Michael W. Ferguson writes in The Inappropriately Excluded:
The probability of entering and remaining in an intellectually elite profession such as Physician, Judge, Professor, Scientist, Corporate Executive, etc. increases with IQ to about 133. It then falls about 1/3 by 140. By 150 IQ the probability has fallen by 97%!
Is that claim backed by trustworthy data?
Executive summary of what follows:
What's the actual question?
In order to figure out what would count as trustworthy data to support the article's assertion, let's begin by looking at its argument. It goes like this:
The first claim is (at least approximately) true by definition; IQ tests are designed to give normally distributed results with that mean and standard deviation.
The second claim is the main thing that might or might not be backed by good evidence.
The third claim is simply a matter of calculation, and I believe the calculation is correct. (This is the claim in the body of the question.)
The fourth claim is a reasonable deduction from the previous ones, but we should distinguish between "makes it less likely" and "makes it more difficult" and be aware that correlation is not causation. (This is the claim that might justify "excluded" in Ferguson's title.)
The fifth claim is reasonable if the previous ones are correct, but again there are some caveats. (This is the claim that might justify "inappropriately" in Ferguson's title.)
The distribution of IQ in "elite professions"
The claim I'm going to focus on here is the second: that "elite profession" IQs are normally distributed with mean about 125 and s.d. about 6.5.
More specifically, the most contentious part of this claim -- which Ferguson assumes but never actually states -- is that IQs within the "elite professions" are something like normally distributed. This is the assumption behind the graph labelled "Excluded Hi IQ people", and the assumption behind the claim that within the "elite professions" "99.98% have IQs between 99 and 151".
I do not see any evidence that any of the references cited by Ferguson support this claim, nor does it seem likely on its face to be true.
If this claim is not true, then everything quoted in the question is unsupported: the peak at 133, the 3x falloff to 140, the 30x falloff to 150. All of these figures come from looking at the ratio of two normal distributions.
It's not, on the face of it, a claim we should expect to be correct. IQ in the population at large is approximately normally distributed, but that says nothing about the distribution in a highly-selected population like "elite professions" (whatever exactly that is taken to mean). For instance, consider the toy model where membership in those professions is selected at random from people with IQ at least 120; the resulting distribution will be very far from normal. (It will also, as it happens, have roughly the mean and standard deviation cited by Ferguson, though I don't think it's plausible that the actual elite-profession IQ distribution looks much like this.)
(Ferguson's conclusions are quite sensitive to the exact shape of the distribution at the tails. For instance, people with IQ>150 are about 0.04% of the general population; if Ferguson's claimed normal distribution is right then they are about 0.006% of the "elite professions"; if the actual relationship between the general population and the "elite professions" followed Ferguson's curve up to its peak at and IQ of 133 and then stayed there (meaning no falloff at all, no "exclusion", but the same advantage for someone with IQ 160 as for someone with IQ 133), the figure would be about 0.5% -- which is much bigger than 0.006%, but still very small in absolute terms.)
So, this claim is key to the argument, Ferguson never states it explicitly, and on the face of it it doesn't seem likely to be true. It could be true, even so. What's the evidence?
Evidence from Ferguson's references
Let's go through the references looking to see what they have to say about that claim. In the body of the article, Ferguson cites two studies.
Gibson & Light, Intelligence among university students, Nature 213. The first thing to say is that the title is actually Intelligence among university scientists. Ferguson summarizes their finding thus: "Gibson and Light found that 148 members of the Cambridge University faculty had a mean IQ of 126 with a standard deviation of 6.3." This is definitely misleading in that the study was specifically of scientists. Unfortunately, I don't have a copy of that article and can't find it available online, but nothing I have seen suggests that Gibson & Light look at the shape of the distribution of IQs and find it normal. [EDITED to add:] See below for more about this; another answerer found a copy of this paper and there is actually some information about the distribution in here.
Matarazzo & Goldstein, The intellectual caliber of medical students, Journal of Medical Education v47i2. PDF on Gwern's website. Note that this is about students rather than actual professionals. This article says nothing at all about the shape of the distribution, unsurprisingly since it's mostly aggregating the findings of other studies. It does remark that its first author has found no correlation between IQ and placement in medical examinations, which weakly suggests that if people with truly exceptional IQs are unable to become doctors this may not do much harm to the medical profession.
Other references in Ferguson's article, in order of appearance:
A very general difficulty in this sort of study
Investigations of the sort done by, say, Hauser are very likely to miss very-high-IQ people altogether, unless such people are an explicit focus of the investigation. So, for instance, Hauser looks at the population at large and breaks them down into maybe 10-30 different professional groups. In any of those groups, the extraordinarily-high-IQ people are going to be a small minority; there just aren't many of them in the population to begin with. People with IQ > 150 are about 0.04% of the population. Hauser plots the 90th percentile of large groups like "college professor", and we shouldn't expect that to tell us anything about whether people with an IQ of 150 or more can get jobs as college professors. In the United States there are about 120k people with an IQ of 150+ and about 2M college professors, so even if all the high-IQ people were college professors you still wouldn't see them at the 90th percentile of college professors. If, more realistically, 10% of the high-IQ people were college professors, then they would be about 0.6% of the college professors, and their presence would make rather little difference to the 90th percentile. Or, of course, to the mean and standard deviation.
Finer-grained data from Gibson & Light
A reference I didn't find a copy of, the Nature paper by Gibson & Light, turns out to have finer-grained information about IQ distribution than the others discussed above. See the answer by Taw -- the paper apparently has only a chart, but Taw has estimated the actual numbers by measuring the chart. For a specific group of people (scientists on the faculty at the University of Cambridge), there are figures at a resolution of 5 IQ points; they do in fact look fairly normally distributed, with roughly the mean and standard deviation used by Ferguson.
