truth considerably if a Bradley Manning in the Ivy League admissions offices, if such existed, began to email relevant data to Mr. Unz.

#35 Comment By David On March 17, 2013 @ 11:12 pm

Prof. Mertz’s comments to this article comparing the experience of East and West Germany are interesting. To speak of the access to child care and career dreams and expectations certainly puts the Pollyana-ish spin on life in a totalitarian police state. Or maybe repression of voluntary career choices is good for female mathemeticians? If that is the case, perhaps the best solution is to force academically gifted young women in the US into math whether they want to or not, and then prohibit them from choosing family life over a career. That said, Ron Unz does need to muster better arguments than presented here.

#36 Pingback By A Minimum Wage Hike as Amnesty-Killer? | The American Conservative On March 18, 2013 @ 4:01 pm

[…] a different matter, I’d noted in my previous column that the diligent research of Prof. Janet Mertz and her colleagues had determined that for decades […]

#37 Comment By NB On March 18, 2013 @ 5:45 pm

A couple commenters appear to be requesting that Prof. Gelman, Prof. Mertz, and I disprove Unz’s claims, and that the burden of proof is on us. It is not possible for any of us to prove or disprove that Asian-Americans and/or white Gentiles are discriminated against in favor of Jews in Ivy admissions. I will be writing up a comprehensive blog post in which I show that no conclusions can be drawn from Unz’s data sets.

Prof. Thomas Espenshade at Princeton found that on average, Asian-Americans applying to a particular set of universities had the same chances of admission as white applicants with SAT scores that were 140 points lower. Yet, he stated:

People may read this and want to say, “Oh, because I’m Asian American, my SAT scores have been downgraded.” That is not really the way to interpret these data. Many times people will ask me, “Do your results prove that there is discrimination against Asian applicants?” And I say, “No, they don’t.” Even though in our data we have much information about the students and what they present in their application folders, most of what we have are quantifiable data. We don’t have the “softer” variables — the personal statements that the students wrote, their teacher recommendations, a full list of extracurricular activities. Because we don’t have access to all of the information that the admission office has access to, it is possible that the influence of one applicant characteristic or another might appear in a different light if we had the full range of materials.

Prof. Espenshade has done far more research on this topic than Unz, Prof. Gelman, Prof. Mertz, or I, and I think it’s instructive to note how cautious he is about drawing far-reaching conclusions from his SAT score data. In contrast, Unz has far less definitive data (as his data on Jewish students is extremely flawed) and drew sweeping conclusions.

#38 Comment By Withywindle On March 18, 2013 @ 9:31 pm

NB: Please note my stipulation above: “by the various standards subject to quantification.” This is what your discipline is equipped to study, and the results it proves are significant. To say that one group of applicants enjoys its collective rate of admissions by dint of qualitative factors–character, broadly and woozily defined–rather than quantitative ones is a significant result. And again, if you lack the necessary data, surely you should join Mr. Unz in requesting the release of that data.

I urge Mr. Unz to draft a letter to the various Ivy League admissions offices requesting a release of the relevant data–suitably anonymized–needed for a statistical study done according to the standards stipulated by NB, Prof. Mertz, and Prof. Gelman. I urge Mr. Unz to circulate his draft to Profs. Mertz and Gelman, so that it may include language mutually acceptable to all three. I then urge that all three (not NB, alas, since s/he is anonymous) sign this letter, and submit it to the various Ivy League admissions offices. I also urge Mr. Unz to publicize this letter to the best of his ability.

Should Profs. Mertz and Gelman fail to sign such a draft, I urge Mr. Unz to send his letter himself, noting where necessary the unwillingness of Profs. Mertz and Gelman to join him in his desire to acquire sufficient data for an inquiry into truth conducted according to their professional standards.

#39 Comment By DT On March 19, 2013 @ 12:17 am

KatherineW writes:

“I’m not ignoring statistics; I’m pointing out that their use is based on controlling for other factors and that social expectations around gender aren’t something you can control for when comparing men and women.”

Statistical variance predicts the disparity in the ends of the distribution. This is what Summers was pointing out. If this is not the case then I think there needs to be an explanation for why variance is less for women and the means for men and women are similar. I think Mertz tried to address this, but ended up dismissing variance between countries as well. Obviously no one wants to address the implications of that, e.g. why East Asian countries have higher mean IQs and less variance.

