Out of all the negative correlates of IQ, my favorite is weight/height ratio. By negative correlation, I mean that the two variables tend to move in opposite directions, so the higher one’s weight/height ratio, the lower one’s IQ tends to be. Why is this my favorite negative correlation? Because it confirms all the stereotypes we see in movies about the skinny nerd being smarter than the beefy jock, and the completely anorexic space alien invader being way smarter than both. It’s also consistent with our evolutionary history. As humans evolved from dumb apes, we gained height and lost muscle. As scientist Steve Hsu once quipped, “we are the geeks of the animal kingdom” and you can kind of look at the way humans slaughtered the burly neanderthals and are now racing to destroy the planet for all the musclebound animals as a kind of inter-species version of Revenge of the Nerds or what the Lion of the Blogosphere calls beta male rage.

But within humans, how real is this negative correlation between IQ and weight/height ratio, what’s causing it, and how strong is it? Blogger Jayman seems to feel the negative correlation is driven by low IQ fat people, rather than the dumb jocks. Jayman writes:

It is commonly known that poorer (i.e., stupider) people tend to be fatter. It is commonly believed that this stems from things associated with low IQ, like poor impulse control and low future-time orientation, and indeed those things likely play a role. But it’s telling to see just how stark the relationship is.

Satoshi Kanazawa (who, despite the removal of his Big Think page, still very much publishes; see his website) did just that. Looking at a nationally representative primarily White British sample (n just under 10,000 in the last waves, 97% White), he found that IQ measured in childhood excellently predicts obesity at age 51:

Technical points (you may want to skip this part)

While the chart Jayman cites certainly makes it appear as though there’s a strong relationship, I respectfully disagree with Jayman’s claim that childhood IQ “excellently predicts obesity at age 51”. What the chart shows is that people with childhood IQ’s below 75 (probably IQ 70 on average) and people above childhood IQ 125 (IQ 130 on average) differ by 2.9 BMI units. Based on using the standard errors and sample sizes reported this source, I was able to calculate that American white men and women in their 50s both have a mean body mass index of 29 and a standard deviation of 7 to 9. While weight is probably lower in Britain, they also probably have a BMI standard deviation around 8. What that means is that people who differ by an astonishing four standard deviations in childhood IQ, differ by only 0.36 standard deviations in BMI. This implies the correlation between childhood IQ and age 50 weight/height ratio is only -0.09. Squaring the correlation, childhood IQ explains less than 1% of the variation in age 50 BMI. Hardly an excellent predictor.

However it may be unrealistic to expect much of a prediction from childhood IQ, since childhood IQ only correlates about 0.7 with adult IQ. Dividing the -0.09 correlation by 0.7 gives -0.13 which probably better reflects the relation between IQ and weight/height ratio. Still a very weak correlation, but a lot more respectable looking.

Anorexic IQ (technical analysis, you may want to skip)

A second way to estimate the negative correlation between IQ and weight/height ratio is to look at the IQ’s of anorexics. According to this meta-analysis, anorexics have IQ’s about 11 points higher than average when measured on the Wechsler scales and 6 points above average when estimated from a reading test. Normally I would split the difference, but a lot of academics are clueless about the Flynn Effect and are probably administering outdated versions of the Wechsler scales that give inflated scores. Since reading tests are much less sensetive to outdated norms, I will assume anorexics are 6 IQ points smarter than average. And since anorexics tend to be overwhelmingly white, and the whites score about 3 IQ points above the national average, anorexics score only 3 points higher than other whites. On the other hand, anorexics are overwhelmingly women, and women score maybe 2 points lower than the national average, and so anorexics are probably roughly 5 points smarter than other white women (+0.33 SD)

How much skinnier than average are anorexics? Well based on this source, white American women under 40 have an average body mass index of 26.5 with a standard deviation of 8.9. Assuming the average anorexic woman is a white woman under 40 with a BMI of 17, then anorexics are 1.07 standard deviations skinnier than normal (for young white women). Given that they are 0.33 SD smarter than normal, this implies a negative correlation of -0.31 between IQ and weight/height ratio.

The Bottom Line

Based on my analysis of the chart Jayman’s cited and my analysis of anorexic IQ, I estimate that among people of the same country, gender, and ethnicity, the negative correlation between IQ and weight/height ratio is -0.13 to -0.31; splitting the difference, about -0.22. This is may be a low correlation, but small correlations can have big effects, and what this correlation really suggests is that among people of the same age, gender, race and nationality, the scrawniest 2% will be a full 13 IQ points smarter (on average) than the least skinny 2%, though virtually the full range of human intelligence can be found at virtually every body type. So before you condescend to the big bury bouncer, just remember, he might be the smartest man in America.

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