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 the classic twin study design, identical (MZ) twin pairs are compared to fraternal (DZ) twin pairs so as to estimate the relative contributions of heredity and environment to individual differences. The classic twin design depends on the equal environments assumption (EEA) according to which the shared environment of MZ twins is not more similar than that of DZ twins.
The claim that the EEA is an unrealistic assumption which is routinely violated in reality is perhaps the most common criticism of the classic twin design. Violations of the EEA generally bias estimates of the effect of heredity upwards and those of the environment downwards. For this reason, there have been a number of studies where the assumption has been put to test with research questions such as:
- Are twin pairs who are misinformed about their actual zygosity as similar as pairs who know their real zygosity?
- Are twin pairs with objectively more similar environments more similar phenotypically?
- Are the results of twin studies consistent with the results of other kinds of behavioral genetic designs, such as adoption studies?
This research has indicated that the EEA is generally valid and that even when it’s violated, the effect on parameter estimates is small (Barnes et al., 2014; Felson, 2014).
I think sex differences offer an underappreciated way of further evaluating the EEA. Half of DZ pairs are same-sex (male-male or female-female) and half are opposite-sex (male-female), whereas MZ pairs are, of course, all same-sex. Differences in twin correlations across these sex categories are informative about the EEA because if the shared environment differs by zygosity, you would expect it to differ by sex, too. Continue reading
Jayman (2016) argues:
There is no reason to suspect that human groups that have been separated for tens of thousands of years in vastly different environments would be the same in all their cognitive and behavioral qualities. In fact, a priori we should expect them not to be, since such equivalence after so many generations of separate evolution is nigh impossible.
We can quantify the expectation.
When it comes to quantitative genetic trait differences between populations, the evolutionary default expectation is that differences will be commensurate with the degree of drift (not to be equated with neutral mutations). For diploids, the formula is:
VA G,B = 2FST*VA, C
VA G,B is the genetic variance between groups
VA, C is the additive genetic variance in a common ancestral population
2FST is 2 times the fixation index with respect to low mutation rate biallelic polymorphs of the type that underlie the traits in question (see: Edelaar and Björklund, 2011) Continue reading
A while back, in “People in the Future Will Not Look Like Brazilians”, Razib suggested that the great amalgamation will stall because those who are inclined to out mix will do so, taking with them their xenophilic dispositions. The suggestion prompted a commenter to question whether there was any evidence that preferences for (racial) endogamy had, as seemingly presumed by Razib’s argument, a non-trivial genetic component. Apparently, there has been very little genetically informed research on this or closely related topics. Nonetheless, I was able to locate eight studies based on five independent samples which provided heritability estimates for some measures of national, ethnic, or racial pride, preference, or prejudice. The study results are summarized in the table below.
There’s a long-standing debate about if and how parental socioeconomic status moderates the heritability of IQ. Research has often but not always found that heritability is lower in low-SES families. See Turkheimer and Horn’s excellent review for details (although some of Turkheimer’s own research on this is less than convincing).
Robert Kirkpatrick and colleagues have conducted what may be the best study on the question so far. They use a big Minnesota sample, comprising about about 2500 pairs of adolescent twins, non-twin biological siblings, and adoptive siblings, and investigate if SES moderates either genetic or environmental determinants of IQ. Continue reading
Or nearly so. I was planning to publish that blog article for the 31th December 2014. As you can see, I failed in this task, and didn’t finish in the right time. Anyway, I wrote this article, mainly because I am bothered that when people cite The Bell Curve the typical opponent responds with a link toward Wikipedia, specifically the part related to the “controversy” of The Bell Curve. It goes without saying that these persons did not read the books written in response to The Bell Curve. In fact, they have certainly read none of them. It is ridiculous to cite a book you didn’t read, but apparently, it does not bother many people, as I see.
For the 20 years of the book, I found appropriate to write a defense of the book. Or more precisely, a critical comment on the critics. I have decided to read carefully one of these books I can have access, and for what I have read here and there, it is probably the best book ever written against The Bell Curve. I know that Richard Lynn (1999) has already written a review before. But I wanted to go into the details. The title of the book I’m reviewing is :
Devlin, B. (1997). Intelligence, Genes and Success: Scientists Respond to the Bell Curve. Springer.
In fact, I have read that book some time ago, but didn’t find the need to read everything in detail. And I was unwilling to write a lengthy review. But I have changed my mind because of some nasty cowards.
Jeffery P. Braden. (1994). Deafness, deprivation, and IQ. Springer.
The book is a compilation of studies on deaf people, which concludes that cultural deprivation due to deafness lowers verbal IQ but not nonverbal IQ. Braden sought to prove Arthur Jensen wrong about his conclusions on the genetic component in racial differences in IQ. At the end, his research culminated in a trauma well known to scientific history, namely, his perfectly good theory was ruined by his data. Being born deaf does not affect g. And genetic theories are the most powerful arguments to account for the pattern of the data.
The PDF and data file are available at Open Behavioral Genetics. You can also read the article below the cut.
Published: September 15, 2014
John Fuerst 
Abstract: The authors conducted a meta-analysis of interactions between behavioral genetic variance components (ACE) and race/ethnicity for cognitive ability. The differences between the variance components for Black and White Americans were small, despite the large average test score differences. More substantial differences were found between Hispanics and non-Hispanic Whites, though results were based on only two studies. A biometric re-analysis of the CNLSY survey was then conducted and new meta-analytic results were provided. Results were discussed in light of the bio-ecological model which proposes that when the scores of subgroups are environmentally depressed, heritabilities will be likewise.
Keywords: Race, Ethnicity, Heritability, IQ, Environment, ACE model, bio-ecological model
One of the more famous studies on the heritability of IQ is Eric Turkheimer and colleagues’ 2003 paper called Socioeconomic status modifies heritability of IQ in young children. According to Google Scholar, it has been cited more than 700 times. Based on a sample of 7-year-old twins, the study found that in impoverished families the shared environment accounted for about 60 percent of IQ variance while heritability was close to zero. In contrast, heritability was high and the effect of the shared environment nugatory in affluent families.
The literature on the interaction between socioeconomic status and IQ heritability is very mixed. Several studies besides Turkheimer’s find such interaction (although in no other study is it as extreme as in Turkheimer et al. 2003), but others, including some with the very best study designs, find none. I am not going to try to adjudicate between these contradictory findings at this time. Rather, I will show some interesting, hitherto unpublished (well, careful readers of Boetel and Fuerst’s The Nature of Race have seen them already) results pertaining to Turkheimer’s study and the question of race differences. Continue reading