# Measuring linear correlation of non-normally distributed variables

How can I measure linear correlation of non-normally distributed variables? Pearson coefficient is not valid for non-normally distributed data, and Spearman's rho does not capture linear correlation.

Thank you

• Linear correlation is defined without regard to the underlying distribution. I do not know what you mean by "Pearson is not valid for non-normally distributed data." Perhaps you are thinking of hypothesis testing? – charles.y.zheng Mar 9 '11 at 9:45
• This question is an extremely close relative of stats.stackexchange.com/questions/3730/… – whuber Mar 9 '11 at 17:09

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.