Hmmmm . . . I think that, by “males and females,” they mean “boys and girls.”
Anyway, I was interested in this paper (by David Lubinski, Camilla Benbow, and Harrison Kell) because . . . I’m one of the kids in the study. I was 11 years old at the time.
What’s happened since then? According to the abstract of the paper:
Across the two cohorts, 4.1% had earned tenure at a major research university, 2.3% were top executives at “name brand” or Fortune 500 companies, and 2.4% were attorneys at major firms or organizations; participants had published 85 books and 7,572 refereed articles, secured 681 patents, and amassed $358 million in grants. . . .
Wow, we’ve really cost the taxpayer a lot of money!
Seriously, though, this surprised me:
That’s me in cohort 2! I think the categories are intended to be mutually exclusive, so I don’t know if they classified me under “Science, Technology, Engineering, & Mathematics” or “Education: Post-secondary Faculty.”
The thing that really stunned me, though, was that 15% of us were chief executives. Whoa! Although maybe that includes self-employed people who have their own business. It’s really not so clear. “Chief executive” sounds like a big deal to me but maybe I’m missing something.
One thing that seems particularly time-bound is the high rate of people working in law, medicine, and finance. I don’t see a strong connection between those fields and mathematical precocity (ok, maybe in some aspects of finance), but they all pay well, and law and medicine were, at least for kids of my generation, natural fields to go into for kids who were good at taking tests.
Recall that the “mathematically precocious youths” were identified by scoring high on the SAT. So it could well be labeled a study of “youths who were talented at standardized tests.” (But it’s not quite as bad as it sounds. Back in the 1970s, we didn’t see standardized tests very often, so we were taking the SAT cold. It’s not like we were sitting there in elementary school taking practice tests every year.)
Given all these high-powered occupations, I was surprised that the median salary for the married men in my group was only $150,000. And was the top centile only $400,000? Hard to believe, with all those doctors and chief executives in the sample. I can’t quite figure this one out. I mean, sure, $400,000 is a lot of money, but “top centile”—that’s the 99th percentile of income, right? There aren’t 3 guys in this group of 249 married men who are making more than $400K? Interesting if true. I guess these aren’t the highest-paid sort of doctors, lawyers, finance professionals, and CEO’s.
My biggest disappointment with the paper is near the end, when they talk about responses to attitude questions. For example, what percentage of (adult) men and women in our group agree with the statement, “Society should invest in my ideas because they are more important than those of other people”? I’d like to know. But all we are told (it’s in figure 6) is that men are about 0.3 standard deviations more likely than women to answer yes to that question. Sex differences are interesting but I’d like to see the averages too. And they’d be so easy to display!
Where they do display means, in figure 7, the results (and the displays themselves) are pretty boring. The authors have a lot of good stuff here; I’d just like to see more. And of course it’s pretty exhausting to see everything written in psychology-journal style with those p-values all over the place.
P.S. I’m disappointed to see that they reported results to fractional percentage points. “23.6%,” indeed. Couldn’t they have run this by me for comments? This sort of hyper-precision is just embarrassing.
P.P.S. Data-detective Weakliem also is suspicious of the top percentile number. It seems like the authors did make a mistake somewhere. Weakliem writes, “they must have measured income by categories and then applied some rule to translate them into the numbers shown.”
Interesting summary. One thing I’m curious about with the figure you posted is the base rates of these occupations in the population (or at least some estimate). It’s difficult for me to tell from the graph whether having 8% lawyers or judges is higher/lower/the same as the expected rate for any student (or even just reasonably well achieving students). Maybe there’s more in the paper and my comment shows I haven’t read it yet…
Hoping this isn’t violating any kind of copyright law, but one of the authors has the full article on her website: https://my.vanderbilt.edu/smpy/files/2013/02/Article-PS-Lubinski-et-al-2014-DECEMBER1.pdf
I’ve been around so many 800 Math SAT types from the 70’s and an appreciable percent simply could not produce anywhere close to their level of intelligence. Being able to ace the SAT math section (even when done cold) isn’t really predictive of much at all in terms of accomplishment–I won’t say the two are orthogonal but my experience is that it’s not that strong. The point is, the relative lack of income/accomplishment/status remarked on by Andrew I find not at all surprising (the group is doing pretty well–$150,000 median income is in the top 5% or so).
