Monday, November 28, 2022

"Super High" IQ Scores - Why They Are Impractical & Meaningless

 Parade  magazine contributor Marilyn vos Savant was once claimed by The Guinness Book of Records to have the highest IQ ever recorded. By one measure- a test first taken by her in 1956 - it was claimed to be 228 or a mental age of 22 years and 10 months at the age of 10.  A recent article ('The 21 Smartest People In The World')  at also claimed to have a list of the "world's highest IQs" with a number even higher than vos Savant's and many with IQs higher that Albert Einstein's (160). But is this really possible? Do such high IQ scores even have any credible meaning?

 In the case of vos Savant, according to Wikipedia:

Alan S. Kaufman ,a psychology professor and author of IQ tests, writes in IQ Testing 101 that "Miss Savant was given an old version of the Stanford-Binet (Terman & Merrill 1937), which did, indeed, use the antiquated formula of MA/CA × 100. But in the test manual's norms, the Binet does not permit IQs to rise above 170 at any age, child or adult. And the authors of the old Binet stated: 'Beyond fifteen the mental ages are entirely artificial and are to be thought of as simply numerical scores.' (Terman & Merrill 1937). ...the psychologist who came up with an IQ of 228 committed an extrapolation of a misconception, thereby violating almost every rule imaginable concerning the meaning of IQs."

 The list of the "world's smartest people" featuring over a dozen with higher IQs than 160 (for Einstein) is also daft and a classic example of what author Charles Seife would call "proofiness", discussed in his excellent book, : 'Proofiness: How You're Being Fooled By the Numbers'.  In page after page Seife decries the use of numbers not merely to lie but to baffle with bullshit. No better example of such proofy twaddle can be seen than in the website below:

But alas, super high IQ scores are also rife with proofiness. Further understanding of what I am about can be grasped by reference to the standard (normal) Gaussian distribution or "Bell curve"  on which the distribution of IQ scores is based, e.g.

Note the percentages of the population decreasing at both the high and the low ends, corresponding to the number of standard deviations  (stds) from the zero point or mean.

We see, for example, that by a 2.2 std dispersion we are effectively at a population fraction of 2 percent - which is the cutoff threshold for qualifying in Mensa. Generally, this is taken as an IQ of 133-35. (Depending on the test used). Note also, how the corresponding population applicable is decreasing as the number of stds gets larger from the central point. At about 2.6 std we are near the threshold (or just slightly beyond it) for the top one percent or Intertel members. At 3 std (about 145 IQ) one qualifies for the Poetic Genius Society.

Using a base of 300 million as the U.S. population, the Bell curve proportions would translate into 6 million who'd qualify for Mensa entrance, and 3 million who'd qualify for Intertel.  By about 3.3 stds we reach the 0.1 percent cutoff and the threshold for the Triple Nine Society. The population qualifying is one-tenth that for Intertel or 3 million/ 10 = 300,000. Divide 300,000 by 300,000,000 and you get 1,000 - hence the Triple Nines are also known as the "One in one thousand society".  

Note how already we are near the effective upper limit of the Bell curve in terms of being able to discriminate between the IQ groups. At near 4.5 stds, however, there is the Mega Society which will have a threshold at the 0.0001 % level. Or doing the same math as I showed in the previous paragraph, only 1 in a million qualifying. This would imply 300 in the U.S. population of 300 million - and with an IQ of 171. But what does that even mean, and is it useful?

As the relevant article in Wikipedia points out:

"No professionally designed and validated IQ test claims to distinguish test-takers at a one-in-a-million level of rarity of score. The standard score range of the Stanford-Binet IQ test is 40 to 160.The standard scores on most other currently normed IQ tests fall in the same range. A score of 160 corresponds to a rarity of about 1 person in 30,000 (leaving aside the issue of error of measurement common to all IQ tests), which falls short of the Mega Society's 1 in a million requirement."

In other words, there aren't even any IQ tests that currently exist which achieve the level of discrimination to identify a would-be Mega Society member! The highest score achievable (and hence measurable) within the constellation of intelligence allows no higher than 160 - which was Einstein's IQ.

Consider the mean or 0 mark which sets the "average IQ" at 100. This means half score above this level and half below. At about 4.5 std, the threshold for the Mega Society we are already in uncharted territory. This is why it is likely impossible to design a test adequate to ferret out those 300 potential members in the U.S. The Mega Society insists it has "unsupervised IQ tests that the test author claims have been normalized using standard statistical methods" but this is very doubtful.  Most psychometricians concur that by 3 std (145) to 4 std (160 IQ) one is already at the limit of the measurable validity for testing IQ in any useful way. Beyond 4 std (again, Einstein's level) the difference between such scores blurs.

Again, in considering such stratospheric IQs one ought to look not only at the std dispersion from the mean but the area under the curve. At 4.7 std the area is essentially nil. What about claims of a 300 IQ? This is even more preposterous. We are now talking about 13.33 std from the mean. As one contributor put it on an IQ- statistics site:

"An IQ of 300 has no useful meaning because there aren't enough people in the world (or intelligent beings in the history of the cosmos) to make it useful".

Or, again, no test that could possibly discriminate that single potential member from 6 billion people. (Other estimates put the proportion in even more rarefied terms, i.e. 1 in 50 billion - or nearly 1 out of every other person who's ever walked the Earth).  In effect, it means that any article bragging on one or more people with supposed IQ scores exceeding Einstein's is preposterous. Even the Mega Society entry threshold is likely a Macguffin, given that in reality there is no living human with an IQ that high that can be satisfactorily verified at the necessary level of statistical confidence.

Even if such a "Mega" person really existed (irrespective of how many claim to be Mega Society members) would one really see a qualitative difference, say from an "Einstein-level" IQ person? I doubt it. I can't see a Mega Society member being able to do any more than Einstein did, including developing the tensor calculus to use in his General Theory of Relativity.

Thus as one of the web psychometricians put it, even a 150 IQ person (near the top of most IQ test standards) would not see a significant difference between himself and a 160 or 170 IQ person. Where the real differences would be seen is where the areas registered for standard deviations are the most.  For example, between a normal IQ person and a Mensa (upper 2 percent) IQ person. Their interests, and even vocabulary would likely be so different as to approach the analogy of an alien trying to communicate with a typical earthling.

But this is precisely why Mensa as an organization was created in the first place, to establish a communal civic space where gifted individuals could meet and converse without being put down by pejoratives (Dweebs, or "geeks") from "normals".  Intertel was launched for similar reasons, though it is interesting to note that many Intertel members also belong to Mensa - simply because it is vastly larger and there are more opportunities for social exchanges.

As an interesting side note, at Monsignor Edward Pace High in N. Miami one of the first  segregations transpired after we all took an IQ test (Stanford -Binet) in 10th grade. In the immediate aftermath I noticed a loss in the diversity of the student body with many of those perceived "slower" (but often more interesting, joking and friendly) leaving Pace for good. I was also encouraged to leave, but for a different reason:  to attend Nova High where I could advance at my own pace and not be held back by a less challenging curriculum. I decided not to take the advice because it would mean 100 extra miles a day total transporting by my dad.

The takeaway from this blog post? Don't trust any claims of pe
ople with IQs over 160!


This post first appeared in May, 2015

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