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January 25, 2005

Comments

Whenever I point out elementary mistakes I'm always worried I'm making one. "Fact Check This" is pretty funny in a sad way.

Yeah, I live in fear of doing that sort of thing. But what surprised me about this one was that, in general, I think it's a lot harder to make this kind of mistake -- a mistake that involves as estimate being off by (probably) an order of magnitude, in your own discipline. You'd think he would have said: wait, that has to be too big. That's the part that struck me.

Or to put it another way: I just noticed that Kevin Drum posted on this too, and he points out that if Luskin were right, Social Security payouts will be higher than total payroll. I would have thought an economist would stop short and say: wait, that's got to be wrong.

But in the end, things like major conceptual errors in calculations will, sadly, not matter at all in the debate over what, if anything is "to be done" about Social Security, and its "problems" (real, perceived or imaginary).
This is, after the all, the Bush 43 Administration, whose preferred method of pushing for changes in the nation's fiscal system is to fix the goal first, present a completed plan to Congress, and push for its unmodified adoption using Republican political leverage.
Contrary viewpoints are usually just dismissed, disparaged, ignored, or, more likely, just lied about: preferably by the method hilzoy decries above: the presentation of biased, dubious, or just plain false figures (albeit with some sort of "authoritative" provenance) - and a concerted political and media blitz to portray any and all opposition to Dear Leader's grandiose plans as motivated by mere "Bush-hatred" or mindless obstructionism - and of course, dislike of Dubya's latest catchphrase of "freedom" worked in there someplace.
It's how they pushed through their deficit-monster tax plans; it's how they pushed for the war on Iraq - what reason is there to think that their push for Social Security "reform" will be handled any differently; regardless of the bogosity of whatever numbers are cited?

Blunders of this magnitude show up at NRO with great frequency. While pointing them out is useful, it is also important to emphasize the only reasonable conclusion that can be drawn: NRO is not worth taking seriously on any matter. The only standard they adhere to is whether an article promotes their cause. Accuracy, logic, basic knowledge of the subject are simply irrelevant.

This is important because, sadly, many people do take NRO seriously, and consider their material solid, if ideological.

Is it possible to convince them how objectively idiotic much of the material is, or is that a "typical liberal elitist" attitude, like opposing the teaching of creationism?

Maybe Luskin was thinking of creationism when he wrote "Fact-check that"

"This is important because, sadly, many people do take NRO seriously, and consider their material solid, if ideological."

I think this is a function of authors. I'll take Goldberg all day and ignore Derbyshire at the drop of a hat.

This is the sort of discussion that normally bores me to tears, but it appears that Luskin made a rather stupid mistake. Still, it rather takes some bite away from pointing it out to use phrases like "stupidest man alive". Just sayin', is all. I expect a little more elegant methof of slaying from Professor DeLong.

"He has published an article in which he makes a mistake so basic that it would get him an flunked out of an introductory economics course."

Not for the first time. A previous article showed that he didn't know that the foreign rate of inflation impacts the real exchange rate; this from a guy who wants to take on Krugman, of all people.

Slarti: I think DeLong's title makes more sense in context.

Well, Krugman's committed his own set of mistakes, and given that Krugman's credentials are a little higher caliber, we expect better of him. Don't we?

Not defending Luskin, hilzoy, just wondering when DeLong traded in the rapier for the blunderbuss.

Some of other Luskin's mistakes are understandable as those made by a guy who doesn't really understand what he is reading. For example, his belief that you calculate a real exchange rate by dividing the nominal exchange rate by a measure of the level of prices in dollars--that's how you calculate real wages and real GDP, so shouldn't you calculate the real exchange rate the same way? The answer is no, and if you understood that a nominal exchange rate is a measure of how much pounds cost in dollars and that a real exchange rate is a measure of how much British-made goods cost in American-made goods, you can figure out why not. However, it is an explicable mistake: you can see how it might be made by somebody looking at a bunch of numbers but over his head.

This one, however: this requires that you be ignorant of what "taxable payroll" means. Which requires that you never have read any Social Security Trustees' Report, ever.

