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.
Cultural Loading, Heritability, and the BW gap
As Meng Hu noted, Kan et al. (2011) showed that subtest cultural-loadings, as they estimated them, correlated both with the magnitude of the B/W subtest gaps and with subtest heritability estimates. The authors interpreted these associations as support for a GxE hypothesis of individual differences and offered a model similar to that proposed by Flynn and Dickens (2001). Moreover, Kan et al. (2011) saw the associations between cultural-load and heritability and between cultural-load and the magnitude of the BW gap as problematic for what they termed a biological g model. Below, I will show that g-loadings fully mediate the association between cultural loadings and the two other variables noted and therefore that what is in need of explanation is only the association between cultural-loadings and g-loadings. I will then proceed to offer an account for this.
First, I looked to see if g-loadings mediated the association between the BW gap and cultural loadings. They did. Then I looked to see if cultural-loadings mediated the association between the BW gap and g-loadings. They did not fully. The results are shown below. As reliability estimates were not presented for all subtests, I ran the analysis with and without reliability corrections. Continue reading
Number 4 in the social science’s top 10 list of “grand challenge questions that are both foundational and transformative” (Giles, 2010) is: “How do we reduce the ‘skill gap’ between black and white people in America?” Presumably, figuring out the cause of this psychometric intelligence differential would help when it comes to deciding how best to minimize it. If so, we can thank Meng Hu for his recent efforts focused on determining the cause. This includes his recent extensive exploration of differential regression.
The IQ differences between blacks and whites lead to differences in sibling regression to the mean. The races regress to different means. Criticisms were made about the hereditarian interpretation of the differential sibling regressions. I will demonstrate that this phenomenon (1) is not a statistical artifact and (2) is consistent with the hereditarian interpretation of it.