I’ve blogged a lot about how Ivy League students regress precipitously to the mean when they go from the SAT to official IQ tests like the WAIS. The obvious explanation for this is that the correlation between these tests is far from perfect, but now I’m wondering if some of them even scored high on the SAT in the first place.

Several years ago 60 minutes did a story about one boy fraudulently writing the SAT for at least 16 other students, and the security was so poor that some of the students he impersonated were girls.

I wonder what percentage of Ivy League students got into their schools by having someone else write the SAT for them.

Recently, Jeff Bezos dethroned Bill Gates as the World’s richest human, however Lion of the Blogosphere writes:

It should be noted that Bezos got married one year before he started Amazon.com, so all of the stock in Amazon.com is community property. 50/50 split. No theatrics. Shares in a publicly traded company are pretty easy to split 50/50. The two parties could argue about the values of Bezos’ various mansions, but they probably won’t. When you’re getting almost 70 billion dollars worth of stock, why worry about whether one mansion is worth a few million more than the other?

As of today Gates is reportedly worth $94.9 billion while Bezos is worth is reportedly worth $135.3 billion, however if his wife takes half, Bezos will be left with only around $68 billion (depending on the value of Amazon stocks on the day she takes his money).

Bill Gates is probably the single best example of the SAT measuring real world intelligence, because here we have someone with a one in a million SAT score (equating to an IQ of 170) becoming the richest human on the planet for decades, and then even after giving away the title through incredible philanthropy, reclaiming it without even trying.

Meanwhile Oprah is probably the single best example of brain size measuring real world intelligence, because here you have a woman with a one in several billion head circumference (+6.3 SD above the female mean) climbing out of extreme adversity to become the World’s only black billionaire (from 2004 to 2007) and the World’s most influential woman.

And part of their success was their ability to avoid costly mistakes. As J.P. Rushton once stated:

All of us have success, all of us have failures; but high IQ people tend to end up further ahead in part because they make fewer mistakes.

Just as Bill Gates scored near-perfect on the SAT because he didn’t make many mistakes, in real life he avoided the mistake of having a costly divorce perhaps by choosing a woman of substance over a flashy trophy wife. Oprah too avoided that mistake simply by never marrying long-time live-in partner Steadman Graham, instead simply showing him as arm candy at award shows.

Although Jeff Bezos likely has a slightly higher IQ than even Oprah (145 vs 140) and will always have far more wealth (though never as much influence or status) he made a HUGE mistake.

Today all human populations have the genetic potential to average IQs in the 85 to 105 range, with a species mean of say 97 (Euro norms). Scientists claim living humans have an average cranial capacity of around 1350 cc, but I believe this is way off, because unlike our well nourished ancestors, most modern humans have been malnourished since the neolithic transition. Even today, virtually everyone outside the developed World has sub-optimum nutrition.

Perhaps the best estimate of living human brain size under First World conditions is the average brain size in the U.S., since the racial diversity of this country mirrors the species as a whole.

The average young American has a cranial capacity of at least 1418 cc, with a within-sex standard deviation of 91 cc. The average is probably closer to 1438 cc since the data comes from the army who tend to be smaller than their civilian counterparts.

The correlation between IQ and brain size (among members of the same sex and country) is anywhere between 0.25 and 0.4, with 0.32 being my current best guess (it changes all the time). This means that for every one standard deviation (91 cc) difference in brain size, IQ differs by 0.32 standard deviations on average (the IQ scale has a standard deviation of 15).

If we extrapolate this logic to chimps, who average cranial capacities of 400 cc, which is 1032 cc or 11.34 SD less than the average human (under First World conditions) we’d expect an IQ that is 0.32(11.34 SD) = 3.63 SD less than 97 (the human mean under well nourished conditions).

In other words, chimps should have an average IQ of 43.

And yet that’s not what we find. Last March I wrote:

In 2007 there was a fascinating study that compared human 2.5 year-olds to chimps and other apes on a battery of intelligence tests.  With the exception of social intelligence, where the human toddlers were way ahead, the apes and toddlers had the same intelligence.

In other words, chimps have the same intelligence as a 2.5 year old (white) human.