Point taken. -- The link you gave actually went to a comment on the Larry Summers comments, which for a slew of reasons I have refrained from commenting on. But here, in an unrelated comment thread, let me just say that when JustOneMinute paraphrases this: "He is probably right that there exist real sex differences, across the entire population, in math abilities, but we know too little about the sources of these differences to be speaking definitively about them in public forums." as this: "Summers is probably right, but he ought to shut up." -- s/he's missing a big point, namely the word 'definitively' in the original quote. I don't know anyone who thinks that it would have been wrong of him to bring up the possibility of genetic gender differences, with qualifications as appropriate to our confidence in our claims and the evidence for them. But I do know people (not at Harvard, haven't spoken to anyone there about this) who object to his having (a) tossed out fairly uninformed speculations on a fairly low level at a scholarly conference; and (b) chosen the particular unhelpful speculations that he chose. (Where this is an objection that would precisely not hold had he made comments that were informed in a serious way by scholarship.) "Shut up" is not at all the point of this line of thought.

You are now returned to the original thread...

My last comment was for Slarti, not Prof. DeLong (welcome :) )

Luskin's field is not economics. He apparently doesn't even have a B.A. in it -- or anything, according to his site*. His field is idiocy, and he is a shining star.

*Not to say you NEED an advanced degree to be educated, but, well, you've already read the entry. Draw your conclusions.

Sebastian,

I think this is a function of authors. I'll take Goldberg all day and ignore Derbyshire at the drop of a hat.

I don't rate Goldberg a lot higher than Luskin myself. He's writing on less technical matters, so the mistakes don't jump out so clearly, but he does often strike me as, shall we say, a logically challenged knee-jerk right-winger.

But even if you're right about Goldberg, is there no such thing as an editor? Is there no one whose job it is to decide what gets published and what doesn't? And if there is such a person, what exactly are they doing?

"I don't know anyone who thinks that it would have been wrong of him to bring up the possibility of genetic gender differences, with qualifications as appropriate to our confidence in our claims and the evidence for them."

There are plenty in the sphere. And as far as I know (not especially), he did "bring up the possibility" etc, even saying he hoped it wasn't the case.

carpeicthus: that explains a lot, but still leaves some questions, like why did NRO hire him? and why did he think he was qualified enough to accept?

Actually, I've thought of an explanation for all this that is both more charitable and more parsimonious: namely, that Luskin's real mistake is not to overlook the difference between a tax base and tax receipts, but to assume that tax receipts are always and necessarily 100% of the tax base. This explains his article perfectly, and it also explains why he isn't more concerned about the fiscal effects of tax cuts (we keep more money, but the government still gets 100%). I haven't checked to see whether he generally argues that government spending is too high, but if so, that would be explained as well: if all government spending is always equal to the value of all income, property, estates, and all the other things that are taxed, plus the deficit, it's got to be too high. And so on.

All that aside, the idea that one ought to fact-check one's own work (or invite colleagues to help out, at least) before publishing it with what amounts to a dare at the end ought to, by now, be burned permanently into Luskin's brain.

Ummm...do you think he'll retract? So far, no sign of any embarrassment over there.

"Luskin's field is not economics. He apparently doesn't even have a B.A. in it"

I believe he has a BS, though.

Heh.

rilkefan: yeah, there probably are such people out there (I mean, there's every other kind), but I've heard more criticisms along the lines of this from Pharyngula"

"People weren’t irate because Summers presented a tentative hypothesis, but because Summers, an administrator with much clout in hiring and firing, presented a badly formed hypothesis with no evidence to support it, that contradicted what we know about the complexity of biology, and he misrepresented it as the result of current, “cutting-edge research.” "

Or this from the original Globe piece: "''Here was this economist lecturing pompously [to] this room full of the country's most accomplished scholars on women's issues in science and engineering, and he kept saying things we had refuted in the first half of the day," said Denton, the outgoing dean of the College of Engineering at the University of Washington."

(Think about this, also from the Globe article: "In his talk, according to several participants, Summers also used as an example one of his daughters, who as a child was given two trucks in an effort at gender-neutral parenting. Yet she treated them almost like dolls, naming one of them ''daddy truck," and one ''baby truck." " Haven't you spent half your academic life having the idea of basing your views on anecdotes like this drummed out of your head? Would you say this at a conference, especially if you were speaking outside your field? I wouldn't.)

