Causal inference studies what would happen under interventions rather than what merely co-moves in observed data. The field connects design, assumptions, and estimation: a randomized trial, a DAG, an IV design, and a weighted estimator are all different ways to argue for the same counterfactual comparison. The core practical question is not whether a model fits well, but whether the identifying assumptions are plausible for the estimand you actually care about. Read the tables as a workflow: define the target effect, map the data-generating process, choose an identification strategy, stress-test the assumptions, and only then optimize estimation.
What This Cheat Sheet Covers
This topic spans 11 focused tables and 109 indexed concepts, 105 flashcards. Below is a complete table-by-table outline of this topic, spanning foundational concepts through advanced details.
A jump-to index of every table row in this cheat sheet.
An interactive map of every table and concept in this topic.
Table 1: Core Frameworks
The potential-outcomes vocabulary — estimands, assumptions, and counterfactuals — is the lingua franca of modern causal inference. Choosing the right estimand (ATE, ATT, CATE, ATO) before touching data prevents the most common framing errors.
| Concept | Example | Description | |
|---|---|---|---|
$Y(1), Y(0)$ observed: Y = TY(1) + (1-T)Y(0) | Counterfactual framework: each unit has an outcome under every possible treatment, only one of which is ever observed. | ||
$ATE = E[Y(1)-Y(0)]$ | • Population-average causal effect • the benchmark estimand | ||
$ATT = E[Y(1)-Y(0) \mid T=1]$ | • Effect for units that actually received treatment • naturally targeted by matching | ||
$CATE(x) = E[Y(1)-Y(0) \mid X=x]$ | • Effect conditional on covariates • the target of heterogeneous-effect methods | ||
$ATU = E[Y(1)-Y(0) \mid T=0]$ | • Effect for the control group • relevant when policy would expand coverage to untreated | ||
$ATO = E[(1-e(X))Y(1) - e(X)Y(0)]$ | • Weighted estimand targeting units with equipoise • minimizes variance and avoids extrapolation. | ||
no hidden versions no interference | • Each unit's outcome depends only on its own treatment, not others'. • Violated by spillovers, network effects, or multiple treatment versions. | ||
$T=1 \Rightarrow Y=Y(1)$ | • Observed outcome equals the relevant potential outcome • requires a well-defined treatment | ||
$Y(t) \perp T \mid X$ | • No unmeasured confounding after conditioning on $X$ • also called ignorability. | ||
$0 < P(T=1 \mid X=x) < 1$ | • Every covariate stratum must admit both treatment states • violations cause near-infinite weights |