pageok
pageok
pageok
Be Careful Trusting Data, Even in Nature:

I found Ben Barres' Nature article, "Does Gender Matter?", to be very interesting; and one thing that quite struck me was this assertion: "[D]espite all the social forces that hold women back from an early age, one-third of the winners of the elite Putnam Math Competition last year were women." Perhaps I overestimated the importance of this assertion because I'm actually familiar with the Putnam Competition (I never participated, and I'm not nearly good enough at math to get anywhere near top scores on it, but I occasionally look at some old problems and enjoy taking a whack at them). Still, the competition seems to test creative math ability and not just rote application of rules, and to test high-end ability: The "does gender matter?" debate in science faculty hiring, after all, has to do with claimed differences between the very far right tails of the male and female math ability bell curves, not between the average man and the average woman or even the average male and female college students.

So, I thought, if one-third of the winners — basically, of the top 15 or so finishers — of the competition are women, despite the social pressures that I'm quite sure would drive down the number of successful women, that really is a powerful data point. (Recall that the question generally isn't whether the disproportionate representation of men and women in high-end science jobs is due entirely to biology, but only whether it's due partly to biology.)

Unfortunately, when I looked more closely at this data point, it turned out to be in error. Here's what I submitted as a letter to the editors of Nature:

Dear Editors:

I read with interest Ben Barres' "Does gender matter?" (13 July 2006), and particularly the statement that "one-third of the winners of the elite Putnam Math Competition last year were women." This struck me as a particularly telling piece of evidence: If indeed so many women performed so well in such a respected competition, this would indeed undermine assertions of substantial biological gender differences in the higher levels of mathematical ability.

Unfortunately, on further research, it seems that this statement is mistaken. Last year's (2005's) top 16 finishers seem to have included only one woman (UNL 2005). Prof. Barres was likely referring to 2004, but even in that year the top 15 included only four women (Hopkins 2005; UNL 2004). In 2003, two of the top 16 were women (UNL 2003; Princeton 2006). In 2002 and 2001, the number was one of 15. Perhaps I'm mistaken, despite my attempts to verify the ambiguous names; but this is the data as best I can determine it.

Prof. Barres' other claims in the article may well be accurate; the data I cite above certainly don't prove that the reason for the low numbers is even partly biological sex differences. On the other hand, I thought it might be helpful to let readers know that one particular piece of evidence mentioned in the article seems mistaken.

Eugene Volokh
Professor
UCLA School of Law

Sources: Hopkins, Nancy, 2005. "Academic Responsibility and Gender Bias," XVII MIT Faculty Newsletter No. 4, pp. 1, 24.
UNL Web site, 2005. "The William Lowell Putnam Mathematical Competition, Announcement of Winners ...."
     2004. http://www.unl.edu/amc/a-activities/a7-problems/putnam/-html/putnam2004results.html.
     2003. http://www.unl.edu/amc/a-activities/a7-problems/putnam/-html/putnam2003results.html.
     2002. http://www.unl.edu/amc/a-activities/a7-problems/putnam/-html/putnam2002results.html.
     2001. http://www.unl.edu/amc/a-activities/a7-problems/putnam/-html/putnam2001results.html.
Princeton, 2006. Telephone Conversation with Mathematics Department at Princeton University, July 19, 2006.

Unfortunately, Nature has decided not to publish the letter; here's their response:

Dear Professor Volokh

Thank you for your letter. We have checked into the figures and it seems that in 2004 four of the fifteen top ranked Putnam winners were women (one other might have been, we can't tell). Although we agree that it is unfortunate that we did not include the year in the relevant sentence in the commentary, we feel that 4 (probably, but maybe 5) out of 15 is sufficiently close to one-third not to publish a correction on this occasion.

Thank you again for writing to us.

Perhaps it's me, but it seems to me that the response is missing my point — not only was the number 5 likely wrong (as Prof. Nancy Hopkins' article agrees), and not only was the year wrong (not just omitted, but wrong, since the story unambiguously says "last year"), but the data that Prof. Barres cites is highly unrepresentative, and its unrepresentativeness is hidden by the omission of the year.

If you see "last year the results were X," that might suggest to you that the results in previous years were similar but only the last year was mentioned because it's the closest data point; or it might suggest to you that in any event the trend is towards last year's X. But if you see "in 2004, the results were X," you'd be much likelier to quickly recognize that maybe the 2005 results were different. And given how different the results are — in reverse chronological order, they seem to be 1, 4, 2, 1, 1 — is it quite right to solely cite the 4 (even setting aside the dispute about whether it's 4 or 5); to suggest that it's the most recent result; and to omit the four data points, one of them a more recent one, that would suggest a very different situation?