When I run across complaints about the content of what he said, they have tended to be the sort that you'd only make given the background assumption that what he said was unscholarly. (Compare: "if you had to just make something up, couldn't you have come up with something that wasn't hurtful and insulting?" I take it the point of that complaint would not be: you must never ever say hurtful and insulting things, however justified. The 'if' clause is key.)

Again, not to deny that there are people making other objections out there. It's just that I haven't encountered them in my cloistered effete ivory tower world ;)

About this part of my last comment: "Compare: "if you had to just make something up, couldn't you have come up with something that wasn't hurtful and insulting?" " -- When I was originally writing that comment, I was thinking of an analogy like this: you (gentle reader) and I are at some party; the conversation flags uncomfortably; I say something just to fill up the awkward silence, something that isn't true and is moreover insulting and hurtful to you; and then you say: "if you had to just make something up, couldn't you have come up with something that wasn't hurtful and insulting?" I started to write the detail I just wrote, decided it was too long and awkward, and cut it out. Then it occurred to me that that comment could be read to refer to Summers (he made things up, etc.). That's not how I intended it at all.

For the record.

"presented a badly formed hypothesis with no evidence to support it, that contradicted what we know about the complexity of biology, and he misrepresented it as the result of current, “cutting-edge research.”

AFAIK all of the above is incorrect - since a greater variance for male mammals is a) expected given their chromosomal setup b) sensible from an evolutionary perspective c) observed, and since some of the above was discussed at the conference, which was d) purposefully off the record so difficult matters could be discussed freely.

(The truck stuff was dumb, but not walk-out-before-fainting dumb, esp given d).)

On the other hand, since you know orders of magnitude more biology than I ever will...

Luskin is an idiot. But then, so is Brad DeLong! I give it a day or two before someone points out something insanely stupid contained in his latest gem.

When two drooling idiots are in a mud fight, it's best not to pick a side, just to enjoy the show and laugh at whomever wins.

rilkefan: FWIW, I thought the problem was less with the suggestion that there are genetic and/or neurological differences between men and women, and more with the idea that we have any reason at all to believe that these explain the fact that there are more men than women in fields like physics. (Or, to be clear: that it might turn out that genetic differences explain some possibly tiny proportion of the disproportionate number of men, sure. That it plays a major role, I don't think we have any reason at all to say.)

The truck bit was dumb, but so was this: "Summers said cutting-edge research has shown that genetics are more important than previously thought, compared with environment or upbringing. As an example, he mentioned autism, once believed to be a result of parenting but now widely seen to have a genetic basis." -- Autism was thought to be the result of parenting ("refrigerator mothers") in the 50s. It has been known to have a genetic basis for decades. I mean, I am not an expert on the biological basis of gender differences, but when I read the account I thought: gee, even I can see why a lot of this is wrong; so why not just say that this is an important issue, and then explain why, and then say how much you therefore look forward to the results of their work?

Of all people, one of my dissertation advisors had a really good comment on this here. -- And it's an odd world when your dissertation advisor starts showing up on blog comment threads.

Luskin is an idiot. But then, so is Brad DeLong!

Umm...isn't this a fairly blatant posting rules violation?

"I thought the problem was less with the suggestion that there are genetic and/or neurological differences between men and women, and more with the idea that we have any reason at all to believe that these explain the fact that there are more men than women in fields like physics."

My version of what I hear (e.g. from the Slate article) - Summers said the disparity came from a) the 80-hour work week demanded at elite institutions b) discrimination c) possibly some component of genetics, but he hoped not. It seems to me that Summers's views have been distorted a great deal in various blogs. Of course there's no transcript, so...

_The Empty Fortress_ was 1967, but yeah, not a cutting-edge comment.

What's quite interesting to me is why math and physics vary from biology (I did a few hours of work on a bio project at Stanford and saw way more women than I do at my job) which varies from law/medicine.

By the way, ever think about how fun a job at Bio-X might be?

Slartibartfast,

The reason the Luskin blunder about real exchange rates stands out, for me, is the fact that his target (as so often) was an economist famous for his work on foreign trade. It takes exceptional stupidity to tackle an acknowledged expert on his home ground without bothering to learn basic facts about the subject.

As to the link, it is quite usual for a Krugman column to inspire a blogger to post a critique which said blogger considers devastating. (This effort looks underwhelming but that's OT.)

