13 ways to look at (Galton-Pearson) correlation

Found this paper on having a nosy around to see different ways of correlating non-Gaussian variables: Joseph Lee Rodgers and W. Alan Nicewander (1988). Thirteen Ways to Look at the Correlation Coefficient. The American Statistician, 42(1), 59-66.

Therein you’ll find details of the history (apparently Gauss got there first, but didn’t care about the special case of bivariate correlation); a range of examples of how to get the coefficient (e.g., standardised covariance, standardised regression slope, a geometric interpretation in “person space”, the balloon rule). Also a nice reminder that, in terms of the maths, the dichotomy between experimental and observational analysis is false: the difference lies in interpretation. Still many people seem to think that ANOVA is for experiments and regression is for observational studies (or that SEM magically deals with causation in observational studies).

All amusing stuff.