Two notes. First, I corresponded with Prof. Barres when trying to track all this down, and he was quite gracious about it. I'm sure his error was entirely innocent; I just wish the Nature editors were willing to correct it. Second, I should stress that the aggregate data does not prove that biology is the reason for disparity; cultural factors may well account for the entire gulf even so. My point is simply that one of the reasons to believe that the biological factors are absent or slight — much closer to par representation of men and women on the Putnam exam — appears not to be correct.

And, more broadly, as the title suggests, don't trust everything you read — even relatively easily verifiable data in a respect journal such as Nature.

zzyz:
Do you have some reason to think that "winners" means the top 15 competitors? I've always understood Putnam scoring to be much more granular than that -- I don't think there's any way to distinguish between the top 15 and the top 25. Below that they're called "honorable mentions", but there's no real difference in how the 6-15 and 16-25 groups are described.
7.25.2006 1:55pm
Joel B. (mail):
And, more broadly, as the title suggests, don't trust everything you read -- even relatively easily verifiable data in a respect journal such as Nature.


My trust in science is shattered, shattered I say. Thanks Eugene! (No really...thanks)
7.25.2006 2:08pm
pp (mail):
And, more broadly, as the title suggests, don't trust everything you read -- even relatively easily verifiable data in a respect journal such as Nature.

But I am sure everything published by the scientific community about the "fact" of global warming is correct.
7.25.2006 2:12pm
Fred Drinkwater (mail):
The real problem with Dr. Barres' recent spate of MSM publicity is not the facts, per se, but the presence of news photogs in the lab. They are interfering with my daughter's ability to properly prepare the vitally needed pureed mouse brains :-)
7.25.2006 2:15pm
The Original TS (mail):
Well spotted, Eugene. I'm surprised that Prof. Barres wouldn't want to publish a clarification. You're quite right that it looks very much like cherry-picking the data.
7.25.2006 2:15pm
Annonymous:
The Putnam releases individual rankings, First, Second, etc.

The raw scores for the Putnam are available at http://www.unl.edu/amc/a-activities/a7-problems/putnam/

There is a substantial gap between #1 and #10 (and an even larger gap between #10 and the typical excellent math student).
7.25.2006 2:24pm
llamasex (mail) (www):
It's sad that they are not correcting the article. It's my opinion that any sort of journal should err on the side of correcting too much as opposed to not correcting inconsequential details. Kudos for Prof Volokh for catching the error and tracking down the right people to send the correction to.
7.25.2006 2:24pm
DJR:
The number of women who "win" this competition is meaningless without knowing how many entered.
7.25.2006 2:25pm
Richard Aubrey (mail):
I'd be careful with this issue, unless, like Larry Summers, you have $50 million to hand.

Where's the fainting couch?
7.25.2006 2:26pm
guest:
In my branch of science, we joke around that if something is published in Nature, that means it will be proven wrong. The articles are very short, and they go for the latest, edgier science. As such, they are often wrong.

I think they've very recently improved this by allowing authors to publish much longer companion articles on-line, so that the science is more easily verified.
7.25.2006 2:27pm
Mike Keenan:
I decided to look up the data. It certainly appears that there were 4 women in the top 16 in 2004. (I don't know who they think the 5th would be). Note that it is possible to google most of the winners to find out something about their backgrounds. Not surprising since they all have hometowns proud of them. Let's look at them:

Ana Caraiani,
a sophomore at the time Princeton who attended high school in Romania

Olena Bormashenko,
attended high school in toronto (but maybe Eastern European background)

Alison B. Miller I couldn't find her background, but she doesn't sound Eastern European. She appears to be a home schooler from Niskayuna, N.Y (http://www.mackinac.org/article.aspx?ID=4364)

Inna I. Zakharevich (well, that sound Eastern European)

So, only one seems subject to the "social forces that hold women back from an early age" (and even then a home schooler is isolated from those pressures!) Or are the Eastern European forces the same? I suspect not.
7.25.2006 2:29pm
TGGP (mail):
Excellent discussion of Barres and the Summer controversy as well as the Pinker/Spelke debate here
7.25.2006 2:41pm
liberty (mail) (www):
This kind of thing is very frustrating. I found some very easily verified mistakes/misleading data-points in a comparative economics textbooks a while back.
7.25.2006 2:41pm
Mike Keenan:
Not to put too fine a point on it, but a fourth or more generation American woman who went to a public high school would be a good data point. I don't think you will find a year with 33% of those. In fact, the social forces on the boys of that description probably preclude them as well.