What adult IQ does a mental age of 2.5 equate to?  The question is a lot trickier than it seems.  One could define adult mental age as 16+ and then use the age ratio method to conclude that since 2.5 is 16% of 16, a mental age of 2.5 equates to an adult IQ of 16.  The problem with this method is it assumes intelligence develops as a function of age in a linear way, which is an oversimplification.

What is needed is an actual intelligence test that’s been given to both adults and to toddlers and one where scores increase on an interval scale.

One such test is digit span.  Since the earliest days of intelligence testing (digit span has virtually no Flynn effect) it’s been known that by the age of three, a white child can repeat two digits, which probably means a 2.5 year old can repeat one digit.

By contrast U.S. adults average a forward digit span of 6.645 with a standard deviation of 1.35 and since races in the U.S. differ very little on forward digit span, this should be taken as the white adult distribution.  This means that an adult who performs like a 2.5 year-old (digit span of 1) is  4.18 standard deviations below the white adult average.

If we assume that most cognitive abilities are like digit span,  then chimps (who score like 2.5 years olds on most tested cognitive functions) perhaps average 4.18 standard deviations below white adults on the average test.

Does this mean their IQs average 4.18 SD below the average white adult?  No, because if you score 4.18 SD below white adults on the average test, your composite score on a battery of tests is actually much lower.  Why?  Because it’s much more rare to average an extremely low score across a battery of tests than it is  to score that low on any one test.  Indeed based on the intercorrelation of WAIS-IV subtests, someone who is 4.18 SD below average on the average subtest, would be 5.73 standard deviations (86 IQ points) below average on the composite score, thus my best guess for the average IQ of chimps is 14 (white norms).

So contrary to what I’ve said in the past, the regression line predicting IQ from brain size in humans, overpredicts chimp IQ by 29 points!

Their expected IQ is 43, but their actual IQ is 14.

This is because apes are not just small brained humans anymore than humans are big-brained apes. No matter how big a chimp’s brain gets, it will never be organized as efficiently as a human’s.

This is because the human brain is spherical which as commenter pumpkinhead noted, is a uniquely efficient shape because it minimizes the distance between any two points, thus maximizing communication between neurons.

This explains why Homo heidelbergensis, (600 ka to 300 ka) despite having a relatively large brain of 1280 cc, was virtually incapable of innovation. In their book The Rise of Homo sapiens: The evolution of Modern Thinking Frederick L. Coolidge and Thomas Wynn write:

…nothing much changed in Africa and Europe between 1.4 million years ago and 300,000 years ago. Hominins made the same types of stone tools they always had-hand axes and cleavers and a range of flake tools…

So despite having a near-human sized brain, Homo heidelbergensis was still an ape in my opinion, and so his expected IQ would fall on the ape regression line, not the human one, and thus his IQ was 29 points lower than an equally big brained human.

And similarly for Neanderthals.

It was not until 300 ka that incipient forms of H. sapiens appear and only then do we start to see a gradual transformation from ape shaped brains to the globular brains of fully modern humans, paralleled by a few isolated signs of human culture. It’s not until 100 ka to 35 ka is the brain transformation is complete and we get the upper paleolithic revolution, the neolithic transition and the ability to finally leave Africa and rapidly colonize the whole world and beyond.

The simplest explanation for this is that IQ genetically increased 29 points over this period, as we leaped from ape shaped brains to human shaped ones.

Punctuated equilibrium (also called punctuated equilibria) is a theory in evolutionary biology which proposes that once species appear in the fossil record the population will become stable, showing little evolutionary change for most of its geological history.^[1] This state of little or no morphological change is called stasis. When significant evolutionary change occurs, the theory proposes that it is generally restricted to rare and geologically rapid events of branching speciation called cladogenesis. Cladogenesis is the process by which a species splits into two distinct species, rather than one species gradually transforming into another.^[2]

Punctuated equilibrium is commonly contrasted against phyletic gradualism, the idea that evolution generally occurs uniformly and by the steady and gradual transformation of whole lineages (called anagenesis). In this view, evolution is seen as generally smooth and continuous

____Wikipedia, April 29, 2018

Although I agree with punctuated equilibrium, I sometimes think Stephen Jay Gould (one of the co-authors of this theory) specifically came up with it for the purpose of discrediting HBD.

