Wednesday, July 30, 2008

Statistical Tests Shows Greater Male Variance

The table above is from the new study in Science Magazine "Gender Similarities Characterize Math Performance" (abstract free, $10 for full study) recently discussed here on CD, in the WSJ, and on Marginal Revolution.

From p. 494-495 of the study: "The hypothesis that the variability of intellectual abilities is greater among males than among females and produces a preponderance of males at the highest levels of performance was originally proposed over 100 years ago. The variance ratio (VR), the ratio of the male variance to the female variance, assesses these differences. Greater male variance is indicated by VR > 1.0. All VRs, by state and grade, are >1.0 (see table above). Thus, our analyses show greater male variability, although the discrepancy in variances is not large (bold italics added)."

Actually, I don't think
that is true, I think the difference in male-female variances IS very large, and is stastistically significant at the highest possible level of significance (.001 level). Here's why:

The statistical test for differences in variance is conducted by comparing the variance ratio to the critical values in an F-test table (test explained here and here), adjusted for sample sizes. Comparing the Variance Ratios in the table above (from 1.11 to 1.21) to the critical F-value of 1.06 for the .001 level of significance with large sample sizes > 1000 (F-table here), suggests that ALL of the variance ratios in the table above are statistically significant at the .001 level of significance.

In other words, the variance of male intelligence (based on standardized math tests) is significantly greater than the variance of female intelligence at even an early age (second grade), at the highest possible level of statistical significance (.001), and the statistically significant difference in male-female variance actually gets greater over time.

Bottom Line: The authors of the study apparently made a conclusion based on "eyeballing the data" ("the discrepancy of variance is not large"), when a statistical F-test of differences in variance shows that the discrepancy of variance is actually VERY LARGE, and is statistically significant at the .001 level (meaning that there is only a 1-in-a-1000 chance that we would find these results purely by chance, and a 99.9% chance that we have established a statistical difference in variances).


At 7/30/2008 8:35 AM, Anonymous Anonymous said...

Let me play devil’s advocate with some emotional connotation. Are we defining the term “intellectual ability” as student performance on a standardized math test? (On line 5 of your post) Why would mathematically ability—that males allegedly excel at—take precedence over verbal ability—that females allegedly excel at? Is there empirical evidence of a linkage between intelligence and mathematical ability? If not, it would be scientifically accurate to separate those words: Would it not?

While the data are probably accurate, I would have to question the credibility of an analysis that does not find the results statistically significant. Professor Perry’s interpretation of the results is statistics taught in a beginning college course. In fact, I got some of my statistics knowledge in his class: Thanks professor!

At 7/30/2008 8:47 AM, Blogger Mark J. Perry said...

This study, and many other studies, and Larry Summers in his talk that led to his firing, are specifically addressing the issue of: underrepresentation of women in science, engineering, and mathematics careers, especially in universities like Harvard and MIT. In that case, intellectual ability measured by performance on a standardized math test would seem to be relevant and valid test of intellectual ability.

At 7/30/2008 8:51 AM, Anonymous Anonymous said...

I've tried to find an article that Science Magazine put out maybe 5-7 years ago that showed that by putting together about seven IQ tests they found that at the upper reaches of IQ (I don't remember where that cut off was) that there at seven times more boys than girls.

By the way this 7:1 ratio shows up in the real world: CEO's, game show winners, senators, etc.

The people who come up with this politically uncorrect but actually correct data are in a real bind. Their squirming is very telling as it shows their biases. (Not unlike what goes on in the Global Warming Religion.)

At 7/30/2008 9:11 AM, Anonymous Anonymous said...

Professor Perry: Thanks for the explanation. It makes perfect sense in that narrow context. As is often the case, when a broader context is used, or more esoteric information is involved, misinterpretation of facts easily happens. Political correctness is one thing, but unintentionally upsetting other people is quite another.

At 7/30/2008 9:20 AM, Blogger Matt S said...

