Thinking, Fast and Slow

17: Regression to the Mean
help of the most brilliant statisticians
: Michael Bulmer, 
Francis Galton: Pioneer of

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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.