Richard Klein is a clear believer in the punctuated equilibrium theory.  On pages 23 and 24 of his book The Dawn of Human Culture, he writes:

Each of the three or four punctuation events that we propose led up to the dawn of modern human culture occurred when human populations were small and geographically limited by modern standards. Each apparently occurred in Africa, and on present evidence, each appears to mark a coincidence of major biological and behavioral change. The first event occurred around 2.5 million years ago, when flaked stone tools made their initial appearance. These comprise the earliest enduring evidence for human culture, and their emergence probably coincided closely with the evolution of the first people whose brains were significantly larger than those of apes. The second event took place around 1.7 million years ago. The people this time were the first to possess fully human as opposed to ape-like body proportions, and they invented the more sophisticated stone artifacts that archeologists call hand axes. They may also have been the first to venture out of Africa. The third and most weakly documented event occurred around 600,000 years ago, and it involved a rapid spurt in brain size, together with significant changes in the quality of hand axes and other stone tools. The fourth and most recent event occurred  about 50,000 years ago and it was arguably the most important of all, for it produced the fully modern ability to invent and manipulate culture.  In its wake, humanity was transformed from a relatively rare and insignificant large mammal to something more like a geologic force.

I think Klein is more or less correct, but I might make a few revisions to his model in an imminent post.

Prestigious black national merit finalist G-man (and others) wanted me to comment on Nassim’s Taleb’s recent tirade against IQ.

It’s amazing how much publicity this issue is getting in the HBD community. Taleb is famous for attacking mathematical models and for attacking “intellectuals”, so it was only a matter of time before he attacked IQ.

But because a lot of Taleb’s fans are high IQ people who love numbers, and thus love IQ, they may be shocked that their hero doesn’t share their enthusiasm.

Taleb writes:

“IQ” is a stale test meant to measure mental capacity but in fact mostly measures extreme unintelligence (learning difficulties), as well as, to a lesser extent, a form of intelligence, stripped of 2nd order effects. It is via negativa not via positiva. Designed for learning disabilities, it ends up selecting exam-takers, paper shufflers, obedient IYIs (intellectuals yet idiots), ill adapted for “real life”. The concept is poorly thought out mathematically (a severe flaw in correlation under fat tails, fails to properly deal with dimensionality, treats the mind as an instrument not a complex system)

Well he’s right that intelligence tests were originally created to identify the learning disabled, not the brilliant, and that the concept was not mathematically well thought out (IQ was originally measured in mental age units, ignoring the fact that the developmental trajectory is not linear, and that newborn babies do not have zero intelligence). However neither of these problems strike me as especially important, especially since IQ testers admit their tests are ordinal scales (or at best interval scales) and not absolute scales. Meanwhile the ceiling on IQ scales have since been extended to better measure giftedness.

But Taleb seems to think the flawed mathematical model of IQ tests is a severe problem under fat tails. I wish he would elaborate on this point. Modern IQ tests are forced to fit a bell curve and when the variable being correlated with IQ does not have a perfectly Gaussian distribution (i.e. income), one can either normalize the distribution as I did here, or one can take the logarithm of income.

But maybe I’m missing the point. Taleb is famous for writing about black swan events:

A black swan is an event or occurrence that deviates beyond what is normally expected of a situation and is extremely difficult to predict. Black swan events are typically random and unexpected.

So maybe Taleb is talking about all the times IQ predictions go wildly wrong, like when when Richard Feynman scores “only” 125 on an IQ test, despite being one of the greatest physicists of all time. Perhaps he’s saying these events are so unpredictable they can’t be foreseen from the correlation between IQ and achievement using the bivariate normal distribution and thus render IQ tests useless in some of the most important cases.

IQ enthusiasts will counter that Feynman’s IQ can easily be explained by the fact that the test may not have measured math ability, however this supports Taleb’s point that test’s fail to “to properly deal with dimensionality”.

Taleb also has a point when he says tests treat “the mind as an instrument not a complex system” if he means what I think he means. Even the best IQ tests like the WAIS measure cognitive abilities in isolation and your final score is just a composite of all your strengths and weaknesses. But in real life, intelligence is a dynamic system that maximizes strengths and minimizes weaknesses. On an IQ test, you’ll lose points for sucking at spatial ability no matter how brilliant you are verbally, but in real life, your spatial disability is irrelevant if you’re smart enough to avoid spatial situations.

Don’t get me wrong; I’m still a huge IQ enthusiast, but IQ testing has room for improvement.