The above makes up about 50% of the population (I am guessing). And less than 5% of the winners, I suspect.
7.25.2006 2:45pm
DJR:
From the page you cited:

The William Lowell Putnam Mathematics Competition is a North American math contest for college students. Each year on the first Saturday in December, over 2000 students spend 6 hours (in two sittings) trying to solve 12 problems. Individual and team winners (and their schools, in the latter case) get some money and a few minutes of fame. Results for a given December's exam usually become available in early April of the following year.

So the 2004 results were announced in 2005, quite reasonably "winners . . . last year." Happy?
7.25.2006 2:45pm
Edward Lee (www):
So the 2004 results were announced in 2005, quite reasonably "winners . . . last year." Happy?

Probably not, unless there's some specific sociological reason that the number of top-scoring women should have jumped between December 2004 and December 2005.
7.25.2006 2:49pm
Eugene Volokh (www):
zzyz: Prof. Barres, as I mentioned, was kind enough to discuss the matter with me; I don't think I'm violating any confidences by saying that he said the "winners" did indeed refer to the Top 15.

DJR: When you read the Barres quote, did you think that it referred to the second-to-latest competition (for which the number was 4), while for the latest competition the number was 1? Or did you think that "last year" was referring to the most recent results?
7.25.2006 3:12pm
Jim Rhoads (mail):
Have there been any male vs female studies of purely socialist populations (like those of Eastern Europe and China) on pure math ability tests to test the hypothesis of negative socialization of women toward scientific or mathematical skills?

Anacdotally, there seemed to be a greater proportion of women in those countries who were active in science and math than in the western capitalist countries.
7.25.2006 3:29pm
Steve:
But I am sure everything published by the scientific community about the "fact" of global warming is correct.

Interesting point. Kind of highlights the importance of peer review, which leads to errors being identified and corrected. Of course, it just so happens that global warming theory has been the subject of hundreds upon hundreds of peer-reviewed studies - which, of course, means that errors will be inevitably found along the way - while the skeptics seem content to avoid the peer review process and simply cast aspersions from the op-ed pages of the Wall Street Journal and similar venues.

Science, last I checked, does not claim to be infallible. It does claim to be rigorous and subject to correction and improvement. In fact, this very post is a classic example of how errors can be detected through peer review.

As to the substantive point, I suspect that the sentence in question was true when written (leaving aside the 4 vs. 5 issue), and that bad editorial oversight during the article's lead time accounts for the discrepancy. If the 2005 results weren't announced until April 2006, it's entirely plausible that the offending sentence was written before that date. Of course it still should have been corrected prior to publication, but there's reason to doubt the author was intentionally trying to cherry-pick a good year.
7.25.2006 3:30pm
Eugene Volokh (www):
Steve: I should stress again what I said in my post: ", I corresponded with Prof. Barres when trying to track all this down, and he was quite gracious about it. I'm sure his error was entirely innocent; I just wish the Nature editors were willing to correct it."
7.25.2006 3:32pm
frankcross (mail):
Good advice here.
Might be extended to the occasional willingness of Conspirators to highlight the significance of a recent press report.
7.25.2006 3:40pm
Steve:
Steve: I should stress again what I said in my post

I would note that not every comment is intended to imply disagreement with the author of the post. :)
7.25.2006 3:42pm
DJR:
When I read "last year," I thought it meant 2005, this being 2006.

When I went to the site, I already knew the whole controversy, but I still thought it meant the second to most recent results. In fact, for a moment I thought you had made a big mistake, because I went to the second-to-most-recent results, assuming that they would be "last year's" results, that would have shown one female, and I saw several females. Then I noticed that the date of the test was December 12, 2004, and figured that the 2006 results had not yet been posted, which made me curious as to when "last year's" results were posted. As it turns out, the results for a test given at the very end of one year are announced in the middle of the following year.

In short, if being in the top 15 makes you a winner, then four of last year's winners were women.

Whether that's "close enough" to a third is another question, but "last year" is both accurate and not misleading.
7.25.2006 3:45pm
Closet Libertarian (www):
Eugene is right here. The explanation of 4 or 5 in 2004 is a reasonable explanation of how a mistake was made but not a reason to not correct a misleading statement.
7.25.2006 3:58pm
James Ellis (mail):
We can quibble about whether 4/15 is "close enough" to 1/3, but it is pretty disturbing to find out that the larger sample and arguably more reliable number (9/77) isn't anywhere close. If this is what passes for good data in Nature, I'd hate to see what they are using in Nurture.
7.25.2006 4:02pm
ras (mail):
To the editors, the story was "too good to retract."