Men, we're both the smartest... and the dumbest.
A higher proportion of nobel laureates, and prison inmates.
ah well.
I think the reason that people are up in arms is, like I said, the fear that instead of treating people equally and giving girls a chance to try to be that smart girl in the sciences, people are just going to shut them out.
I hope not.
Anyways, you can often make up for lack of genius-level skills by working really hard.
The person who was second in my HS graduating class was a pretty smart girl, but her real intelligence came from being able to multitask, understand what the teacher wanted, and work her ass off. She probably would have been valedictorian if she didn't take a basic art class freshman year. She lost out because my valedictorian friend is one of those wonder geniuses who have incredible amounts of brainpower coupled with the complimentary budding psychoses.

At 7/30/2008 9:35 AM, Blogger GW South said...

Walt's 1st Post - Absolutely correct. I took a data processing course recently in the fall of my sophomore year (with a Geography focus) and everything that Prof. Perry detailed I could easily understand and recognize. This was stuff I was taught in the first few weeks of the class, and it's amazing how a scientific study would not incorporate a simple F test. Hell, just get some graduate student to do it.

This reminds me of a Time Magazine cover I once say - which was "Men and Women are Differant". It was about a study that concluded that men and women are born differant, and raising a girl the way you'd raise a boy wouldn't mean that she'd be more likely to get in a fist fight instead of hold it all in and be passive agressive, or be less likely to cook, etc. What I found interesting was that the Time editors found this to be such a shocking revelation, that they had to put it on the front cover. What a joke - it's almost as if we're supposed to believe that every race/gender has the exact same traits. What's wrong with being differant?

At 7/30/2008 9:51 AM, Anonymous Anonymous said...

Is it relevant that the five researchers who analyzed the data and found “variation differences not large” in standardized scores between male student and female all have female-sounding names? Did they miss the statistical significance of the data, or did they slant the analysis to their favor hoping the naiveté of the reader would miss the findings? Either way, there are credibility issues in the report analyses.

At 7/30/2008 10:00 AM, Blogger the buggy professor said...

Thanks for continuing this weighty topic, Mark . . . doubly so because, as you noted yesterday in an earlier thread here, the average politically correct faculty member hasn't even a grasp of basic statistics and what the variance around a mean --- measured by standard deviation (among other things) --- amounts to.


As it happens, the same topic has been unfolding in a couple of threads at the Marginal Revolution site, run by your former Ph.D. superviser --- Tyler Cowen.

With hopefully your permission, I will post here my lengthy commentary left at the M.Rev. last night. Among other things, it cites the Scientific American study that Norman Said mentions without his recalling the name.


1) It is dispiriting, after decades of systematic and replicable research on IQ --- and thousands of articles on the debate --- to see how some people in this thread and a great many other people in our universities and elsewhere deny that there are intrinsic differences in the behavior between males and females that show up within hours of birth . . . and that, additionally, not only is the variance around the shared male-female average IQ of 100 far greater for men than women, but also women continually do better on a battery of verbal and other tasks than men. Oppositely, though, there are "large differences favoring males appear on visual-spatial tasks like mental rotation and spatio-temporal tasks like tracking a moving object through space.”

The quoted words are taken from a prestigious 11-member task force of the American Psychological Association published in a 1995 report entitled "Intelligence: Knowns and Unknowns.

As the panel agreed unanimously, “There are both social and biological reasons “for these differences."

An intrusive personal comment or two before continuing. Those just quoted words from the APA 1995 report --- plus those that follow from the work of Persson Benbow, Doreen Kimura, and Steve Pinker are taken from an outstanding journalistic survey of the IQ gender debate by Stuart Taylor Jr., a journalist who writes for the National Journal and Newsweek. The article in question, condensed from the National Journal, appeared in the Atlantic Monthly in March 2008 just as the Larry Summer affair went sky-hooting toward pc-pietistic-heaven . . . or, depending on your views, pc-crackling-hot hell. ---

I trust Taylor, should he read the comments in this thread, would be happy with my acknowledgement here, along with acknowledging that I have paraphrased a few of his own comments. All the other references have been dug up by prof bug elsewhere and are strictly his own concoction.


