Experimental Research Design

Experimental research design connects probability, statistical inference, and causal identification. The central question is not merely whether two variables are associated, but whether a treatment caused a change in an outcome.

Use this course in this order:

  1. Foundations for Experimental Research
  2. Regression Models for Experimental Research
  3. Randomized Experiments
  4. Observational Causal Inference
  5. Experimental Research Design Formula Sheet

Practice after each section:

Course map

probability and sampling distributions
-> tests, confidence intervals, and ANOVA
-> regression as a model and adjustment tool
-> potential outcomes and the missing counterfactual
-> randomized assignment
-> Neyman and Fisher inference
-> blocking, pairing, and regression adjustment
-> observational identification under assumptions
-> propensity scores, weighting, and matching

The three layers to keep separate

  1. Design determines how treatment is assigned and which comparisons are credible.
  2. Estimation defines how the treatment effect is calculated, such as a difference in means.
  3. Inference quantifies uncertainty or tests a hypothesis under the assignment or sampling process.

Random assignment supplies identification by design. In observational studies, identification instead depends on assumptions such as Unconfoundedness and Overlap.

Core notation

  • $i=1,\ldots,N$ indexes units.
  • $W_i\in{0,1}$ is the treatment indicator.
  • $Y_i(1)$ and $Y_i(0)$ are potential outcomes.
  • $Y_i^{obs}$ is the observed outcome.
  • $N_1$ and $N_0$ are the numbers assigned to treatment and control.
  • $\tau_i=Y_i(1)-Y_i(0)$ is an individual treatment effect.
  • $\hat\tau$ is an estimated average treatment effect.

Exam-first route

  1. Identify the design: independent, paired, stratified, randomized, or observational.
  2. State the estimand and assumptions.
  3. Select the estimator and its standard error.
  4. State the null hypothesis and reference distribution.
  5. Compute an interval or $p$-value and interpret it in context.
  6. Use Experimental Research Design Formula Sheet for rapid recall.

Connections