Human Varieties

Category: Sibling Regression

Regression to the mean, RTM for short, is a statistical phenomenon which occurs when a variable that is in some sense unreliable or unstable is measured on two different occasions. Another way to put it is that RTM is to be expected whenever there is a less than perfect correlation between two measurements of the same thing. The most conspicuous consequence of RTM is that individuals who are far from the mean value of the distribution on first measurement tend to be noticeably closer to the mean on second measurement. As most variables aren’t perfectly stable over time, RTM is a more or less universal phenomenon.

In this post, I will attempt to explain why regression to the mean happens. I will also try to clarify certain common misconceptions about it, such as why RTM does not make people more average over time. Much of the post is devoted to demonstrating how RTM complicates group comparisons, and what can be done about it. My approach is didactic and I will repeat myself a lot, but I think that’s warranted given how often people are misled by this phenomenon.

In his classic work, Educability and Group Differences, Arthur Jensen presented a number of lines of evidence in defense of his thesis that the Negro-White difference in psychometric intelligence had a congenital component. On the basis of full sibling correlations and relations, Jensen offered the following arguments:

(a1) The full sibling correlations for Blacks and Whites are comparable; (a2) unshared environmental hypotheses, such as nutritional ones, would predict otherwise (pg. 338-339).

(b1) The full sibling correlations for Blacks and Whites are comparable; (b2) a shared environmental hypothesis of group differences would predict otherwise, assuming that the within population heritablities were the same (pg. 108-109).

(c1) The average absolute difference between full siblings is no greater for Blacks than for Whites; (c2) unshared environmental hypotheses, such as nutritional ones, would predict otherwise (pg. 338-339).

(d1) When matching Blacks and Whites on IQ, one sees differential sibling regression, a differential regression which does not decrease with increasing IQ; (d2) an environmental hypothesis of group differences would not predict this (pg. 118-119). Continue reading

Hu (2013, September, 5; 2013, July, 5; 2013, August, 18) has raised some interesting points. I will comment on a few of them here and present several new analyses.