 Distinguishing mediators from common causes is crucial for analyses of Simpson’s Paradox. For example, the causal models \(C\to Z \to E\) and \(C\leftarrow Z \to E\) exhibit the same conditional independencies: \(C\) and \(E\) will be associated unconditionally, but independent conditional on \(Z\). Only causal knowledge enables us to decide how we shall deal with the association reversal, and whether we need to condition upon \(Z\) when estimating the causal effect of \(C\) on \(E\) (we do in the second model, but not in the first). See also  Section 3.4.