I am reading Pearl, J. (January 1998). "Why there is no statistical test for confounding, why many think there is, and why they are almost right". UCLA Computer Science Department, Technical Report R-256, as cited under 'Further Reading' in the Wikipedia article on confounding.
Pearl gives the following 'associational criteria' for no confounding where $Y$ is the response to the intervention $X: X$ and $Y$ are not confounded in the presence of $T$, if for every $Z$ in $T$:
$(U_1) P(x|z)=P(x)$; or $(U_2) P(y|z,x)=P(y|x)$.
Surely these conditions will never hold exactly for any empirical data set subject to random effects. Does one then replace equality by "no statistically significant inequality" in these conditions? If so, could some pointers on doing this be provided, or a reference.