More women are clustered around the mean, leading to less numbers at the tails of the distribution. This makes me want to ask then: Are social constructs responsible for there being more men of very low intelligence relative to women? Likewise do social constructs explain why there are more women clustered around the mean relative to men? I would like to see this played out on every factor that is normally distributed.

Additionally, if we are going to through out statistical inferences from variance, should we not also throw out the statistical means showing that women and men, on average, are of equal intelligence? Then we can be finally done with this topic since we won’t have the tools to run random sample studies. I’d rather we all just shrug and say ” I dunno,” rather than ignore fundamental statistical analysis when it does not suit our interests.

#40 Comment By Gaeranee On March 19, 2013 @ 12:22 am

What Prof. Espenshade and Unz are saying are two different things. Unz’ point is that admissions should be based completely on meritocracy (which he defines as academic achievement), a point Prof. Espenshade never advocates. While I agree that soft variables should be considered by admissions officers, it’s highly subjective and prone to bias so they should be monitored. There’s clearly a problem if Asian-Am academic achievements have been going up recently and yet admissions rates don’t reflect that. And there’s clearly a problem if Jews’ academic achievements have been going down but admissions rates have been going up. In such cases, I’m sure people would want to know what are these “soft” variables that Jews seem to have that Asian-Ams don’t? Could it be the administrations of these schools favoring one’s own kind, as Unz implies?

Unz mentions statistical analyses done by Griffe on the Minimum Wage and Amnesty article. Griffe says: “In brief, we have seen tonight 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; that culture plays a role in math performance, albeit small.” He writes that there are “formidable biological barrier to overcome (by women) before the math gender gap can be closed.”

I’m still not convinced. Just because men are proven to be better in math than women across cultures doesn’t mean that they are “biological” better in math. In every culture I know, men are the dominant gender – in politics, military, socio-economically, in upper levels of management, within households…. So it’s not surprising that men have performed better in math across all cultures (and not just in math, in many other fields as well). Of course, if Unz and Griffe can show me a society where the women are the dominant gender, and men still outperform women in math, then I may be convinced. Until then, comparing cultures is rather meaningless as sexism is pervasive across all cultures that I am aware of. [Note: Griffe mentions that Korea and Japan were Math PISA high scoring countries “with a progressive outlook on women’s emancipation.” And yet, sexism is rampant in those countries; so you have to wonder just how great women could be in math if they were given an equal chance.]

#41 Comment By Annek On March 19, 2013 @ 4:00 am

Prof. Mertz says:

“In the 1950s and 1960s, only 5% of math Ph.D.s awarded to US citizens went to women; in the 2000s, ~30% did. Humans don’t evolve this quickly. These large differences and fairly rapid changes must be largely due to sociocultural differences and changes.”

In the 1950s very few women received PhDs in any subject, not just math.

#42 Comment By Annek On March 19, 2013 @ 4:08 am

Withywindle said:

“I do think the tone, the rhetoric, of Gelman, Mertz, et al., is off-putting: they make too much of ‘we are scientists, we seek the truth, you uncredentialed others are mere ignorant fools with no interest in the truth.’ That last bit is not what they say explicitly, but the tone does lend itself to that summary. This can only irritate anyone who lacks their credentials, it seems incomplete as a description of reality, and it isn’t necessary. They can make identical points without reference to their doctorates, their peer-reviewed credentials, etc. Or if they must make reference to their professional character, as some sort of relevant authority, there must be some less annoying way to do so. I recommend that they make the effort to recast their mode of argument.”

I agree. It sounds like they are using their credentials to shut down the discussion. It also seems like it would be a good idea, as Withywindle suggests, for Ron to hire a statistician to do some research on the subject for him.

Many good points, Withy!

#43 Comment By NB On March 19, 2013 @ 2:11 pm

Prof. Espenshade found that Asian-Americans applying to a particular set of universities had the same chances of admission as white applicants with SAT scores that were 140 points lower. He said that his results do not prove that there is discrimination against Asian-American applicants. In contrast, Unz claimed his data proves discrimination against white Gentiles (yet curiously not Asian-Americans) based on similar data (NMS status being used as a proxy for SAT scores, which is a flawed analysis due to the fact that the NMS qualifying score varies by state). I think it’s clear that Prof. Espenshade would disagree that Unz’s data proves bias.