Note that the participants took the SAT when they were 13 or younger. A high score at that age is certainly very predictive of all sorts of adult outcomes: https://www.dropbox.com/s/pninfxyby2sde1d/Beyond%20the%20Threshold%20Hypothesis%20Even.pdf?dl=0
In school they teach (or used to) the three significant digit rule. So you’d report 23.6%, not 24% or 23.63%. etc. I don’t know where this so-called rule comes from, though.
My guess: It comes from slide rules, which normally have about this precision.
Hmm . . . this probably deserves its own post . . .
If you have a physical measurement, sure give as much precision as you have. If a length of wood is 34 7/8 inches, I want to know it. Don’t do me any favors by rounding it off to 35.
The issue is that, in the human sciences, there’s a lot of variation and a lot of measurement error. Put that together and I rarely see fractional percentages that are meaningful.
Here’s a quick calculation. Suppose you have a yes/no response with a sample of 1000 (which is bigger than in the paper discussed above, by the way). The standard error is 1/sqrt(1000) = .03, that is, 3 percentage points. So any fractional percentage point is just meaningless.
But it’s not a general principle about significant digits, it depends on the context.
Nevertheless, I suspect that the percentage of individuals this bothers — besides you — is approximately 0.01%. ;)
Well, I am in that 0.01% also, then. It doesn’t bother me as much as it apparently bothers Andrew, but it’s distracting. And the practical precision is worse than Andrew’s example: this isn’t a random sample of all mathematically precocious kids. If they had tested all such kids in the whole country, instead of “4.1%” being tenured at a major university they might find that it’s 1.5% or 6%.
As Andrew notes, it’s hard to find a general rule that works well but it’s clear (to me) that giving a meaningless digit past the decimal point is bad. It’s not the worse sin in the world.
I don’t disagree that it’s a bit silly to have a useless digit past the decimal point. I guess I just find the vehemence amusing in a harmless sort of way. There are more awful things to worry about in the world, like people who use tabs for the indentation of source code.
+1
Similar reasoning seems appropriate for considering a difference practically significant — for example, in an exam with 12 questions, each marked correct or incorrect, is a difference of .8 points between average scores of two groups really saying anything?
For some perspective, I’m pretty sure I was borderline “mathematically precocious” (always 99th percentile on NY State standardized tests in elementary school, 750 SAT-M in 1982 w/no prep, 5 on AP Calc A/B), but I never enjoyed math much, took none in college, and now I’m a lawyer (who haunts stats and econ blogs).
I always assumed that when they called me “precocious” they just meant that I was particularly obnoxious for my age.
I got A’s in math, but I got a Crocodile in sitting still.
By that standard I’m still precocious.
Not surprising to me that the median is “only” $150,000 (which is still awfully high compared to society at large!) Lots of the occupations one might pursue out of sheer problem-solving love pay in that range or less (like the software engineers and professors so highly represented on that chart).
Indeed, what stands out to me more is how very many more men there are in the most highly-paid categories, and how many more women in the unpaid categories.
I always get a kick out of seeing the various follow-up studies of these cohorts, though. (I missed being in cohort 4 myself by an accident of dates.)
“The average SAT
mathematics score (SAT-M) by age 13 was 539 (SD = 77)
for Cohort 1 males, 509 (SD = 62) for Cohort 1 females,
567 (SD = 65) for Cohort 2 males, and 521 (SD = 59) for
Cohort 2 females.”
A 539 isn’t a great score, except that they are 13. But at 13, some kids may have been pushed in math, others may not have had the ability to be pushed in math. Push is going to be some function of parental push and school quality. So it may be as much a function of environment???
Zbicyclist:
That could be, but I have the impression that pushing kids to take standardized tests early wasn’t something that was done back in the 1970s. I think things have changed (in part perhaps due to programs such as SMPY).
“good at taking tests?” You don’t believe in intelligence? Believe me, the evidence supporting the construct validity of intelligence exceeds that for any other important construct in the social sciences.
Michael:
I think you’re having an argument with someone who isn’t me. Here’s what I wrote:
I think that’s a fair description. I never said anything about not believing in intelligence. It’s perfectly possible to (a) believe in intelligence (in the sense in which I think you are using it) and (b) describe a study of youths who scored high on a standardized test as a study of youths who were talented at standardized tests.
Actually, I think that Arthur Jensen had a useful response to the issue of whether “intelligence” or “IQ” (or g) was the right term to use in these contexts. Basically, his argument was that it is “intelligence” that has no clear meaning, not the other, more precise and scientific terms. Yes, we use the term “intelligence” all the time informally — but that doesn’t entail that it is a term with a definite and unambiguous meaning. We use all manner of sloppy terms in our informal discourse, and we are better off moving past many of them into something more rigorous when we can.
