 Equation (5)  reveals that can be possible to derive a causal effect in a population by averaging over the effects in subpopulations partitioned by \(Z\). This is what we already saw in  Section 2.2:  if there is no dependence between being treated and being a part of a subpopulation, associations cannot reverse at the general population level. Yet such a derivation is only licensed by causal assumptions about the relationships between the variables. The reader can verify that given the DAG in  Figure 2,  the variables satisfy the back-door criterion (with  \(\b{Z}=\{\textit{Gender}\}\)).[7]