I was reading a study on the correlation between IQ and obesity which is a misleading term, because the study did not make any attempt to measure fat. It simply measured weight/height ratio. The study was very old but I love old studies because they get right to the point and the study seemed to include a fairly representative sample of Americans.

The body height and weight were measured, the age checked and AR-B intelligence test administered with 554 adult subjects, employees of various plants. The whole sample consists of 334 men between the ages of 18 to 58 ( the mean age being 30.5 yrs ) and 220 women between the ages of 18 to 50 (the mean age being 28.1 yrs) with various levels of education and from various occupations ranging from manual workers through members of the technical staff to clerks. The percentage of overweight was calculated from standards of normal weights for our healthy population ( Hejda and Hátle, 1961 ) . Subjects who were 20% or more overweight, were classified as obese.

Source: Relationship between Intelligence and Relative Prevalence of Obesity
Author(s): A. Kreze, M. Zelina, J. Juhás and M. Garbara
Source: Human Biology, Vol. 46, No. 1 (February 1974), pp. 109-113

As you can see from table 1, in women with IQs of 111+ (average IQ 118?) the obese were the top 10.66% in weight/height ratio while in women below IQ 70 (average IQ 66?), they were the top 71.42%. In other words, as one moves from an average IQ of +1.2 SD to -2.27 SD (a decline of 3.47 SD), obesity goes from having a normalized cutoff of +1.3 SD to -0.53 SD ( a decline of 1.83 SD).

This suggests a correlation of -0.52 (1.83/3.47) between IQ and weight/height ratio.

Similarly in men, for those with IQs of 111+ (average 118?), the obese were the top 9.35% in weight/height ratio, while for those IQ 71 to 80 (average IQ 76?), the obese were the top 22.2%. So as one moves from an average IQ of +1.2 SD to -1.6 SD (a decline of 2.8 SD), we see the normalized cutoff for obesity drop from +1.33 SD to 0.8 SD (a decline of 0.53 SD).

This suggests a standardized regression slope (aka correlation) of 0.53/2.8 = -0.19.

The correlation appears to be much stronger in women than in men and it’s tempting to ascribe this to the fact that women have much more body fat and that it’s fat, not muscle, which is driving the correlation. However since comparing men and women was never an a priori stated goal of the study, reporting on it post-hoc would be a classic example of the kind of sloppy p hacking that has caused a scientific replication crisis.

So for now I will simply average the two estimated correlations and cite -0.36 as the correlation between IQ and weight/height ratio, though it’s worth noting that this study is from 1974. It’s unclear how, or if, the explosion in obesity over the last half century has affected the correlation.

It’s worth noting that Jensen dismissed the correlation as a function of social class.