What better can we do, as social scientists, than attempt to quantify certain traits as best we can, and then predict from them important outcomes as best we can? If there’s no better substitute for the predictive trait than IQ or g, why disparage them as representing “only” talent at standardized testing? People have launched a million attempts to come up with a better predictive trait, and have failed utterly. Why not give IQ and g their due? Really, after over a century of attempts to come up with alternatives, it’s all we’ve got.
Candid:
Like Michael, I think you’re arguing with someone who’s not here. You write, “why disparage them as representing ‘only’ talent at standardized testing.” But no one in this discussion ever said that.
Andrew,
I wasn’t really arguing that you, in particular, were disparaging talent at standardized testing (though I can see how you might have taken it that way). I mainly brought it up because it is an exceedingly common point of view, and worth refuting.
My larger point is that it is really, after over a century, all we’ve got — and it tells us a lot. Pitting that talent against “intelligence”, with the assumption that our intuitive and subjective assessment of “intelligence” is more important and more on track, is to miss the point of what that century of work has told us.
I think Arthur Jensen was completely wrong on this subject.
This is a subject better left to another post, but I think “intelligence,” like “athleticism” or “creativity,” covers such a broad swath of territory that it’s as silly to try to precisely quantify it as it is to pretend it doesn’t vary between people.
To go with the “athleticism” analogy, the decathlon is scored by summing the scores across each of the ten events. Scores are highly correlated among some of the events: scores in the 100m dash, 110m hurdles, long jump are highly correlated; so are scores in the shot put and discus, and to a lesser extent the pole vault). But scores in the speed events are poorly correlated with scores in the strength events. Sure, you can add a bunch of scores together and define the person with the highest score to be the “greatest athlete”, but in some alternate universe the scoring system is different or the mix of events is different and somebody else wins that title. LeBron James is clearly a better athlete than I am, because he can (I suspect) outperform me at _every_ athletic contest that could be devised except frisbee throwing. “Athleticism” is a useful and meaningful concept. But if someone wants to claim there is some underlying “athleticism factor” that they can measure with a battery of tests I think that is obviously nonsense.
Similarly, Andrew could outperform some 13-year-olds at just about any cognitive task — he and I were already friends then so I know this is true — so he was clearly “more intelligent” than most of them. But there were others who were better at him at some cognitive tasks and worse at others. As with “athleticism”, “intelligence” is a useful concept that does mean something, but it doesn’t correspond to a single real “thing”. At this point it is irresistible to quote Alfred Binet, godfather of modern intelligence testing, who was well aware of the perils of summarizing a highly dimensional attribute with a single number: when asked to define intelligence, he said “Intelligence is what my test measures.”
But…to try to avoid having this comment string get completely off-topic…by saying “good at taking tests” Andrew isn’t saying everyone is equally intelligent. Some people are good at taking tests because they’re more intelligent than other people!
Phil,
The deepest problem with your analogy, and your overall argument, is that the supposed “multidimensionality” of “intelligence” is exceedingly difficult to find in any empirical study.
It is a remarkable fact — one of the more surprising in social science — that so much of what we loosely categorize as “intelligence” seems to reduce in very large measure to one number: g (more precisely than IQ). Yes, we can find some wiggle room between various aspects of g, such as crystalized g and fluid g, and between mathematical ability and verbal ability, and between verbal IQ and performance IQ. But by far the dominant effect is captured by one number, corresponding to the degree of g, the generalized factor. Over the previous century, countless attempts have been made to get out of the grip of this one number, and to find alternate measures that seem to correspond to a component of “intelligence” as we loosely think of it. But they have all failed utterly to find a significant and significantly independent measure that has any kind of real predictive value for the outcomes we care about, such as academic and economic success. This is all remarkable, but it also all true. The reducibility of so much of this domain to a single measure is one very good reason to dispense with the term “intelligence” –especially as it is employed as some kind of grab bag for cognitive ability– as useful, particularly if we have any desire to be rigorous. g seems to give us everything we should want in that domain, especially if it is supplemented with some further (if relatively minor) “multi-dimensionality” by breaking out verbal vs math ability, crystallized vs fluid, etc.