On a tangential note, Eugene, you mentioned "the competition seems to test creative math ability."

Reminds me of the story of a very young Master Gauss (yes, that Gauss) who was kept after school for misbehavior. His penance was to add all the numbers from 1 to 100. He immediately replied 5050 and his teacher honorably let him go, but only after Gauss explained how he had deduced the answer so quickly.

In his precocious mind, he had realized that there are 50 pairs of numbers, such as 1 and 100, 2 and 99, 3 and 98 etc, each totalling 101. 50 * 101 = 5050.
7.25.2006 4:06pm
Nick P.:
While I am disappointed that Nature did not see fit to publish Professor Volokh's letter, I think it is potentially misleading for him to characterize Dr. Barre's Commentary as an "article." In the context of a scientific journal, particularly Nature "article" implies a peer-reviewed scientific paper. In Nature the "articles" are specifically the longer, more detailed scientific papers. Barre's commentary is essentially an opinion piece or letter to the editor, and I don't see any obvious evidence that it was peer reviewed. It lacks the typical "Received...revised...accepted" dates of a peer reviewed article.
7.25.2006 4:07pm
Nothing Rhymes with Orange:
Kudos to you, Eugene. You've redeemed yourself following the harsh (and out-of-character) letter to Captain Copyright.

The Original TS got it right: It appears Barres cherry picked data that were consistent with his preferences while ignoring data that were not so consistent.

The overall percentage across all years -- which is more heavily favors males -- would be a more reliable estimate of sex differences.

Barres's cherry picking undermines his claim and casts doubt on his motives. Barres almost certainly had access to Putnam data from other periods (and ignored it) or could have easily acquired the data (but failed to do so). Neither possibility reflects well on Barres's integrity.

On a related note: The Putnam data are consistent with (but, taken alone, do not confirm) the "fatter (extreme) tails for males" hypothesis, which predicts a more leptokurtotic distribution for males (in math ability). "Fatter tails for males" has a nice ring to it.

BTW, Eugene: Although *Barres's* cherry picking does not reflect well on his integrity, let's not impugn other scientists with the last name Barres by using the possessive *Barres'*. Put the apostrophe in the right place, please.
7.25.2006 4:14pm
Donald Kahn (mail):
"social forces that hold women back from an early age..."

Balderdash. How can any serious observer write this when the number of females attending university is a majority? Barres, it appears is just one more scab-picker.

I'll give you a reason why most top class mathematicians are men:

Mathematics is a solitary pursuit: almost a characterological peculiarity. (No one seems upset that the great majority of stammerers are boys.) Women, who are known to be more adept at interpersonal relations, most likely choose branches of high science more in keeping with this inclination: for example, medicine and medical scientific research.

Why should anybody, other than sad cases like Professor Hopkins, care about numbers? All that is required is that candidates receive access and encouragement for their innate skills. That is what Summers should have said. Lacking the skills of, say, a courtroom lawyer, he booted it.
7.25.2006 4:14pm
Nothing Rhymes with Orange:
Hmmm. Should have said, "Use the correct form, please."
7.25.2006 4:20pm
John (mail):
The M.A.A., which runs the competition, awards William Lowell Putnam "fellowhips" to the top five finishers, who are listed here (going back to 1938): http://www.maa.org/awards/putnam.html

There are no other "winners."

In 1992, an "Elizabeth Lowell Putnam" prize was added for the top scoring woman. (The fellowships and Elizabeth Lowell Putnam prize are described here: http://math.scu.edu/putnam/prizecJan.html)

I don't know why the Elizabeth Lowell Putnam prize was added.
7.25.2006 4:57pm
The Real Bill (mail):
D. Kahn said it well, but I'll still give my (simple) opinion:

Boys like math more and girls have better things to do. Unless you are the loner type, advanced mathematics just isn't for you.
7.25.2006 5:03pm
orson23 (mail):
Steve write (above, first quoting from further above)):
"'But I am sure everything published by the scientific community about the 'fact' of global warming is correct."'

"Interesting point. Kind of highlights the importance of peer review, which leads to errors being identified and corrected."

Which it has not led to, in the case of global warming.

