Thinking, Fast and Slow

17: Regression to the Mean
help of the most brilliant statisticians
: Michael Bulmer, 
Francis Galton:
Pioneer of Heredity and Biometry
(Baltimore: Johns Hopkins University
Press, 2003).
standard scores: Researchers transform each original score into a
standard score by subtracting the mean and dividing the result by the
standard deviation. Standard scores have a mean of zero and a standard
deviation of 1, can be compared across variables (especially when the
statistica {he deviatiol distributions of the original scores are similar), and
have many desirable mathematical properties, which Galton had to work
out to understand the nature of correlation and regression.
correlation between parent and child
: This will not be true in an

---

environment in which some children are malnourished. Differences in
nutrition will become important, the proportion of shared factors will
diminish, and with it the correlation between the height of parents and the
height of children (unless the parents of malnourished children were also
stunted by hunger in childhood).
height and weight
: The correlation was computed for a very large sample
of the population of the United States (the Gallup-Healthways Well-Being
Index).
income and education
: The correlation appears impressive, but I was
surprised to learn many years ago from the sociologist Christopher Jencks
that if everyone had the same education, the inequality of income
(measured by standard deviation) would be reduced only by about 9%.
The relevant formula is v (1–r
2
), where 
r
is the correlation.
correlation and regression
: This is true when both variables are measured
in standard scores—that is, where each score is transformed by removing
the mean and dividing the result by the standard deviation.
confusing mere correlation with causation
: Howard Wainer, “The Most
Dangerous Equation,” 
American Scientist
95 (2007): 249–56.