Correlation between non-independent variables

I want to conduct correlation between two variables, that have common term (difference scores).

Originally there are three variables X, Y, Z. I want to conduct correlation between two variables that are computed as:

First variable: X - Y Second variable: Y - Z

I know, that the correlation will be spurious and I wonder whether it is possible to correct it in some way. From theoretical reasons, I need correlation (or some other measure of relation) between variables that have this common term.

I will add also, that what I am interested is not the value of correlation coefficient, but I want to compare relative strength of correlation between these variables in different conditions. That is why I thought that maybe I can transform r values to Z values using Fisher's transformation, because I assumed that even if values of correlation coefficents will be inflated, it still would be possible to compare they relative strength.

• $\operatorname{cov}(X-Y,Y-Z)=\operatorname{cov}(X,Y)-\operatorname{cov}(X,Z)-\operatorname{var}(Y)+\operatorname{cov}(Y,Z)$ – Dilip Sarwate Sep 18 '14 at 2:12

$$\operatorname{cov}(X-Y,Y-Z)=\operatorname{cov}(X,Y)-\operatorname{cov}(X,Z)-\operatorname{var}(Y)+\operatorname{cov}(Y,Z)$$ – Dilip Sarwate