As a public service, I am going to offer two propositions about correlation.

1. Where there is correlation, there is signal.

2. Where there is noise, correlation is understated.

The other night, I met with a large group of people to discuss Gregory Clark’s new book. Many people made comments that were uninformed regarding these two propositions.

For example, I gather that people who are strongly into political correctness are wont to say that “There is no reason to believe that IQ measures anything.” I think that is untrue.

Measured IQ is correlated with other variables, including education and income. Any variable that is reliably correlated with other variables must have some signal. It must be measuring something. It may not be measuring what it purports to measure. It may not have a causal relationship with the variables to which it is correlated. But to deny that it measures anything at all moves you deeply into science-denier territory.

Other comments suggest that people believe that if the correlation between parents and children on some variable is, say, 0.4, then this represents a ceiling on heritability. In fact, if measurement of the variable in question is subject to noise, then true heritability could be higher. For example, if IQ tests are inexact (which I assume they are), then it could be that the heritability of “true IQ” could be 0.6, even though the heritability of measured IQ is only 0.4. The opposite is not the case–random noise will not cause the measured IQ to appear more correlated than it really is. The bias is only downward.

I have written a review (may appear next month) of Clark’s book, and in my view the main contribution of his multigenerational studies of social mobility is to give us a means for assessing the impact of noise on heritability estimates. The affect appears to be large, meaning that some characteristics are far more heritable than one-generation correlation studies suggest.