Many faces of the correlation coefficient


Book: 
Journal of Statistics Education
Authors: 
Falk, R., & Well, A. D.
Category: 
Volume: 
5(3)
Pages: 
Online
Year: 
1997
URL: 
http://www.amstat.org/publications/jse/v5n3/falk.html
Abstract: 

Some selected interpretations of Pearson's correlation coefficient are considered. Correlation may be interpreted as a measure of closeness to identity of the standardized variables. This interpretation has a psychological appeal in showing that perfect covariation means identity up to positive linearity. It is well known that |r| is the geometric mean of the two slopes of the regression lines. In the 2 x 2 case, each slope reduces to the difference between two conditional probabilities so that |r| equals the geometric mean of these two differences. For bivariate distributions with equal marginals, that satisfy some additional conditions, a nonnegative r conveys the probability that the paired values of the two variables are identical by descent. This interpretation is inspired by the rationale of the genetic coefficient of inbreeding.

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