backdoor criterion

Confounding is the problem of spurious paths: a common cause sends influence into both the treatment and the outcome through a 'back door', creating an association that is not effect. The backdoor criterion is a purely graphical recipe for choosing a set of covariates that, once you condition on it, seals every such back door while leaving the genuine causal path open. It tells you precisely what to adjust for, reading the answer off the diagram rather than off intuition.

A set Z satisfies the criterion for the pair (T, Y) if no node in Z is a descendant of T, and Z blocks every path from T to Y that begins with an arrow pointing into T. Blocking is in the d-separation sense, which means Z must not inadvertently open a collider. When such a Z exists the interventional distribution is identified by the adjustment formula: average the conditional outcome distribution over the distribution of Z.

The criterion is the graphical face of the ignorability assumption used in potential outcomes, and it carries two sharp warnings: do not adjust for descendants of the treatment (you would block part of the effect), and do not blindly add more covariates, since conditioning on a collider or a mediator can create bias where none existed. It is a special case of the do-calculus.