Perhaps there is some general component in “athleticism” that comprehends, say, strength and speed and general coordination and hand-eye coordination, but I’m certainly not aware of it, and I rather doubt that it would be terribly large. It would be interesting to do such a factorial study of course. But if it really does have the multidimensionality I would expect, then one can see the point of continuing to talk about “athleticism” as some kind of crude function and summary of these component parts.
candid_observer:
Is it so hard to find multidimensional ways in which people vary in ability? or just hard to find ones that “has any kind of real predictive value for the outcomes we care about[sic], such as academic and economic success”
perhaps it’s just hard for those people studying this field to acknowledge that it might be worth caring about things like “visual artistic ability independent of its ability to earn the artist income or points on tests” or “ability to compose amazing complex multi-instrumental jazz ensemble music” or “ability to empathize and provide comfort to people undergoing stressful situations” or “ability to lead people into military battles”, or “ability to dance Argentine Tango with virtually anyone”
Principally because those abilities aren’t easily turned into cash or grades….
I suspect that you’re correct that economic and academic outcomes are both highly correlated and that they correlated and are summarized well by a single scalar constructed from a multi-dimensional set of measurements… but I’m not convinced that all mental talents and abilities are therefore summarized by a single number.
candid_observer:
I’ve heard it said that g is a very good predictor of lots of things *if* your population is broad (e.g., “all adults in the U.S.”), but that if you restrict to smaller populations that are more homogeneous in g (e.g., college students — whose g tends to be in the higher than average range), then the multidimensional view of intelligence gives better predictors and indicators of ability than g alone. (I don’t know references for this — I just remember it being said by a statistician in a course I was auditing once. Can anyone supply references that support or refute it?)
I’m very familiar with the arguments of people who reify “g” and I find them not just unpersuasive but flat wrong.
“Idiot savants” can be very good at some cognitive tasks but extremely poor at others. So I think it’s, well, flat wrong to say ‘”multidimensionality” of “intelligence” is exceedingly difficult to find in any empirical study.’ I’d make a distinction between what I’m saying and the “theory of multiple intelligences” that posits specific “intelligences” that use different “neural pathways” whatever that means. I’m just saying “intelligence” isn’t a single measurable thing any more than “athleticism” is.
Mozart, Newton, Michelangelo, and Shakespeare were all very intelligent people, I think we can agree without requiring a quantitative definition of intelligence. I’m sure Newton could have learned to paint or sculpt reasonably well, Mozart could probably have written the librettos and not just the music, etc. But you’ll never convince me that Newton had the musical genius of Mozart, or that Mozart had the mathematical brilliance of Newton.
If you take a bunch of correlated attributes of people and perform a principal components analysis, you can often find a component that “explains” a lot of the variation between people. That’s true of the decathlon and it’s true of performance on cognitive tasks. I understand the appeal of quantifying that component and calling it “athleticism” or “intelligence”, respectively. But to me that’s just an “intelligence is what my test measures” type of definition.
I’ve thought about this exact analogy and I’d bet real money that some sort of generic strength-to-weight ratio would do the work for athleticism that g does for intelligence — sort good athletes from nonathletes very cleanly at the population level while not measuring the real qualities we call athleticism. Being strong for your weight is a great predictor but is not the thing itself.
> This is a subject better left to another post, but I think “intelligence,” like “athleticism” or “creativity,” covers such a broad swath of territory that it’s as silly to try to precisely quantify it as it is to pretend it doesn’t vary between people.
Indeed. But I might add,
*and* vary “within” people.
Phil, I suspect LeBron is a better frisbee thrower than you, too.
Dan wins the thread with that comment.
A few responses.
Daniel Lakeland,
Most of the examples you raise are not plausible examples of “intelligence” as we ordinarily think of it. Certainly talent at jazz or dance or capacity for empathy don’t fall under the rubric of “intelligence”, but rather are mostly independent abilities. No one really disputes this. The trick is to find something that plausibly falls under that rubric, but is importantly independent of g, and which is predictive of the sort of outcomes we expect to be correlated to “intelligence”. The predictive aspect of suggested alternative traits is particularly telling as to the centrality of g. Any number of tests of seemingly alternative abilities have been composed, often more specific to a job or function than a general test of g, yet, again quite surprisingly, it is the g component of those tests that does virtually all of the prediction of outcome, not the specific component left over after g is extracted.
Martha,
It is actually true that at the higher ranges of g, certain more specific components tend to become more prominent. For example, ability at math vs. ability at verbal material tends to be more easily separable, and the more specific components have greater predictive value than at lower ranges. Nonetheless, even if the multidimensionality becomes more relevant, the number of useful dimensions is still pretty low, and g continues to play a very important role. It’s probably worth mentioning here that one dimension which at all ranges plays an important and somewhat independent role is visual spatial ability. This comes to play in many technical areas, and has clear predictive value in outcomes. This ability (captured in tests typically by the ability to perform mental rotations) tends to be distinctly tilted toward males, presumably based on the need of males over evolutionary history to negotiate far larger regions in hunting and/or control of resources, so that the average male is roughly .7 SD better at it than the average female.