2) According to a 1983 study of of 40,000 young adolescents published by four psychologists --- Camillia Persson Benbow and three others --- there was "an exponential intensification" of the male-female ratio in the higher ranges of SAT math scores, with 13 times as many boys as girls found in the highest range. (That was the 700-to-800 range, on tests normally taken by much older students.)” Remember, this and other quotes by Benbow, Kimura, and Pinker are taken from his Atlantic Monthly article of March 2008

Other studies show boys consistently winning a very disproportionate share of the very highest SAT math scores, and sex differences in mathematical precocity turn up in early childhood . . . yes, even before kindergarten.


3) Note that the phrase “before kindergarten” is vague about just how early these differences in test scores turn up. From a biological view, they start spawning in the mental development of females and males in pre-natal life . . . that is, in fetal biology, or so several scholarly studies (including many by women scientists) have found.

As the American Psychological Association report of 1995 observed in this connection: If girl babies have been exposed in- utero “to abnormally high levels of androgens (male hormones)”, they will turn out to perform better than other girls when tested for spatial ability. More intriguingly yet, when women are treated with androgens in the run-up to sex-change operations , they immediately perform better on tests of mental rotation and --- no less intriguing --- they perform worse on tests of verbal fluency. Nor is that all. It turns out that when older males are treated with testosterone, their performances in visual-spatial tests improve.


4) At this point, it’s important to drive home the point that these biological differences between males and females.

Tersely put, if you want more evidence on this latter score, pause and ponder if you will some earlier buggy stuff left in another Tyler-Cowen thread that appeared a few days ago week on the Summers’ flapping fracas. To wit:

“Here is a list of distinguished female scientists who have devoted their working lives to research on the brain, hormones, or behavior --- all of them considered among the leading scientists in their disciplines, and all stressing the behavioral differences (including IQ in verbal vs geometric (math-oriented)tests)due in part to biology:

“Laura Allen, Camilla Benbrow, Laura Betzig, Monique Borgerhoff-Mulder, Patricia Draper, Anke Ehrhardt, Held Fisher, Patricia Coldman-Rakie, Kristen Hawkes, Sarah Blaffer Hrdy, Melissa Hines, Connie Hutt, Julianne Imperato-McGinsley, Carol Nagy Jacklin, Alison Jolly, Doreen Kimura, Annelise Korner, Marie-Christinede Lacost, Jane Lancaster, Jerre Jevy, Bobby Low, Eleanor Emmons Maccoby, Diane McGuiness, Alice Rossi, Meredith Small, Barbara Smuts, Judith Stern, Dominique Toran-Allerand, Beatrice Blyth Whiting, Patricia Whitten, Sandra Witelson, and Carol Wothman.

All of these prominent women scholars are listed at the start of chapter 6 in The Tangled Wing: Biological Contraints on the Human Spirit (revised edition, 2002) by Melvin Konner . . . who holds both a Ph.D. in anthropology and an M.D. degree from Harvard and hass been at Emory University for a fairly long time now.

“As Konner notes in the rest of chapter 6, the differences in boy and girl baby behavior show up --- according to the several studies, including by women --- within even hours of delivery.


We can go farther too.

In particular, consider these remarks taken from an article in Scientific American (May 2002) by Doreen Kimura, a psychologist at Simon Fraser University in British Columbia. "The effects of sex hormones on brain organization occur so early in life that, from the start, the environment is acting on differently wired brains in boys and girls.” (Again, taken from the Taylor Atlantic Monthly article.)


5) What are the evolutionary origins of such differences in our species development?

The answer: these differences derive from the fact that for millions of years, pre-modern and modern humans --- the latter about 100-200,000 years old (cro-magnums, originating in Africa and exiting there, it seems, northward, eastward, and westward around 50,000 years or so ago) --- men were hunters and women nurtured children, gathered plants near their caves and other home-based settings, and were sensitive to signs of debility and weakness in their children (or those of the rest of the clan, roughly a dozen to 60 or 70 in total number, all biologically related).

The evolutionary outcomes?

