Propensity score matching (PSM)

Propensity score matching estimates a causal effect from observational data by first modeling each unit's propensity score, its estimated probability of receiving treatment given its observed characteristics, then pairing each treated unit with an untreated unit that has a similar score. Comparing outcomes within these matched pairs approximates the comparison a randomized experiment would have produced, at least with respect to the characteristics used to build the score.

The method only controls for selection bias arising from variables that were actually measured and included in the model. Any unmeasured factor that influences both treatment and outcome, a classic confounder, remains uncorrected, and no statistical test can rule this out from the data alone; it depends on domain judgment about what else might matter.

PSM is used where randomization was never possible, comparing customers who opted into a loyalty program against similar customers who didn't, for instance, and it sits alongside difference-in-differences and instrumental variables as a standard toolkit for causal claims from non-experimental data. Its main pitfall is treating a matched comparison as equivalent to a randomized A/B test: it can only be as good as the variables chosen to compute the propensity score.