Phil,
Idiot savants are of course an exceptional and pathological case, so present no real counterexample to the significance of g.
And, as I said just above, some abilities are obviously mostly independent of g, such as musical talent or artistic talent, but don’t count reasonably as “intelligence” in any case. And, as I also said above, at the very upper ranges, such things as math ability and verbal ability (both of which reasonably do count as constitutive of “intelligence”) do tend to disentangle from each other, which explains in part the difference between a Newton and a Shakespeare.
As for the “reification” of g, that’s just mostly an independent issue. As I said, there are remarkable facts about g that demand explanation. Why is it that a single component seems to play such a huge role in those cognitive abilities we might deem “intelligence”? Why is it so powerfully predictive of outcomes we care about? Why is it the component that is the most heritable? These facts are all surprising, and cry out for some account. A plausible explanation is that g represents some fundamental biological feature of the brain, and indeed there is increasing evidence that this may be so, perhaps something to do with the myelination of neuronal fibers. If that proves out, then indeed g is “reified” organically.
candid observer:
Re “the average male is roughly .7 SD better at it than the average female” — Is this based on recent studies or on old ones? I have read (sorry, no references at hand — I haven’t looked at this area of research for several years) that the male/female differences in spatial abilities had been decreasing, suggesting that the differences are at least partly a matter of socialization.
Also, my reading (again, from a number of years ago) suggested that male/female differences in spatial abilities seemed to be a function of the ratio of male hormones to female hormones — in particular, that males with high spatial abilities tend to have lower than average male levels of androgens, whereas females with high spacial abilities tend to have higher than average female levels of androgens — but that in the high spatial ability groups, males have higher androgen levels than females with the same spatial ability levels, but it seems to be the ratio that counts, not the absolute levels. (I recall one researcher in this area was Doreen Kimura).
Your assertion that my examples are “not plausible examples of ‘intelligence'” just makes Phil’s point that basically g measures “intelligence” and “intelligence” is what g measures….
in other words, your *definition* of intelligence is basically “what g measures” so we need not discuss any further, since we’re arguing not about substance but about the definition of words.
In my world, the talent it takes to compose and arrange music for multiple people is “intelligence”. The ability to hold multiple lines of music in your head and imagine what they will all sound like is “intelligence”. Beethoven, who composed whole symphonies while stone deaf was highly “intelligent”. But lots of musicians struggle to make money, so it’s not predictive of economic or academic performance.
Also, I’ve been taught Tango by someone who was extremely good at figuring out what the “hang up” was for each student, he could easily choose just the right technique for showing you how to perform a certain set of steps… this talent for figuring out what was needed is clearly in my mind “intelligence”… but you won’t find it predictive of his high school grades, undoubtedly.
There are aspects of athleticism that have to do with strength, endurance, speed, etc, but there are aspects as well, especially in team sports, that have to do with predicting how other players will respond, how best to make use of other players, and how to organize teammates, I imagine it would be similar to skills needed in a Platoon of marines as well… it’s so clearly intelligence it’s just obvious to me, yet you claim it’s “not [a] plausible example”… so we’re arguing over definitions, you’ve defined intelligence to be “what g measures” and then can’t understand why other people disagree with you.
Martha,
Although I haven’t tracked this very carefully, I do have the impression that the estimates of the gender gap on spatial abilities may have in recent years gone down from the rough .7 SD. Oddly, as best I can make out, the best evidence that the gap may be due in significant part to culture is not based on any direct evidence from developed Western cultures, but rather from other cultures, such as the Eskimos (who may have, for all we know, been subjected to very different selection pressures for such abilities across genders in any case).
I do in general find it rather frustrating that more is not known about spatial abilities as a separate cognitive component. Among other things, this means that estimates must be taken with a big grain of salt.
As for the question of the effect of hormones, I think your general impression is consistent with the literature I’ve read on the subject. Namely, and somewhat strangely, the males with the highest level (among males) of androgens don’t do as well on these tasks, but rather those with the lower levels. On the other hand, females with the highest level (among females) of androgens do best. It’s important to remember the salient point that the average level of androgens among males is much higher than the average level among females — as I recollect, by a factor of 9? — so that there is relatively little overlap between the curves, except in more pathological cases (such as Congenital Adrenal Hyperplasia — CAH).