Commenter Mikey writes:

Pumpkin could you do me a solid and calculate my IQ based on my GED score? (I want Pumpkins opinion)

I dropped out of hi school after graduating from,the 9th grade. And was held back one grade, but it should have been 2 (my father convinced the school to let me pass)

I studied evolutionary psychology , along with other general social sciences nearly eery day for the next 4 years straight

I passed the GED exam. On my 1st try.
I was 19,years old,
My scores were

Language arts/writing. 440. 27th percentile rank
Social,Studies. 660. 95th percentile,rank
Science. 520. 58th percentile rank
Language Arts/reading. 550. 69th percentile. Rank
Mathematics. 480. 42nd percentile
Total score. 2650

Passing score is 2250 passing score in each category is 410

I grew up abused and neglected by family members, paternity uncertainty was a big factor for several years,single parent household I’m male but was raised as a woman had my 1st suicidal thoughts in elementary school,. Had to see the psychologist at the school because I wrote my mom only loved me sometimes, when we had to make a letter to our parents. my father was surprised when I told him I was straight at 13, one of the first girls I dated made me take my shirt off to prove I was a boy, I would occasionally be mistaken for a girl during puberty. Not so much after although I still had a “girls voice” My father came out to me saying he is bisexual when I was 19. Everyone in the family new, “hey son do you want to get your nails painted with me?” He asked me that twice when I was 13 ill never forget it.
My aunt is a lesbian, and my uncle has Autism,
At 16 my mom decided that starving me would change my behavior, it did not, I simply adapted to the caloric deficit. I bought multivitamins and supplements and began experimenting with liquid diets In order to survive.
I have been in handcuffs 5 times but never been booked or charged
I have been homeless more than a dozen times as a teenager.
One night was so cold if I had not stolen some gasoline from a nearby garage and made a bonfire out of a couple flower pots and tree leaves I wouldn’t have survived the night.
I took steroids for a few months at 18, because I knew I naturally didn’t have the moxy it would take to make it out of my situation, I ended up injecting myself with more than 10 times the average amount of testosterone as well as trenbolone and other roids in the hope of a long lasting permanent affect. My voice got permanently deeper, my aggression skyrocketed, I grew pecs permanent arm definition my face got wider and more scoelish and I grew a Windows peak. I essentially went thru a second puberty.
I ended up terrorizing my family into submission while holding down a 9 to 5 and got my crush from high school pregnant, and almost ahem “took care of” her whole family and mine too. The juice helped me turn my life around but desperate times had to call for desperate measures.

Despite these problems I never had any difficulty making friends although I do tend to get into a lot of fist fights thru out life even before the juice
I was diagnosed with ADHD at 14, and I really had it. To my surprise I grew out of all,of the Attention Deficit issues over a period of 6 months from age 20 and 6 months going into age 21 (symptoms vanishing into adult hood is actually the most common scenario according to a few studies I have seen) Now I have one of the longest attention spans any one could have. Also I never was a drug addict which I believe is a huge reason,why I grew out of that disorder. I now have an extraordinarily long, i would even say superhuman attention span because my brain is still hyperactive.
Im just laying out all the info maybe you would need for the most accurate analysis.

Well let’s focus on your GED scores where you averaged 530 on the total battery. According to some data I found, GED takers have a mean battery average of 519.9 with a standard deviation of 77.64.

This means you scored 0.13 standard deviations higher than the average GED taker. Of course the GED is not an official IQ test, but if one were to try to crudely map GED scores to IQ, one would need to know the IQ distribution of those who take the test. Those who take the GED are primarily a mix of those who remain high-school dropouts (IQ 88.77 [U.S. norms]) by failing the GED and those who get their GED and seldom more than than that (IQ 97.28).

The chart below shows the average IQ of various education levels:

So on average, I would guess that people taking the GED average IQ 93 with a slightly restricted standard deviation of 13.5 (typical of people with similar education). Thus, if Mikey scored 0.13 SD above this group, it would equate to an IQ of:

0.13(13.5) + 93 = IQ 95 (U.S. norms) or IQ 92 (U.S. white norms)

Such a score would be higher than 37% of the U.S. population and 30% of the U.S. white population.

