Back in February, a reader asked me to estimate his IQ. He wrote:
I’m a long-time reader of your blog. I particularly enjoy your estimates of the I.Q.s of historical and contemporary personalities.
Would you perhaps be interested in estimating my I.Q.?…
…I am underweight, but my head is decidedly small. I am currently unemployed and have never had a job that could be called ‘good’ by any reasonable standard…
A small-skulled, unemployed…
When I asked him to elaborate, he had a lot more to say but in part 1 we focus only on the bio-demographic data. He writes:
My height is 5’9″, and my weight is 121.6 lbs.
I have no formal education to speak of beyond high school. I believe that I graduated around the middle of my class.
I am 30 years old, white …
…I’ve long suspected that I have Asperger’s (and scored 1.9 SD above the mean on Paul Cooijmans’ ‘Aspergoid’ scale), but I have not sought a formal diagnosis…
… My current favorite writers are Schopenhauer and Cioran (I don’t know whether this is relevant or helpful)…
…Politically, my sympathies are broadly anti-democratic. Wilhelmine Germany is close to my ideal society…
…Strictly speaking, I am an atheist, but I find much of value in Theravada Buddhism. I believe that I will survive the death of this body…
…My head circumference is 21.75 inches…
I begin with the fact that he’s a long-time reader of my blog. Anonymous polls suggest my readers average genius level IQ of about 129 (U.S. norms). Not because of the quality of my writing, but because the topic of IQ interests a lot of super high IQ people.
The next question that needs to be answered is whether this reader is brighter or duller than my average reader. The fact that he is unemployed doesn’t tell me much because he’s still young, may have psychological issues, and we’re in the middle of a pandemic. But with only a high school education, he’s certainly much less educated than my average reader and education is perhaps the single strongest demographic proxy for IQ (though not as strong as it was in the 1950s).
On the other hand his favorite writers are Schopenhauer and Cioran, implying more intellectual interests than most of my readers.
But with a head circumference of only 21.75″, his brain is way smaller than my average readers’.
But part of the reason it’s small is because he is so light and low weight/height ratio is a sign of genius.
Head size adjusted for body size
Using 2012 data from the U.S. army, the reader’s head circumference is about 1.36 standard deviations below average for an man (bottom 10%).
But the reader’s weight is 2.12 standard deviations below average for a man, and since the distribution of weight is positively skewed, his normalized deviation from the mean is 2.66 SD below the mean (bottom 0.4%).
Given that head size correlates about 0.41 with weight in U.S. men, his weight predicts his cranium would be be 2.66(0.41) = 1.09 SD below average.
Thus his cranium is only 0.27 SD smaller than his body mass predicts, so adjusted for body size, his head circumference is roughly -0.27 SD.
Statistically expected IQ
However given the average reader’s cranium is predicted to be +0.44 SD, even after adjusting for body mass, he’s about 0.67 SD smaller headed than the average reader.
And given that head circumference correlates about 0.23 with IQ, I’d expect him to be about 0.23(-0.67 SD)= 0.15 SD less intelligent than the average reader (who is a genius).
In other words, about 2 IQ points below the genius mean of 129, or roughly 127.
Of course, this is a very crude estimate with an enormous margin of error, and as the series continues, we’ll see how close it is.