Taking correlation before or after log-transformation of variables

Is there a general principle on whether one should compute pearson correlation for two random variables X and Y before taking their log transform or after? Is there a procedure to test which is more appropriate? They yield similar but different values, since log transform is non-linear. Does it depend on whether X or Y are closer to normality after log? If so, why does that matter? And does that mean that one should do a normality test on X and Y versus log(X) and log(Y) and based on that decide whether pearson(x,y) is more appropriate than pearson(log(x),log(y))?

• @vinux has a nice answer, and provides an informative link for understanding the role of normality in correlation. I just wanted to point to this question: stats.stackexchange.com/questions/298 which is very good for understanding what logs do in regression. – gung Feb 13 '12 at 17:46

Because $\log(X)$ and $\log(Y)$ are monotonic transformations of the data $X$ and $Y$, you might also choose to use Spearman's rank correlation ($\rho_S$) and not worry about transforming your data, as you would get $\rho_S(X,Y) = \rho_S(\log(X),\log(Y))$