An IQ of 92 (white norms) is not low, it’s only 0.53 standard deviation below the white mean. A man who is 0.53 SD below the white mean in sex-adjusted height would be a respectable 5’8.5″.

Of course the GRE is NOT an official IQ test, and given your tumultuous upbringing, it’s quite possible that it dramatically underestimated your ability.

Even Arthur Jensen admitted that black kids raised in extremely deprived environments (i.e. rural Georgia) saw their IQs decline by 15 points. Given the adversity you describe, and given that you have a lot of high IQ interests, your true IQ could be 15 points higher than what your GRE scores equate to, so perhaps 107 (white norms).

On the other hand, if your IQ truly were 92, than a life of adversity is exactly what one would expect you to have, so it’s a chicken and egg problem.

During the 1990s to the early 2010s, it was believed that the brain-size IQ correlation among adults living in developed countries was about 0.4.  Then in 2015, a meta-analysis by Jakob Pietschnig, Lars Penke, Jelte M. Wicherts, Michael Zeiler, and Martin Voracek surfaced claiming the brain size-IQ correlation was only 0.24!  The paper argued that the 0.4ish figure that was typically cited was inflated by publication bias and these authors went out of their way to counter this.

But then in 2017, a meta-analysis by Gilles E. Gignac and Timothy C. Bates, published in the peer reviewed journal Intelligence showed once again that it was 0.4.  The authors reviewed the research cited by Pietschnig et al but corrected for range restriction, test quality, and sample quality and a 0.4 correlation was found.

Now, we have a massive new study to help settle the debate. The paper is called Are Bigger Brains Smarter? Evidence From a Large-Scale Preregistered Study by G. Nave et al.

Here’s the abstract:

A positive relationship between brain volume and intelligence has been suspected since the 19th century, and empirical studies seem to support this hypothesis. However, this claim is controversial because of concerns about publication bias and the lack of systematic control for critical confounding factors (e.g., height, population structure). We conducted a preregistered study of the relationship between brain volume and cognitive performance using a new sample of adults from the United Kingdom that is about 70% larger than the combined samples of all previous investigations on this subject (N = 13,608). Our analyses systematically controlled for sex, age, height, socioeconomic status, and population structure, and our analyses were free of publication bias. We found a robust association between total brain volume and fluid intelligence (r = .19), which is consistent with previous findings in the literature after controlling for measurement quality of intelligence in our data. We also found a positive relationship between total brain volume and educational attainment (r = .12). These relationships were mainly driven by gray matter (rather than white matter or fluid volume), and effect sizes were similar for both sexes and across age groups.

This study is important not just because of its colossal sample size, but the fact that it was preregistered, meaning they agreed to publish the results before they knew what said results were. Critics of this research have worried there’s a file drawer effect, where studies not finding the desired result get shelved, and mostly larger positive correlations get published.

Also interesting is that the correlation between intelligence and brain size remained even after controlling for sex, height, population structure and socioeconomic status. One could even argue this is an over-correction, since socioeconomic status is itself a crude measure of intelligence, and yet even after this over-correction, the correlation remained, suggesting the link between brain size and intelligence is causal and not just a byproduct of a shared correlation with body size (i.e. height) or the nutrition that comes from high SES.

However IQ enthusiasts might be disappointed by how low the correlation is. Only 0.19. And as the matrix below shows, even before they corrected for anything, the correlation was only 0.21 (only half the 0.4 correlation long cited by IQ enthusiasts and confirmed by Gilles and Bates, 2017)

The most likely explanation for this low correlation is that in order to get such a huge sample, they needed a really short test. And indeed the Fluid IQ test used in the study is just the two minute Verbal Numerical Reasoning test sometimes administered on more than one occasion to improve reliability. But as we can see from the 0.31 correlation between Fluid IQ and Education Attainment, the test is not that g loaded.

Indeed on tests with near-perfect g loadings like the WAIS-III, IQ correlates 0.55 with education (though this is in America). If we divide the Fluid IQ test’s correlation with education by the WAIS-III’s, we might get a very crude estimate of the Fluid IQ test’s correlation with the WAIS-III and that correlation is 0.56. If we further divide brain size’s 0.21 correlation with the Fluid IQ test by 0.56, we might get a crude estimate of brain size’s correlation with the WAIS-III and that correlation is 0.38. Thus confirming Gilles and Bates, 2017.