In time, the better hunters --- who could read and interpret tracks of animals and other signs and see or scent them sooner (as well as show more killing-skills) --- would eventually grow in number and the inferior hunters tend to decline in number and eventually disappear . . . reproduction success, over tens and hundreds of thousands of generations, you see, the measure of such superior biology however acquired: whether by random change, major mutations, genetic drift, and maybe other processes not yet fully understood.

In particular, the superior visual skills and interpretative abilities of the more successful hunters would b handed down over millions of years. And note carefully. By a similar logic, those pre-modern and modern female homo-sapiens with superior verbal and sensory-skills in relating to their children would, over time --- in similar ways --- grow in number and mate more and more with visually and geometrically gifted men.

These legacies would be transmitted over thousands and tens of thousands of generations.


6) The latter point can be nudged a step or two farther.

As it happens, the current female descendants of these earlier and biologically superior women not only turn out to display better verbal and sensory skills than men on an average --- or additionally to relate more effectively than men to their children, to other women and their children (a clan-based evolutionary development, with pre-modern and modern female humans staying close to a clan-based home 24 hours a day, while the men were out hunting often for days on end and remaining silent in their hunting endeavors) --- but also, as it turns out, contemporary women are in Steven Pinker’s words “better [than men] at remembering landmarks and the positions of objects ... more dexterous ... have better depth perception, match shapes faster, and are much better at reading facial expressions and body language ... retrieve words more fluently, and have a better memory for verbal material." (Again, taken from the Taylor article.)


7) Then too, as noted earlier by other posters in this thread, brainy female students who opt for graduate school work tend not to enroll in programs of mathematics, engineering, or the hard sciences (and if it’s the hard sciences, usually biology and genetic research or, if want to include it here, medicine).

Why? Well, quite possibly in certain instances they haven’t been encouraged enough by their parents, peers, teachers, or professors . . . and for whatever reasons, including possibly some patronizing treatment by males as boy friends, teachers, or professors.

Whoa! Despite feminist scare-mongering, there can’t be many teachers or professors like that these days . . . not with the strenuous efforts of all major research universities for three or four decades now to encourage women to enter scientific and math-driven disciplines.

What then instead?

Well, according to the 1983 psychological study by Camille Pereson Benbow and her colleagues mentioned earlier that studied carefully 40,000 adolescent boys and girls, women have more notable verbal skills than men, and they show, moreover, far more interest in careers that deal with people, rather than with things and abstractions , compared to men. As a female social scientist put it (Patti Hausman), "reinventing the curriculum will not make me more interested in learning how my dishwasher works," the social scientist Patti Hausman once said. (Once more from the Taylor Atlantic Monthly article.)


Something else here.

In particular, recall what Steven Pinker was quoted as saying a few moments ago about superior female verbal and people-oriented skills, a result of millions of years of evolution? Well, not surprisingly he also has observed that whereas "large difference in favor of men" in visual-spatial and related abilities is especially important in engineering, mathematics, and certain hard sciences, Pinker explains. “And those are the only academic fields in which anyone has seriously suggested an innate male advantage.” By contrast, since women show "interest in people” than men, "some relatively prestigious professions are dominated by women," including "my own field, the study of language development in children."


8) Given all this, Pinker has rightly noted this about politically correct shibboleths: the pc claim that "the differences between men and women have nothing to do with biology, but are socially constructed in their entirety . . . has handcuff[ed] feminism to railroad tracks on which a train is bearing down." That is the train, it turns out, of scientific truth.

As for the rest of the Summers fracas, keep in mind that he was speaking as the invited keynote speaker of an NBER --- National Bureau of Economic Research --- conference on women and the sciences. I have discussed his speech, his claims, his alternative hypotheses, and the politically correct, totalitarian-like assaults on him and others in university life who don’t share their views --- including yours truly --- in three or four commentaries left the last two days at Carpe Diem, the remarkably informative libertarian site run by Mark Perry . . . a professor of economics and business at the University of Michigan and one of Tyler Cowen’s former Ph.D. student.

