In the potential outcomes framework, each unit has potential outcomes $Y(1)$ and $Y(0)$. The average treatment effect is $\tau=\mathbb{E}[Y(1)-Y(0)]$, which is generally not directly observable because only one potential outcome is realized per unit.

Randomization makes treatment independent of potential outcomes, enabling unbiased estimation of causal effects. In observational studies, identification requires assumptions such as unconfoundedness, overlap, and correct adjustment for confounders.

Good experiments prioritize randomization, blocking, stratification, blinding, and pre-specification. Power analysis and sensitivity to noncompliance or attrition are essential at the design stage.

Propensity scores, inverse probability weighting, matching, marginal structural models, instrumental variables, regression discontinuity, difference-in-differences, synthetic control, and doubly robust estimators are central methods for observational causal analysis.