The Potential Outcomes Framework

Units, treatments and potential outcomes; the science table; and why the assignment mechanism decides what the data can tell you.

When one unit's treatment affects another's outcome, or the "treatment" comes in several versions. How to spot it, define new estimands, and design around it.

Which average effect answers which policy question, how the averages relate, and why the distribution of effects is mostly out of reach.

Why naive comparisons fail. Decomposing them into the ATE, selection bias and heterogeneity bias, and the Roy model of people choosing treatment.

How random assignment makes treatment independent of everything that came before, what balance tables can and cannot tell you, and internal versus external validity.

The exact variance of the difference in means over all possible randomisations, why it cannot be estimated without bias, and why the standard estimator is conservative.

Exact p-values from the randomisation itself, under the sharp null of no effect for anyone, with no distributional assumptions.

Randomising within blocks of similar units removes chance imbalance on the blocking variables and can sharply reduce variance.

Using baseline covariates to sharpen experimental estimates, Freedman's critique of ANCOVA, and Lin's fully interacted fix.

Randomising schools, clinics or villages instead of individuals; the intra-cluster correlation, the design effect, and why the number of clusters is what buys power.

When people do not take the treatment they are assigned. Intention-to-treat effects, compliance types, and the effect for compliers.

The two assumptions behind every "selection on observables" method, what they buy, how to probe them, and what to do when overlap is poor.

One number, the probability of treatment given covariates, is enough to remove all confounding by those covariates. Why it works and how to use it.

Re-weighting treated and control units by the inverse of their propensity scores to recreate the population each group is missing.

Combining an outcome model with a propensity model so that the estimate is right if either one is. The bridge from Phase 3 to double machine learning.