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In addition to Anscombe's quartet as mentioned by Peter Flom, here is a very nice paper in the risk-management context illustrating the problems of using linear correlation with non-normally distributed variables. In a nutshell, much of our intuition about how correlation behaves -- all values of $\rho \in [-1, 1]$ are possible; an exact monotonic relationship implies $|\rho | = 1$; $\rho = 0$ implies independence; etc, doesn't necessarily apply in the case of normalitynon-normality.

In addition to Anscombe's quartet as mentioned by Peter Flom, here is a very nice paper in the risk-management context illustrating the problems of using linear correlation with non-normally distributed variables. In a nutshell, much of our intuition about how correlation behaves -- all values of $\rho \in [-1, 1]$ are possible; an exact monotonic relationship implies $|\rho | = 1$; $\rho = 0$ implies independence; etc, doesn't necessarily apply in the case of normality.

In addition to Anscombe's quartet as mentioned by Peter Flom, here is a very nice paper in the risk-management context illustrating the problems of using linear correlation with non-normally distributed variables. In a nutshell, much of our intuition about how correlation behaves -- all values of $\rho \in [-1, 1]$ are possible; an exact monotonic relationship implies $|\rho | = 1$; $\rho = 0$ implies independence; etc, doesn't necessarily apply in the case of non-normality.

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source | link

In addition to Anscombe's quartet as mentioned by Peter Flom, here is a very nice paper in the risk-management context illustrating the problems of using linear correlation with non-normally distributed variables. In a nutshell, much of our intuition about how correlation behaves -- all values of $\rho \in [-1, 1]$ are possible; an exact monotonic relationship implies $|\rho | = 1$; $\rho = 0$ implies independence; etc, doesn't necessarily apply in the case of normality.