As Taw says, Gibson & Light's numbers fit a normal distribution well enough that they wouldn't entitle us to reject the hypothesis of normal distribution at the 5% (or even the 15%) level. There is, of course, quite a gap between that and citing them as evidence that the distribution actually is normal, especially at the tails (Gibson & Light have a sample size of 148, and they found no IQs above 145 or below 110). For Gibson & Light's numbers to be strong evidence of normal distribution, we would need that distribution to fit much better than any distribution differing substantially from normal, and we just don't have enough data for that to be the case.
For instance, we get an almost exactly equally good fit (measured by log-likelihood of the observations estimated by Taw from the chart in Gibson & Light) for a pdf that's parabolic but clipped where it crosses 0, with peak at 126.6 and dropping to 0 at a distance of +-15. For the avoidance of doubt, I don't think it's at all likely that the real distribution looks much like that, and if it did then it would indicate an "inappropriate exclusion" of very high IQs; the point is just that it's quite different from a normal distribution but the fit is just as good.
More to the point, we can get a pretty decent fit from a probability distribution designed to describe selection for higher IQ applied to the general population. Consider the "logistic function" a(x) = 1/2 (1 + tanh (x-t)/s). This is 0 for very small x and increases smoothly to 1 for very large x; most of the increase takes place near x=t, on a scale defined by the parameter s; for instance, we have a(t-s)~=0.12 and a(t+s)~=0.88. Suppose that your chance of getting an academic post at Cambridge doing science is a(your IQ), with parameters t=124.7 and s=6.1; so e.g. with an IQ of 100 your chance of success would be about 0.03% and with an IQ of 140 it would be about 99.3%. And suppose that we take the population at large -- IQ distributed normally, mean 100, standard deviation 15 -- and give everyone a probability of ending up a Cambridge scientist that's proportional to a(x). Note that there is definitely no "exclusion" of very high IQs here; higher is always better. How well does this fit the numbers in Gibson & Light? Worse than the best-fit normal distribution but still well enough to pass Taw's chi-squared test at the 5% level. (The p-value is somewhere around 0.07, versus 0.17 for the best-fit normal distribution.)
Evidence from the references: summary
That's all the references. So far as I can tell, Gibson & Light is the only one that offers anything like evidence that "elite professions"' IQ distribution is close to normal. The evidence it offers (1) is for one specific subset of one specific "elite profession" only and (2) from a sample too small to give strong evidence about what happens at the tails of the distribution. The numbers Gibson & Light report do look fairly consistent with normal distribution (with roughly the parameters claimed by Ferguson), but they are not strong evidence for that particular distribution over others that would lead to very different conclusions from Ferguson's. The other references offer no further support for the normal-distribution hypothesis. No plots (other than one very crude one in the last reference, which looks extremely not-normal to me and in any case is based on a very small sample), no Kolmogorov-Smirnov or similar statistical tests. We have some means and standard deviations, some 10/25/50/75/90 percentiles, but nothing more detailed and in particular nothing that looks at the shape of the tails (which Ferguson would need to justify his claim about what happens at an IQ of 150, for instance).
So, I say that Ferguson's article does not offer any "trustworthy data" to speak of for the key claim that IQs of people in "elite professions" are close to normally distributed with mean ~125 and s.d. ~6.5. And that normal distribution is essential for his conclusion.
Some other dubious things in Ferguson's argument
This isn't directly relevant to the specific claim in the question here, but since "inappropriately excluded" is in Ferguson's title I think it's worth a bit of a look at whether that language would be justified if the claim were true. Readers interested only in the specific claim under discussion can safely stop reading here.
Let's suppose arguendo that in fact Pr(in elite profession | IQ) does drop off as one looks at extremely high IQs.
Ferguson calls the very high-IQ people inappropriately excluded. For this to be reasonable, there would need to be actual exclusion and it would need to be inappropriate.
Is there exclusion? (Some other possible hypotheses: very-high-IQ people may find the "elite professions" boring, or very cleverly analyse the costs and benefits of getting into them and decide to do something that saddles them with less student debt, or something of the sort.) Ferguson offers neither evidence nor argument for this. He tells a handwavy just-so story about how "it is an artifact of a culture that fails to provide them with audience or followers ... the leaders are not persuaded and often won't even understand the advice", but telling stories is easy and giving good evidence that the stories match reality is hard, and Ferguson has done only the former.
Is it inappropriate? (Some other possible hypotheses: very high-IQ people don't outperform in most "elite professions" but expect better treatment or higher pay; very high-IQ people tend to have personality quirks that make them not work so effectively with others; very high-IQ people tend to have outright intellectual deficits in particular areas that make them ineffective.) Ferguson mentions that Towers and Sternberg (none of whose work is in Ferguson's bibliography) propose alternative hypotheses of this kind. Ferguson does offer a little bit of evidence that they're wrong: he quotes Roe's book mentioned above as showing that top scientists have very high intelligence. But "top scientists" is a very different group of people from "people in elite professions". It could well be (and anecdotally it seems likely to be true) that science is exceptional among professions in how valuable intelligence (in the what-IQ-tests-measure sense) is for its practice.
The nearest thing to an explanation for Ferguson's "exclusion", if it should happen to be real, that I find in his references is the one suggested by Gross's work on exceptionally intelligent children: if such a child is expected to stay with their equal-age peers up to age 18, then there's a danger that they find the educational process boring and demoralizing, which may mean that they drop out of education, or resent being with the children they have to spend time with and never learn to relate to them in healthy ways, either of which will be bad for their prospects of entering "elite professions". Ferguson does discuss this and what he says about it seems plausible; but none of it seems like a good fit for the term "exclusion".