Gaeranee stated:
There’s clearly a problem if Asian-Am academic achievements have been going up recently and yet admissions rates don’t reflect that. And there’s clearly a problem if Jews’ academic achievements have been going down but admissions rates have been going up.

There is no evidence that the admissions rates of Jews have been increasing, as we don’t know the % of Jewish applicants in the Harvard applicant pool. In addition, Hillel’s data for the Jewish enrollment at Harvard and Yale exhibit such stark statistical anomalies that they can’t possibly be considered reliable data. Furthermore, Unz’s Asian-American enrollment data for Harvard (and presumably other universities) is quite simply wrong for reasons already discussed. e.g. Asian-Americans represent 21% of the Harvard College Class of 2016 according to the Harvard College Office of Admissions.

#44 Comment By FredR On March 19, 2013 @ 3:01 pm

I started out on Unz’s side, but I think he’s lost this debate, and this stuff about unrelated research by Mertz is just a cheezy distraction. It only makes sense as part of Unz’s argument if you already believe he’s right and that Mertz is wrong. Then you can go along with “oh she’s a biased ideologue” kind of thing. But it seems pretty clear that Mertz’s criticisms are unanswerable (or else Unz would have answered them).

#45 Comment By Joe College On March 20, 2013 @ 10:39 am

The broad question of corruption in university admissions is getting more play in the media, and Unz’s research seems to have played a role in that.

I think we’d all like to see this sorted out and some hard facts established as a basis for determining whether (and if so the extent to which) admissions processes have been corrupted.

The latest – admissions offices faking numbers to boost their US News rankings:

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#46 Comment By Sock Puppet of the Great Satan On March 20, 2013 @ 11:14 am

Evidently the utility of comparing the IMO (a contest where there’s peer-, teacher- and self-selection) with across-the-board test scores for gauging the level of cultural bias in a society has escaped Unz.

#47 Comment By Sock Puppet of the Great Satan On March 20, 2013 @ 11:17 am

“But it seems to me that he is just saying that the conclusion of Mertz certainly does not follow from the data”

Take a look at the comparison in Mertz’s paper (linked above) of the distribution of Math test scores for females vs. males in the Czech Republic. Pretty hard to make an essentialist on male vs. female math ability argument given that data.

#48 Comment By Franklin Evans On March 22, 2013 @ 3:40 pm

I’m a bit late to this discussion, so I’ll just offer a comment on the disputed notion of the validity of laypersons criticisms of experts (i.e. Withywindle’s first bullet point).

I am a software engineer. My standard response to the question what do you do is “got an hour?” even to someone with a general understanding of things, such as the abstract differences between a mainframe computer and a PC network.

For those few brave enough to say “yes, go ahead” the hour is spent trying to summarize 13 months of direct training and more than 20 years of full-time experience during which I learned or encountered enough to fill another 13 months or more of direct training.

So when a person decides to make a claim, assertion or criticism of some specific aspect of my work, and it is immediately clear to me that the person can make no rational claim to a valid foundation for the statement, I find it perfectly appropriate to reply “You are wrong, and I have the credentials to back up my rejection of your statement.”

Mine is largely an experiential job. We do much learning-by-doing because computers are just like that. There is too much to know — let alone commit to memory — from just an academic background which the vast majority of laypersons simply don’t have.

I also recognize that my practice of learning-by-doing (trial-and-error) is only a trivial similarity to what research scientists do. I am as much a layperson to Prof. Mertz as Mr. Unz or the rest of us sharing this forum, and I will make a personal assertion based on my claim of empathy for her perspective: Ego-based rejections of credentialed authority is all I’ve seen here so far (with very few exceptions), and while I might join the critique of her choice of tone and phrasing in her responses, I stand completely with Prof. Mertz on the content.

Withywindle: You make a civil case, but I must point out that no matter how nicely I try to put things, someone is going to object to it in some other way — I’m patronizing, condescending, the like — and I see it as a classic catch-22. The only solution is for laypersons to stash their egos at the door and bring a sincere desire to learn.