In any field a guy with a high profile can expect lots of this. When Oscar Wilde was at the height of his popularity critics churned out numerous carpings about how facile his plays were. One dissenter remarked "I seem to be the only man in London who can't write an Oscar Wilde play."

The dissenter was George Bernard Shaw.

Hilzoy, I didn't know Hamilton Lovecraft was your thesis advisor!!

Oh, or were you talking about that Scanlon guy?

Oh, nevermind, I see now that Yglesias has permalinks to comments, and you tried to link to the right one but a gremlin intervened. I thought we were meant to figure out which commenter was the advisor. Consider my sorry attempt at humor retracted.

rilkefan: from the Globe again (I keep citing it since it is, as far as I know, the original reporting):

"He offered three possible explanations, in declining order of importance, for the small number of women in high-level positions in science and engineering. The first was the reluctance or inability of women who have children to work 80-hour weeks.

The second point was that fewer girls than boys have top scores on science and math tests in late high school years. ''I said no one really understands why this is, and it's an area of ferment in social science," Summers said in an interview Saturday. ''Research in behavioral genetics is showing that things people previously attributed to socialization weren't" due to socialization after all.

This was the point that most angered some of the listeners, several of whom said Summers said that women do not have the same ''innate ability" or ''natural ability" as men in some fields. (...)

Summers' third point was about discrimination. Referencing a well-known concept in economics, he said that if discrimination was the main factor limiting the advancement of women in science and engineering, then a school that does not discriminate would gain an advantage by hiring away the top women who were discriminated against elsewhere."

The point being, in order of importance, genetics first, then discrimination. Also, I thought the econ point was odd: saying 'competitors who do X gain an advantage, so if X offered an advantage, more competitors would do X' makes most sense for Xs that you can just decide to do, or at least clearly identify once someone else does them. I do not think 'stop discriminating' is among these things, once one moves beyond really overt forms of discrimination and into the realm that's presumably at issue here.

I can point to a field in philosophy (Kantian ethics) that's now stronger than a lot of others in part because John Rawls (my other dissertation advisor) was a deeply fairminded person who didn't have to try not to discriminate against women. As a result, a lot of very strong women philosophers (I'm leaving me out of it) blossomed under his tutelage, and became some of the best ethicists out there. (Also a fun example since people who talk about 'women's distinctive moral voices' always say that men are more focussed on principles and women on relationships, and yet Kantian ethics, in which women currently dominate the field more than any other, is the most principle-y form of ethics there is. Take that, Carol Gilligan.) But -- the point of this -- it's one thing to notice his success as an advisor, and another thing to replicate it. No one could just decide to do that.

Anyways.

kenB: Scanlon.

Referencing a well-known concept in economics, he said that if discrimination was the main factor limiting the advancement of women in science and engineering, then a school that does not discriminate would gain an advantage by hiring away the top women who were discriminated against elsewhere."

This "well-known concept" is one of those intensely irritating ideas that seem logical only if one overlooks people's actual motives and behavior in favor of some abstract and oversimplified notion. It argues that the bigot pays a penalty for discrimination, and that this penalty serves to eliminate bigotry. This would be great if it were true, but it's not. Bigotry may be rewarded as well as penalized, and a glance at the empirical evidence on the matter suggests that, despite many centuries of economic incentives supposedly fighting it, bigotry lives on.

BTW, I thought, as rilkefan suggests, that the "innate ability" issue related to greater variance, not a higher mean. What is the status of this argument?

Yeah, it is about greater variance; specifically, about the fact that on math ability tests, more men than women turn up in both the high and low tails of the distribution curve, and that the 'high tail' part of this might explain why more physics professors are men. The counterargument would be, basically, that there's a lot of explanatory distance to travel between 'men are overrepresented among people with alarmingly high math scores' and 'this is why men are overrepresented among physics professors', distance which really no one is in a position to do more than gesture at. I mean, clearly there's more to being a successful physicist than raw math ability (let alone: whatever it is that the relevant test actually measures.) Is it even true that the more math ability you have, the better you do, once you're past a certain (high) threshhold? If no, what's the ratio of women to men among people over that threshhold? Among the other things that affect performance as a physicist, are there others that are skewed by gender (in either direction)? Etc. etc., and on and on. As I said above, what I don't get is why he didn't just say: this is important; I await your work with more than the usual interest. If he had to say more, thoughtful comments about why it matters would probably have been better. And pretty much anything would have been better than talking about his daughters and their trucks before an audience of scientists.

