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! 
 A: The value of the correlation coefficient is of importance to qualify its uncertainty. It can be shown with the Cramer-Rao lower bound.
In the particular case of a correlation coefficient, you can find results here: CRLB for Pearson linear correlation, slides 12 and 13.
It means that the variance of an unbiased estimator cannot be lower than that.
You can notice that the higher the correlation, the more precise the estimation can be.
The coefficient you propose SD(x)/Mean(x) has the same idea in it (well done), but is totally ad hoc, and, to the best of my knowledge, not theoretically supported.
Also, be careful, what is the mean correlation? The arithmetic average of the estimated correlation values? There are arguments (cf. information geometry) to show that it is not a good definition. For example, in the multivariate case, an arithmetic average of correlation matrices will not even yield a correlation matrix: there are good chance that the resulting matrix is not positive semi-definite.
If you want to work further these questions, you can google "information geometry of the multivariate normal" to have a glimpse of what you can/should do. Good luck!