The latest twist in the anthropogenic climate warming debate finds that the Hockey Stick study (by Mann, et al) in 1998 - which became an icon in the IPCC (ie, UN) report of 2001 - showing that the 1990s was the hottest decade in the last thousand and later (1999) two thousand years, is wrong.

It took the Wegman report - a pro bono committee headed the National Academy of Science's chair of the Applied Statistics section - to proclaim this totem of a small portion of climatology's total work as unverifiable bunk.
(See links at http://www.climateaudit.org)

Where have the news stories on this been (it's two weeks old? They are, as of today, non-existent. Which is why this is real news to everyone reading this thread.

As Deborah Rumsey write in "Statistics for Dummies": "Statisticians...think of themselves as the keepers of the scientific method." Touche! Lord knows we can't count on scientists corrupted by the $6.5 billion (FY2007) in federal monies spent on this problem to fessl up to the truth.
7.25.2006 5:19pm
zzyz:
Anonymous: Individual rankings for the Putnam are not released (though the scores are, anonymously). The order of the listing in the individual rankings is alphabetical within each grouping.

E.V.: Perhaps the top 15 is what Prof. Barres was referring to by the "winners", but it's not consistent with my understanding of how the Putnam is scored. I think top-five and top-25 are both more defensible categories to consider the "winners". (Note that this has no effect on the underlying conclusion about the gender balance.)
7.25.2006 5:44pm
Donald Kahn (mail):
Real Bill- Glad to have company. Many thanks.
7.25.2006 5:44pm
dearieme:
Nature was wrong and should be ashamed of itself. Now, the big point here: Barres' and Barres's are both valid possessives for Barres, at least in good English. (Oh all right, in British English. Ain't it so in the US?)
7.25.2006 6:04pm
Steve:
It took the Wegman report - a pro bono committee headed the National Academy of Science's chair of the Applied Statistics section - to proclaim this totem of a small portion of climatology's total work as unverifiable bunk.

Right, except the conclusion of the "hockey stick" study has been separately confirmed through multiple independent methods of analysis, so even if you toss out all the "hockey stick" data entirely, the conclusion is still that the late 20th century was the warmest period of the last 1000 years.

All part of the scientific process. Now, since aspersions have been cast upon the methodology of the "hockey stick" study itself, I understand why skeptics would want to claim that the hockey stick is the sole edifice upon which the entirety of global warming theory rests, but that ain't so. See here if you're actually curious.
7.25.2006 6:05pm
Bjartur:
Here is Prof. Hans von Storch's comments on Nature's (and Science's) math and methodology from the recent congressional hearings on the broken hockey stick/global warming):

"Another relevant aspect is the functioning of the two prestigious journals "Science" and
"Nature". The journals enjoy high esteem within and outside of the scientific community as
having the highest scientific standards, which is not always the case. The contents of Nature and
Science also receive exceptional attention in the media world-wide. However, different from
"normal" scientific journals, the editorial decision to accept a scientist's contribution to Science
or Nature is also based on the newsworthiness of the research contribution. The presented results
must not only be valid and innovative but must also be of interest for a wider community of
readers. Such a criterion is reasonable from a economic point-of-view, but it clearly introduces a
filter in what is reaching the public is not solely based on the scientific merit of research.
Research results with stronger media appeal fare better in this competition of scientific findings;
results biased towards higher sensitivity to human interference are more interesting to a broad
audience than findings that report low sensitivities. In addition, there may also be a bias towards
certain authors, who are well known, because they enjoy public visibility, or command appealing
writing skills, "sell" well. Sometimes such contributions are invited.
Another problem with the same journals is that their articles must be relatively short so that
technical aspects cannot be described in any detail; indeed, the MBH publication was cursory on
the methodical side -- thus the statistical method, the validation and the reproducibility, have not
been seriously subject to the review process. Ironically, after publication in "Nature" the method
was considered "peer-reviewed" and thus valid. However, this was not the case, as the method
had not been properly described."
7.25.2006 6:40pm
Toby:
Kahn has it right.

1) Males are characterized (in almost all species - but the few outliers are informative) as having a wider bell curve than females. This means more Geniuses of whatever kind, (whether usefull or rain-men) and more idiots.

2) Anyone who has been to a parent-teacher conference in the last 20 years knows that the teacher will natter on and on about taking care of the girls first, even if the student the parents are interested in is a boy. How this can be persistently holding girls back is beyond me.

