# Coefficient of variation of correlation values

I have the following problem that I am not sure of whether I treat it correctly:

I run repeated simulations, where the output of a single simulation replicate is a single correlation value. The simulation is replicated (let's say) 1,000 times and finally the mean correlation is calculated for a certain parameter setting of the simulation.

The goal is now to compare for different parameter settings not only the mean correlation, but also to which degree the correlation varies across simulation replicates in comparison with other parameter settings. My first approach was to compare the standard deviation of the correlation across the different parameter settings, but I am uncertain about how this is influenced by the actual mean value of the correlation. Would it be appropriate to use the coefficient of variation, i.e., SD(x)/Mean(x), x being the vector of the 1,000 correlation values of one parameter setting, and to compare this value to those of other parameter settings?

Thanks in advance for any help!

• I do not know if your coefficient SD(x)/Mean(x) can be helpful in your case. I'm just saying that it is not well supported in theory. What you can do is using for example the Kullback-Leibler divergence (close formula can be found in wikipedia) between two bivariate centered Gaussians (parametrized by your estimated average correlation), and you can use the dissimilarity it gives. Kullback-Leibler (Hellinger, and others called the $f$-divergences) are in fact locally taking into account the CRLB: when correl is low, the divergence grows slowly, high correl yields fast divergence. – mic Aug 31 '16 at 14:44