Randomized Experiments
Randomized experiments use a known chance mechanism to assign treatment. This makes treatment and control groups comparable in expectation and permits causal inference from observed outcomes.
See
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Potential Outcomes Framework
- Defines causal effects and the missing-counterfactual problem.
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Randomized Assignment
- Bernoulli and completely randomized assignment mechanisms.
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Neyman Repeated-Sampling Inference
- Estimation, variance, standard errors, and confidence intervals for an average effect.
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Fisher Randomization Inference
- Exact or simulated tests of a sharp causal null using the assignment mechanism.
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Blocked and Paired Randomized Experiments
- Design and estimation within strata or matched pairs.
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Regression Adjustment in Experiments
- Unadjusted and covariate-adjusted regression estimators.
Design before analysis
The assignment mechanism should be recorded before outcomes are analyzed. The analysis must respect that mechanism: complete randomization, independent Bernoulli assignment, blocking, pairing, and clustering produce different randomization distributions and variance calculations.
Core estimator
For a two-arm experiment,
\[\hat\tau=\bar Y_1-\bar Y_0.\]The formula is simple because random assignment does the identification work. Neyman Repeated-Sampling Inference and Fisher Randomization Inference attach different inferential questions to this or another chosen statistic.
Worked problems and practice
Randomized Experiments Exam Workshop works from a finite potential-outcome schedule through Neyman inference, Fisher’s tea experiment, blocking, and paired designs. Exercises require both calculations and design interpretation.