I want to know when the girls will break free of their fierce conditioning that holds them back from equal oportunity to commit felonies after dropping out of school. Clearly until this is dealt with, the upper reaches of organized crime will not have a representative number of females.
7.25.2006 7:06pm
Sidebar-for the other half (mail) (www):
Why this intense interest in proving that men are inherently smarter than women (especially when it comes to math and science)? And why is it that nearly all of the people that purport to offer "rational" comments regarding the inherent inadequacy of women, the failure of women to make it up through the ranks, the biological weaknesses of women--are men?

And, someone above raised a good point--that the data discussed in this post is meaningless absent information re: the number of female humans that actually entered this contest. If the ratio of men to women was 75/25, then of course the likelihood that ratio of women in the top 15 will be lower than that of men increases.

Bottom line--men and women are different--and our society views them differently as well.

And, one man is different from another just as individual women are different from one another. Of course hormones affect the way that our brains function. And, of course our environment and culture also affect the decisions that people make throughout their lives.

There's no way to effectively separate nature from nurture in these discussion. Why insist on trying to do so--if not to try to prove the innate superiority of men. But, if that's the goal, then by all means, don't let me interfere.
7.25.2006 9:53pm
David M. Nieporent (www):
Why this intense interest in proving that men are inherently smarter than women (especially when it comes to math and science)?
Sigh. You've managed to be yet another person who has missed the point. "Inherently smarter" is not correct. Nor is "innate superiority."

When you understand the difference between that and the actual topic of discussion, then you can discuss it usefully.

There's no way to effectively separate nature from nurture in these discussion.
But in fact there is.
Why insist on trying to do so
Aside from the general pursuit of knowledge, because it matters. If the "biological explanation" is true, then Harvard is wasting fifty million dollars.
7.25.2006 10:51pm
Reader55:
"Why this intense interest in proving that men are inherently smarter than women (especially when it comes to math and science)?"

That's not the argument however. The question is how is intelligence distributed in each gender? The theory is that in terms of ability the bell curve for males is much wider and shorter than the one for females. The average intelligence of all individuals of both genders may be identical, but the distribution is not.

Why? One theory is competitive reproduction. Females can reliably count on being able to breed regardless of how exceptional they are. Genetically it doesn't make sense to go for broke--it's a safer strategy to reliably aim for the middle.

Males on the other hand are a different story. A male who is only mediocre stands as much chance of reproducing as one which is genetically weak or defective. The alpha males will hog all the available females, so there is no point in playing it safe.
7.26.2006 9:32am
Colin (mail):
Why? One theory is competitive reproduction. Females can reliably count on being able to breed regardless of how exceptional they are. Genetically it doesn't make sense to go for broke--it's a safer strategy to reliably aim for the middle.

I see a lot of just-so stories like this, but no actual research...
7.26.2006 1:03pm
Sidebar-for the other half (mail) (www):
"Why? One theory is competitive reproduction. Females can reliably count on being able to breed regardless of how exceptional they are. Genetically it doesn't make sense to go for broke--it's a safer strategy to reliably aim for the middle."

I'm not so sure about that. I know a lot of men who are complete idiots who have fathered more kids than I can count. Anecdotal indeed.
7.26.2006 3:07pm
Sidebar-for the other half (mail) (www):
"Males on the other hand are a different story. A male who is only mediocre stands as much chance of reproducing as one which is genetically weak or defective. The alpha males will hog all the available females, so there is no point in playing it safe."

Yep--should have included that quote as well in the comment above.
7.26.2006 3:08pm
John Armstrong (mail):
Sidebar: I have to second Reader55. The interest is not to show that one sex is "inherently" better than the other, or even to attempt that. You're reading two facts into the position that are simply not there (though I admit that there are some who are actually sexist).

(1) The purported difference is a universal.

As covered, the difference in direct question is not even of mean. The model proposed for testing says that on average the sexes perform the same, but that standard deviation for males is higher than that for females. The result is that whatever "innate mathematical ability" exists, there are more males at the very highest and very lowest level. If you only look at the top end, there seems to be an imbalance.

(2) The purported difference is deterministic.

Nobody worth listening to is seriously saying that the biological predisposition to "mathematical ability" (whatever that may be) is the largest, or even a major, determining factor for mathematical achievement. Yes, sociology has a lot to do with it, but Ph.D.-level mathematicians at top schools are so far out on the Bell curve that tiny differences going in can have major effects coming out.

The problem at hand is that one side believes that even asking these questions is inherently wrong, and that side has completely abandoned the underlying positivism (philosophical sense) of modern science and academics at large.
7.26.2006 3:32pm