The explanation for this curious (presumed) fact might be that high levels of androgens in males serve a useful purpose in reproductive success, even though it induces some damage to abilities that might otherwise prove useful. Evolution and selection often have only very blunt instruments at their disposal. If all they can readily do is shift the curve of androgens one way or the other, then they will settle on the best outcome overall.
candid_observer, some very respectable scholars might disagree with you on the evolutionary basis of sex differences in spatial ability. For instance, Diane Halpern and colleagues noted that female gatherers may have needed spatial ability as well for various tasks, knitting. There is also the challenge that findings can be explained post-hoc.
For instance, Diane Halpern and colleagues and Steve Ceci, Wendy Wiliams, and Susan Barnett both concluded that the available evidence is not adequate to make strong statements on sex-related variation in spatial ability.
The Halpern et al. (2007) team differed among themselves, with evolutionary
psychologists maintaining that “the male brain is naturally better
prepared to perform some spatial tasks and others who feel the
weight of the evidence is clearly on the environmental side” (p.
24). We endorse their summary position that the available evidence
is insufficient to determine the impact of evolution on sex
differences in cognitive ability, although it presents intriguing
suggestions.” pp. 237
Also, is there really a single best outcome in terms of hormones? There is evidence that the lower normal range is associated with stronger spatial ability and medium-term planning success. Higher androgen levels may be one route, but not the only, one that allows for surivival and successful reproduction of progeny.
candid_observer:
Thanks for your reply.
In my earlier comments, I said nothing about your “evolutionary” speculations. However, since you have added some more, I should mention that I tend to be very skeptical of evolutionary explanations of human behavior and abilities. My skepticism is largely based on my experience with evolutionary biology. In light of that experience, I see comments such as the last two sentences in your reply as viewing evolution in a much more mechanistic and simplistic way than is warranted by the randomness and complexity of evolutionary processes.
A few months ago, I saw a review (in Nature or Science) of a book (I forget the author/title) on evolutionary psychology. The reviewer seemed to share my skepticism of the field — he described the “explanations” in the book as “just-so-stories.” That is the way they seem to me, too.
A great excuse to point folks to George Davey Smith’s paper on the wild goose chase of disciplining the random nature of the world with respect to which particular individual will whatever – http://www.dcscience.net/Davey-Smith-2011.pdf
Thanks for the link.
Also of interest: http://arxiv.org/abs/1208.2250
On my desk for Monday morning – thanks.
While “males” and “females” normally makes me cringe, in this case I’m actually sympathetic to that wording. I think “boys and girls” would be awkward here, because the sentence spans not just the point in time when they really are “boys and girls” but deep into the period when they are “men and women”.
“And was the top centile only $400,000? Hard to believe, with all those doctors and chief executives in the sample.”
In medicine, the surgeons, surgical subspecialists, and other procedure-based specialties are the most highly paid. You get paid more for working with your hands than for cognitive work. I think that the cognitive specialties are likely to attract more of these mathematically precocious people. As for CEOs, I know several mathematically precocious individuals (from my own cohort, about 10 years earlier than the ones being reported on here) who are CEOs of small businesses, often in STEM related products or services. They live comfortably, but typically their incomes are in the low, not the high 6-figures. The really big money for CEOs is in Fortune 500 firms–and, indulging stereotypes, I suspect that their ranks are not drawn from the pinnacle of mathematical ability (nor any other particular discipline) so much as from people who are broadly very good but not outstanding intellectually and have strong social skills as well.
+1
In terms of “being good at taking standardized tests,” it is of interest to note that participants in the profoundly gifted cohort 3 were 500 times more likely than the typical test taker to earn a perfect score on the GRE. Clearly, these participants have strong skills in areas related to verbal and quantitative skills. But the odds ratio on perfect GREs are higher than many outcomes they documented.
It is interesting that with CEOs in “name brand” organizations that more did not earn very high incomes. It does deserve mentioning that a lot of rich people get their money from capital gains rather than wages.
There’s something wrong with the income numbers. According to Figure 2a, the top centile cutoff for married men in both cohorts is about $400,000. But the top quartile median, which would be the 12-13th centile, is also about $400,000 in both cohorts, implying there’s a big clump earning almost exactly $400,000 and almost no one earning much more than that. Given the typical distribution of top incomes, that’s not credible. So they must have measured income by categories and then applied some rule to translate them into the numbers shown. But they don’t give any information on those points.