Cause and effect
Methods for answering whether one thing caused another when you cannot randomise, and the biases that make an observed difference look like a causal one.
A randomised experiment answers a causal question by construction: assignment is independent of everything else, so a difference in outcomes has nowhere else to come from. When randomisation is impossible — because the change is already live, or applies to whole markets, or is a decision somebody else made — the causal claim has to be built rather than assumed, and the terms here are how.
What every method in this group is doing is constructing a counterfactual: an estimate of what would have happened without the change. Difference-in-differences builds it from a parallel group's trend, synthetic control from a weighted combination of untreated units, and propensity score matching from comparable individuals. They differ in what they assume, and the assumption is always the load-bearing part.
The failure mode they exist to avoid has two names here. Confounding is a third variable driving both the treatment and the outcome; selection bias is the treated group differing from the untreated one in a way that was never measured. Both produce a clean correlation and a wrong causal claim, and neither is detectable from the data alone — which is why the design matters more than the model.
This is most of what we are hired for. See our causal inference work.
Causal Inference Analysis at Bell Statistics
We build causal measurement for teams that cannot randomise — geo tests, synthetic controls and the models that calibrate against them. See how we work.