Of course Pietschnig et al can counter that brain size in this massive study only correlates 0.14 with education. Dividing 0.14 by the WAIS-III’s 0.55 correlation perfectly confirms their 0.25 correlation between IQ and brain size.

Thus, the only solution is to average 0.38 and 0.25, which gives a 0.32 correlation between IQ and brain size. Still a moderate correlation, but the low end of the moderate range. Indeed long before MRIs, a correlation of 0.3 was considered the best estimate of IQ’s correlation with brain size. The figure was achieved by adjusting the weak correlation between head size and IQ for the fact that head size was only a rough proxy for brain size.

So even though IQ doesn’t correlate quite as well with brain size as IQ enthusiasts would have liked, the good news is that the correlation barely declines when you control (even over-control) for other variables, implying it’s overwhelmingly causal.

A reader wrote the following:

Hello PP, I was wondering if you could give a rough approximation of my IQ based on scores from different tests I’ve taken. I’ve never considered myself all that smart, and writing is not something I’m especially fond of so please excuse any grammatical errors.
SAT (taken in 2014): Math 660, Reading 630, Writing 620
ASVAB (2016): 96th percentile, GT Score 129
Queendom.com Classical IQ Test (December 23, 2018): 140 Overall, 137 Crystallized Intelligence, 147 Fluid Intelligence

I’m gonna post some pictures of the test scores below.

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From the SAT picture you can also see my PSAT scores and a previous SAT score. The other scores are average. For context, I was unfamiliar with nearly all the formulas needed when taking the PSAT both times. I’ve also always been a very anxious test taker; literally shaking and sweating in a 70 degree room. I was also diagnosed with anemia around this time which might also be a factor. Weighing in at about 120 lbs standing 5’10, I was a walking stick. Was also put on free lunch at school and my mom was on food stamps, welfare, the whole gamut. My parents were pretty indifferent. On the first SAT test I took, a friend of mine recommended taking an adderall pill. This led to profuse sweating, blurry vision, frequent bathroom breaks, and uncertainty in all my answers. Before my second round with the SAT I tried studying but was never able to sit down and do it. Instead, I just familiarized myself with the test so I knew what section was gonna come next and knew the time constraints. I know studies show people don’t usually increase their SAT scores by more than 20 points per section, but I’ve personally heard of dozens of people increasing their scores by 100’s of points per section by taking multiple practice tests and learning the tricks on the SAT. Plus, some of my friends started studying for the SAT years in advance. Some as early as middle school.

When I took the ASVAB it was right after a hot and long 2 hour bus ride to the MEPS center. This was in California during the summer, and they didn’t feed us until after we took the test. I also didn’t really put forth my best effort because I was joining the Army and was kinda lackadaisical about it. It was pretty easy in all honesty though.

I heard about Queendom from Aaron Clarey on youtube and he said it gives a pretty good estimate on IQ because it averages from a pool of all people that took it. It also has some studies showing it correlates pretty well with the RAIS test. I took it in about 30 minutes although I’m skeptical because of how high it put me. In short, based on my previous scores where would you rank me? Is it possible my IQ went up from when I was a teenager? I also weigh about 170 now and have adopted the ketogenic diet. That’s one of the main differences between now and then.

Aaron Clarey’s video on Queendom’s IQ test:

Using my formula (IQ = 0.0566(SAT score) + 20.15094) your SAT scores of 1910 and 1660 (out of 2400) equate to IQs of 128 and 114 respectively (U.S. norms).   Similarly, your 96th percentile on the ASVAB equates to an IQ of 126.

Given your health issues and test anxiety, I’d probably ignore the IQ 114 you got the first time you took the SAT as an outlier, and judge your teenage IQ based on a composite of your second SAT score (IQ 128) and your ASVAB score (IQ 126).  Given the high correlation between these two tests, the composite score would be about 129.

As for your 140 overall IQ on the Queendom; this might be because the Queendom needs to improve its norms.  The below chart shows that a sample of college students who took both the RIAS and the Queendom scored 111.12 (SD 8.35) and 117.88 (SD 11.5) respectively.

Given that the RIAS is an extremely well-normed test, this implies that Queendom gives scores that are (a) too high, and (b) too extreme.

