Article by Nassim Nicholas Taleb (source: https://www.academia.edu/39797871/Fooled_by_Correlation_Common_Misinterpretations_in_Social_Science_)
Rule 1: Subadditivity: Correlation cannot be used for nonrandom samples
Rule 2: Variance is superadditive for the subexponential class, and subadditive outside of it
Rule 3: Correlation should never be interpreted linearly without translation via some rescaling
Rule 4: Nonlinearity: One cannot use total correlation entailing X_1 and X_2 when the association between X_1 and X_2 depends in expectation on X_1 or X_2
Rule 5: Dimension reduction: One cannot use orthogonal factors or apply a principal component reduction for r.v.s. X_1,...,X_n if for all i \neq j the association between X_i and X_j depends in expectation on the level of either X_i or X_j. (The flaw infects the "g" in psychometry
To-do: write articles for each rule, breaking them down into example-driven explanations