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 recent book Hive Mind economist Garett Jones argues that the direct effect of IQ on personal income is modest, and that most of the benefits of higher IQ flow from various spillover effects that make societies more productive, boosting everyone’s income. This, he says, explains the “IQ paradox” whereby IQ differences appear to explain a lot more of the economic differences between nations than within them.
Jones does not say in his book what he thinks the exact effect of IQ on personal income is, but on Twitter he has asserted that “Fans of g would do well to look at the labor lit: 1 IQ point predicts just 0.5% to 1.2% higher wages.” He has also said that, in terms of standardized effect sizes, IQ accounts for only about 10% of variance in personal income (a correlation of ~0.32).
While I don’t doubt Jones’s overall thesis that the effect of IQ on productivity is broader than its effect on personal productivity or income, I think he understates the importance of IQ in explaining income differences between individuals. I analyzed a large American population sample and found a substantially larger effect of IQ on permanent income than previous investigations. It appears that the literature Jones refers to has failed to pay sufficient attention to various measurement issues. Continue reading