To equate Queendom’s distribution with the RIAS distribution we must convert the Queendom score into a Z score with respect to this reference group that took both tests, and then multiply it by the reference group’s RIAS SD (Standard Deviation) and then add to their RIAS mean.

So since your Queendom score of 140 has a Z score of 1.92 in this reference group, it equates to an IQ of 1.92(8.35) + 111.12 = 127

So it seems your IQ has been quite stable and extremely high since your teenage years. An IQ in the high 120s puts you in the same range as U.S. presidents, Fortune 500 CEOs and (on non-college admission tests) the most elite university students on the planet.

A commenter named “Ray” writes in the comment section:

…I’d like to ask you if you can estimate the IQ of a cousin of me based on his intellectual milestones:
-Prior to his 1st birthday he spoke very well and he was very inquisitive
-At age 3 he learned to read and write on his own (my aunt taught him the alphabet, but she never taught him to read per se).
-At age 6 he was reading a college textbook on ondontology and he grasped a great deal of it, though he got bored afterwards-
-At age 6 he used to read textbooks on mathematics (prealgebra), social studies, Spanish Literature and 6th grade physics, chemistry and biology
-At age 12 he began reading Marx’s “Das Kapital” and became obsesed with economics and political philosophy afterwards

He’s currently 17, an avid reader and very well-versed in philosophy, economics and biology (genetics).
Based on this what would you think his IQ is? It’s clear that he has an astounding verbal IQ, though he is depressed because there are better students in math than him.
I hope you answer 🙂

I’ll focus on the three least ambiguous data points.

Research suggests that  at first toddlers “will be able to mutter only about four to six words, but at around 18 months, a real spurt in vocabulary will take place, and your Chatty Cathy’s list of go-to words will increase to about 50.”

It sounds like your cousin had acquired the speaking skills of a 1.5-year-old by age 0.9 or so, which would imply he was functioning at 167% of his chronological age and thus a ratio IQ of 167 (1.5/0.9 = 1.67)

Meanwhile reading and writing are not typically acquired until age six, so having achieved this at three implies he was functioning at 200% of his chronological age and thus a 200 ratio IQ (6/3 = 2.00)

Lastly, doing grade six (age 11) physics at age six implies a ratio IQ of 183 (11/6 = 1.83) though doing physics of any kind seems way beyond even 11-year-olds.

Averaging all three ratio IQs together (unlike deviation IQs, ratio IQs can be averaged) gives a ratio IQ of 183.

However ratio IQs are only normally distributed from IQ 50 to 150 (though with a slightly inflated mean and SD).

Source: Bias in Mental Testing by Arthur Jensen

Above 150 there is an excess of scores, perhaps because the variance is greater at some ages than others and this becomes noticeable at extremes or perhaps because the linear relationship between age and cognitive development is limited to a narrow range, causing the ratio to become meaningless beyond these limits.

Modern IQ tests get around this problem by forcing scores to fit the bell curve.  So since it’s known that only one in 72,000 to 109,000 have ratio IQs in the 180s we can locate the normalized IQ (sigma 15) that fits this rarity, and we end up with an IQ of 164.

Of course this would only reflect your cousin’s early childhood IQ.  Given only about a 0.62 correlation between early childhood IQ and late adolescent IQ,  the typical IQ 164 child regresses into an IQ 140 young adult ((164 – 100)(0.62)) + 100 = 140 with 95% of cases ranging from 117 to 163.

However by age 10, IQ begins to solidify, and the fact that your cousin was enjoying Marx by age 12 implies his (verbal) IQ had remained above 140 (top 0.5%).  Charles Murray notes that just under 10% of even young adults can score high enough on the verbal SAT to likely understand traditional college reading and I’ve found that the top 10% of young adult verbal skill equates to the top 0.5% of age 12 verbal skill.  And Marx might be a lot harder than even traditional college material so I might be dramatically underestimating your cuz.

But even 140 (white norms) is incredibly high.  It might not sound that impressive when you hear that Harvard’s average SAT score equated to an IQ of 143, but just as your cousin’s childhood IQ of 164 might have regressed to an adult IQ of 140, Harvard’s SAT derived IQ of 143 likely regresses to an IQ in the 120s on official IQ tests.

So even 140 is enough to tower at even the most elite universities on the planet (at least in the non-STEM departments).

140 is to IQ as 6’6″ is to height: Head and shoulders above the competition.