Not a libertarian myself, I am happy to reiterate that Mark’s data-driven posts are without parallel in blog-land and --- whether you agree with all of his commentaries or not --- are always illuminating and a prod to self-reflection. Click here for the Carpe Diem thread:


Michael Gordon, AKA, the buggy professor.


PS. The single best survey of evolutionary theory and human history --- modern and pre-modern --- appeared two or three years ago, written by a gifted New York Times science journalist, Nicholas Wade. Entitled “Before the Dawn”, it ranges widely, wears his vast knowledge with deft agility, and is written with a remarkable vigor and clarity. It is also fairly short, an extraordinary tour-de-force. Read it, and your understanding of our evolutionary heritage will shoot up and multiply in all directions. It will likely persuade you, moreover, that any social science that balks at coming to terms with biological influences --- always, remember, interacting with family environment, childhood peers, and our wider cultural and social life --- will be relegated eventually to some sort of intellectual Dark-Age status.

At 7/30/2008 11:57 AM, Blogger Matt S said...

Buggy professor,
thanks for the mini evolution lesson. I guess that really helps explain why my mother knew I had swollen tonsils two years before either my dad or stepdad (all three of them MD's) picked up on it, along with a string of other medicals problems (mostly nonserious) that I've had as part of being a kid.

At 7/30/2008 1:43 PM, Blogger juandos said...

Hmmm, discussing this seems to me a lot like discussing in which direction the sun rises in the morning...

At 7/30/2008 2:11 PM, Blogger Tom Davis said...

Empirically and subjectively, granted, it seems to me that researchers who confuse the terms gender (e.g. masculine or feminine) with sex (male or female) tend to be swayed by social pressures in their conclusions more than those who observe that distinction.

At 7/30/2008 4:51 PM, Blogger Matt S said...

your snark is pretty much the example I was thinking of when I gave a reason why people tread lightly over this issue. people on the far left start being super-PC and people on the far right start figuring out how many buttons they can push without a huge backlash.

At 7/30/2008 5:10 PM, Anonymous Anonymous said...

Some interesting posts here.

With regard to the evolutionary hypothesis, men in western cultures have not been living a hunting and gathering existence for a considerable period of time. The development of agriculture in ancient Ur lead to the rise of specialized trades ie. pottery, metal work, etc.

If one considers the evolution of the russian silver fox, it appears that evolution can actually happen much more quickly than was previously believed. The domesticated silver fox became radically different from its wild relatives in appearance and behavior in only a few generations of breeding for tameness. Variations in fur patternation appeared much to the surprise of researchers.

Can we continue to explain math and spacial acuity in males strictly by reference to the evolution of man? Cro-magnon man also was a great hunter with a far, less developed cortical areas of the brain, the areas that process math and spacial thinking. We must also consider the very limited cortical areas in highly successful predators in other species.

The evolutionary theory does not seem to fully explain the differences between male and female brains.

The assumption that the biological is the only correct view seems to fail to take into account the fact that historically there have been three different interpretations for human behavior, namely, biological, behavioral, and psychological. Research in the area of brain chemistry and the development of tri-cyclic drugs over the last 30 years has elevated the biological model over the other 2 models.

There are still many things about the brain and human cognition that we do not understand. We do not understand for example, why patients respond to both talk therapy and anti-depressants.

At 7/30/2008 7:23 PM, Blogger juandos said...

Hey matt s, do you always have to say something that shows you are so abysmally stupid that it must make your parents cringe in shame?

Is that your goal in life?

"why people tread lightly over this issue"...

People tread lightly over this because like you they are gutless cowards pandering to the politically correct agenda...

Do you honestly think anything being discussed here is new?

Silly lad if you think so...

All these studies were done years ago (repetitively since it was a typical 300 level stats exercise) before sniveling, obsequious obeisance to LOSERS was the norm on college campuses...

At 7/30/2008 7:38 PM, Blogger Webutante said...

As a woman who earned a degree in civil and environmental engineering and loved every difficult minute, I know beyond a doubt that this post is right on. And Larry Summers was fired by feminist vigilantes who want to mold scientific evidence into political correct agendas.