Also, it's my understanding that research on a biological, rather than a social, explanation for greater male variance is lacking. I can spin social stories (Teachers expect boys to succeed in math -- they encourage the high performers to shine and scorn the weak because they don't meet expectations, causing them to fall further behind. They expect girls to do poorly, so they discourage high performers by failing to recognize them, and nurture the weak, which improves their performance) without evidence, and they don't seem to me to be intrinsically less persuasive than the genetic explanations (maybe the gene for math is on the X chromosome! maybe males were more reproductively rewarded for math skills than females!).

Again, to the best of my knowledge, neither the genetic nor the social explanation for the greater male variance is supported by much, if any, hard evidence.

"maybe the gene for math is on the X chromosome!"

I think that's in fact what one version of the hypothesis would be. Men have X chromosomes too. The story would be, a rare X allele is more likely to be expressed in men, hence greater variance. See Gene Expression for links on what hard (not especially I guess) evidence there is.

One needs to consider whether a slight imbalance in high-talent male mathematicians could contribute to discrimination in terms of mentoring/lack of role models/etc or just flocking effects, leading to a large supply imbalance through feedback.

Re other elements of good math profs, I'd suggest ambition, obsession, competitiveness - traits which may be sex-linked.

And the econ story seems not crazy to me in an environment where there is affirmative action.

And finally, arguing in scattershot fashion since I should be working myself, there was a paper at the conference arguing that tenure-level disparities could be explained by the imbalance in the entrant pool, so looking at earlier, even high-school-level imbalances seems sensible.

I know that the X chromosome thing is a possible explanation -- my point was just that evidence supporting it really isn't there. All of the biological stories are perfectly plausible, it's just that they're as unsupported as the social stories.

More so -- the gap in achievement was much bigger in 1950. To the extent that it's closed, we know it was socially caused. We don't know, in the same way, that any of the gap is biologically caused.

And the econ story seems not crazy to me in an environment where there is affirmative action.

This statement is not clear to me.

I meant, "affirmative gender action" or something. I'd expect any smart woman math undergrad at a good school to get a lot of attention/encouragement/opportunities and to be fought over on graduation. Not that she wouldn't be likely to run into some neanderthal profs too.

AFAIK no one is asserting that the hypothetical innate difference clearly plays a role - the debate is (or should be) over whether it could.

Again, I'd have a better understanding of where to stand if I had a better understanding of the differences among math and bio and law.

rilkefan: I think you'd be surprised. Attention/encouragement/etc. depends so heavily on the person giving it, and many professors I know just don't think in terms of trying to encourage members of any particular group. This would also have to be counterbalanced against the possibility that being one of a very small number of women in a department would make one very likely to get hit on a lot by the socially maladroit grad students etc. (At least, this is how it played out when I was one of two women in my department as an undergrad, the other being a senior professor who I never met. The grad students and junior faculty who had lives and social skills were fine, but the others -- as best I could tell, I was about the only woman they ever encountered. You can imagine the joys of this situation for yourself.) Also, there's the thrill of sexism, subtle and blatant. In some departments I imagine there aren't any faculty members who make women's lives worse than they have to be, but in many there are, and it would take a fair amount of mentoring to compensate.

In my experience, what really, really helps is having faculty members for whom it's just obvious, too obvious to require an effort, that women are first and foremost people, and should of course be treated decently. The 'too obvious to require an effort part'' needs to be there in order for them to make not a great big effort that screams 'I am a great big effort, gosh what a great person this guy must be for making me' -- which can be sort of offputting in its own right --but to do it right, in both obvious and subtle ways, as a matter of course.

Or to put it another way: when I was the only woman philosophy major at Princeton, during my junior year, this was not an accident. (I mean: that there was only one, of over twenty in my year.) Nor was it an accident that the only woman philosophy major was me: a woman who is a faculty brat, was raised having more or less continuous and delightful arguments with law professors, and who had never been given any reason to suspect that there was anything the least bit odd about that. I have a thick skin to start with, but in this case it would have taken something absolutely huge to make me so much as notice any sexism around me, since it had never really occurred to me that intelligent people acted that way. But in this I was obviously very, very atypical.

