Experimental Design and Causal Inference Primer Cheat Sheet

Key Facts

• The individual causal effect is $\tau_i = Y_i(1) - Y_i(0)$, but only one of $Y_i(1)$ or $Y_i(0)$ is observed for each unit.
• The average treatment effect is $ATE = E[Y(1) - Y(0)]$, which summarizes the mean causal effect in a target population.
• In a randomized experiment, treatment assignment satisfies $T \perp \{Y(0),Y(1)\}$, so treated and control groups are comparable in expectation.
• A simple difference in means estimator is $\hat{\tau} = \bar{Y}_T - \bar{Y}_C$, where $\bar{Y}_T$ is the treated mean and $\bar{Y}_C$ is the control mean.
• Confounding occurs when a variable $Z$ affects both treatment $T$ and outcome $Y$, creating a backdoor path such as $T \leftarrow Z \rightarrow Y$.
• Blocking or stratification improves precision by comparing treatment groups within levels of an important variable, then combining stratum estimates.
• A standard error for a difference in independent means is $SE(\bar{Y}_T - \bar{Y}_C) = \sqrt{\frac{s_T^2}{n_T} + \frac{s_C^2}{n_C}}$.
• A common approximate confidence interval for a treatment effect is $\hat{\tau} \pm z^{*}SE(\hat{\tau})$, where $z^{*}$ depends on the confidence level.

Vocabulary

Random assignment

A design method where units are assigned to treatment conditions by chance so that groups are comparable before treatment.

Potential outcome

The outcome a unit would have under a specific treatment condition, such as $Y_i(1)$ under treatment or $Y_i(0)$ under control.

Average treatment effect

The expected difference between potential outcomes in a population, written $ATE = E[Y(1) - Y(0)]$.

Confounder

A variable that influences both the treatment and the outcome, which can make an association look causal when it is not.

Blocking

A design strategy that groups similar units before random assignment to reduce variation and improve precision.

Causal diagram

A graph using arrows to represent assumed causal relationships among variables.