I could care less if men are better, smarter and faster at this than I am. They are and I am at peace with it.

At 7/30/2008 7:45 PM, Blogger juandos said...

"I could care less if men are better, smarter and faster at this than I am"...

Well you might be happy to note that women as a rule could make better fighter pilots (from a physical standpoint) than men are now...

Women handle the stress better and their physical coordination under stress is quite a bit better...

The Soviets proved it (I'm sure to the chagrin to many egotisical male pilots) in the 2nd World War...

At 7/30/2008 10:41 PM, Anonymous Anonymous said...


Women are outgrowing the present incarnation of the feminist movement and its petty atavisms.

A confident, self-possessed adult who is able to reach his or her full potential has very little interest in attacking others.

At 7/30/2008 11:14 PM, Blogger OBloodyHell said...

> A higher proportion of ... prison inmates.

Well, that's not necessarily intellect, although I agree that's also a factor.

Other factors include, but are not limited to: propensity for violence, aggressiveness, individualism, greater risk-taking.

You can wind up in jail for mistakenly thinking you could safely run that yellow light just as you can for being a complete idiot. Maybe 99.9999% of the time you would be right, but juuuuuust one time you hurt someone as a result. You can argue it was stupid, but I say that's just a willingness to "cut it fine" more often which is prevalent in males. One chance in 1,000,000 is not bad odds for most things.


At 7/30/2008 11:17 PM, Blogger OBloodyHell said...

> What's wrong with being different?

Well, for one thing, it fucks up liberal ideas on diversity....


At 7/30/2008 11:40 PM, Blogger OBloodyHell said...

> By a similar logic, those pre-modern and modern female homo-sapiens with superior verbal and sensory-skills in relating to their children would, over time

If you consider this carefully, you can see elements that rationally make sense even if no one has done a study proving them --

If, in pre-medical times, a baby smelled wrong, was making sounds which were juuuussst slightly different from normal, a mother might be able to act earlier to save a child's life -- particularly recognizing the onset of repeatable conditions (i.e., "that sound" meant the onset of a fever and lung infection, so use a poultice on them tonight, even thought they appear otherwise fine), etc., could notably decrease the individual chances of infant mortality, clearly a problem as little as 100 years ago.

I'd also throw out an anti-PC bomb, and that would be why women are more prone to schizophrenia:

If you stop and think about it, childbearing is a pretty dangerous process. Pre-medicine, the chances of dying in childbirth -- esp. with the first child, but even later, given being without modern antisepsis ideas, lots and lots of women would die as a result of having kids.

It seems to me that, once you realize what "causes babies", that to engage in it is basically a substantial risk to your life. If you have a rational view of it, the selfish, rational female individual is going to say "Nope, not me! Not going to have any kids!". Yes, even with the natural impetus against that behavior.

But any woman who actually did that, didn't reproduce.

I'd argue that the nature of things gave favoritism to any female who could look at the data and engage in the mild schizophrenia it takes to say "... but not me".

Such women were more likely to have more kids, and thus more success in passing on their genes, compared to women who were highly rational and fully grasped causation.

As Nicholson's character put it, "I think like a man, but take away all reason and accountability".

Women with reason and accountability didn't have kids.

It was the ones who lacked those qualities who passed on their genes.

No, no proof or justification for that argument beyond reasoning alone, but it makes a great deal of sense to me. Not enough to say it is "obviously correct", but enough that I think someday someone is going to figure out a way to prove it that there is a genetic advantage for any pre-tech culture for a female to "lack all reason and accountability".

At 7/31/2008 8:34 AM, Blogger juandos said...

"A confident, self-possessed adult who is able to reach his or her full potential has very little interest in attacking others"...

O.K. qt, I hear you...

Remember one thing though, hysterically hysteric public pronouncements drive revisionist history...

At 8/07/2008 2:02 PM, Anonymous Anonymous said...

"a statistical F-test of differences in variance shows that the discrepancy of variance is actually VERY LARGE"...

Effect size is NOT the same thing as statistical significance. With a large enough n, you will find significant differences everywhere you look.


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