AFAIK no one is asserting that the hypothetical innate difference clearly plays a role - the debate is (or should be) over whether it could.

Check out Mark Kleiman. Generally a smart guy, and a decent one, but he strongly implies that he believes the biological explanation for the achievement gap to be well supported: "For excellent evolutionary reasons, human males display higher variance than human females on many important traits, including measures of mental capacity." If he had an open mind to non-biological explanations, the "excellent evolutionary reasons" thing wouldn't make any sense. (He may, in fact, have an open mind and just be writing sloppily, of course.)

No one that I have seen is discouraging research into possible biological explanations of the achievement gap. What pisses people off is the unstated or half-stated assumption, like Kleiman's, that the research has been done already, and we know that biology accounts for a significant portion of the gap. It simply isn't so.

hilzoy, you're of course in a better position to know.

LB, I disagree with your reading of Kleiman and (I think) your assessment of "evolutionary reasons".

Well, what do you think he meant by "for excellent evolutionary reasons"? I can't figure what a non-genetic 'evolutionary reason' would be. And I certainly don't se a caveat that none of this is proven -- instead, he's reproving Matt Yglesias, more in sorrow than in anger, for not accepting the research. Research which, as pointed out above, doesn't really exist yet (in the sense of anything that rules out a totally social explanation of the achievement gap).

Note -- I don't think Kleiman is a bad guy, just that he is understandably mistaken about the state of current science in this regard. Lots of people are, and the more people that are, the more it becomes mistaken conventional wisdom.

Can't speak for Kleiman, and I can't claim anything in the same continent as expertise, but I thought that a) mammalian sex chromosomes and b) the usual disparity in the offspring/male and offspring/female distributions are excellent evolutionary reasons for greater male variance in phenotype. Also I thought this is backed up by research in mammals and consistent with what research there is on humans.

And I think "totally rules out" is an unreasonable standard here. Unless I'm mistaken, you're arguing - well, I'd probably mischaracterize your take since I likely don't understand it - so let me just say that it would surprise me if creatures with 1% different genomes showed perfect overlap in the tails of almost any distribution. What effect that has in the current case I obviously can't say, but I don't think it can be dismissed as a possibility.

Hmmm. Do we see a greater male variance in height? More very tall and very short men, while women cluster in the middle? As far as I know, we don't -- the male bell curve for height is about the same shape as the female bell curve for height. So the arguments you give for a greater male varience in phenotype don't apply to phenotype generally. If they do, they've been falsified. If they don't, you need some way to link the arguments to intellectual attributes specifically, and that research hasn't been done.

You have a greater measured male variance with respect to several intellectual measures. That, by itself, does not make a link to the possible biological mechanism you offered. It merely suggests that researching the link might be fruitful. Again, forming a hypothesis: That males' single X chromosome causes the greater male variance in intellectual achievement, does not constitute evidence that the hypothesis is true -- the research still has to be done.

Lack of evidence doesn't mean that the hypothesis is false, either. The greater male variance in intellectual attainment could be biologically caused. Research is a good idea. But Kleiman doesn't seem to be aware that research that actually establishes a genetic cause for the greater male variance has yet to be done. I'm not dismissing the possibility, I'm asking that everyone remember that the status of the biological explanation is still only a possibility.

(BTW, you misquoted me. I didn't ask for research that "totally ruled out" a social explanation; I pointed out that research ruling out a "totally social" explanation, has not been done. If we find out twenty years from now that the difference in mathematical achievement between the sexes is totally due to social factors, it won't contradict a single thing that biologists now believe to be true.)

"Hmmm. Do we see a greater male variance in height? More very tall and very short men, while women cluster in the middle? As far as I know, we don't -- the male bell curve for height is about the same shape as the female bell curve for height."

Since the means are quite different, your "cluster in the middle" description doesn't test the hypothesis. A quick google yielded me no strong evidence (a couple of higher-male-variance links not worth reporting). It's worth pursuing.

Didn't intend to misquote you (not clear to me I did) - but it seems to me you're asking that someone show effect x is 0 before discussing whether effect x is order alpha. Sorry if unclear, dinner time.

As far as I know, we don't -- the male bell curve for height is about the same shape as the female bell curve for height.

IJWTS that although I have no dog in this fight, the statement that probability density functions derived from two independent samples have the "same shape" is tautology. All normal distributions have the same shape.

What I'd question is that they have the same variance. The gauge that I'd use for similarity is whether they scale: whether the variance scales the same as the mean. Obviously the sample of males has a different mean than that of the females. Are you saying it has the same variance? I'd be very surprised if that were true.

IJWTS that although I have no dog in this fight, the statement that probability density functions derived from two independent samples have the "same shape" is tautology. All normal distributions have the same shape.

Which reminds me: did you see my post about the CLT, Slarti? And if so... ummm... what thread was it in again?

Italics B-gone!

Same shape = same measures of spread. A tall, skinny bell is a different shape than a short, fat bell. Sorry if I was confusingly imprecise.

Oh good -- posting comments is working for me again. For some reason I couldn't post earlier this morning.

And I do think that male and female populations have the same variance for height, just different means. Admittedly, my basis for this is "I read it somewhere" in the context of the intelligence debate; I've poked around on the net and can find nothing to the contrary. Under the assumption that positive results (a sex difference) are more likely to be reported than negative results (no sex difference) I think it's very probably true, but I haven't got a link and don't expect anyone to take my word for it.

Donald Luskin has now modified this article and admitted the mistake described in the original post.

Huh. Apparently the modification "does not affect my thesis, so nothing else requires correction and nothing else has been modified in any way." How... steadfast of him.

Hmmm...Anarch, I'll go back and look. If it was the thread that made a glancing reference to a previous thread where I missed something, then I know approximately where to look for it.

About the differences: Kevin Drum linked to this article, which
had some usefull insights IMO.

Dr. Urry cited a 1983 study in which 360 people - half men, half women - rated mathematics papers on a five-point scale. On average,
the men rated them a full point higher when the author was “John T. McKay” than when the author was “Joan T. McKay.” There was a similar, but
smaller disparity in the scores the women gave.

Dr. Spelke, of Harvard, said, “It’s hard for me to get excited about small differences in biology when the evidence shows that women in science are
still discriminated against every stage of the way.”

A recent experiment showed that when Princeton students were asked to evaluate two highly qualified candidates for an engineering job - one with
more education, the other with more work experience - they picked the more educated candidate 75 percent of the time. But when the candidates were
designated as male or female, and the educated candidate bore a female name, suddenly she was preferred only 48 percent of the time.


I thought it was interesting that OECD just
published a report about math and science scores amongst children in two agegroups. In the summary (pdf of 3.5Mb) you'll find a.o.:

PISA found that in most countries males outperform females, but the overall difference is usually not large. Despite the absence of a large overall
gender difference in mathematics as there is in favour of females in reading (see page 32), gender differences in
mathematics warrant continued attention for several reasons:
See Table 2.5c, Fig. 2.18, main report
• The contrast between countries where such differences persist and those where they are not visible suggests that unequal performance by gender in
mathematics is not an inevitable result, and that some countries do provide a learning environment that benefits both genders equally.
• Differences in the picture among different areas of mathematics show that some areas require particular attention. Males are ahead in performing
space and shape tasks in all but five OECD countries: Finland, Iceland, Japan, the Netherlands and Norway. Gender difference is much less
widespread for tasks involving quantity: they are measurable in only 12 out of 29 OECD countries.
• In most countries, the gender differences are larger within schools than they are overall, since females tend to attend the higher performing,
academically oriented tracks and schools at a higher rate than males but, within these, often perform well below males in mathematics. This raises
issues for teachers and teaching.

Gender differences
OECD countries with no statistically significant gender
difference in mathematics overall:
Australia, Austria, Belgium, Japan, the Netherlands, Norway, Poland
In other countries there remains a male advantage,except Iceland where there is a female advantage.


The graph in the actual report is even clearer... the difference in the gender difference is much bigger than the difference in the (high scoring)
countries. So my conclusion is that there might be an inate component, but that the impact of it would be hard to measure against all the other
obviously contributing factors.

dutchmarbel, that 1983 study is indeed damning - would be interesting to see it redone today. Re the other study, I'd be as surprised if there are innate differences in the bulk of the distribution as if there are no innate differences at the tails.

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