Two-stage randomized experiments are becoming an increasingly popular experimental design for causal inference when the outcome of one unit may be affected by the treatment assignments of other units in the same cluster. In this paper, we provide a methodological framework for general tools of statistical inference and power analysis for two-stage randomized experiments. Under the randomization-based framework, we propose unbiased point estimators of direct and spillover effects, construct conservative variance estimators, develop hypothesis testing procedures, and derive sample size formulas. We also establish the equivalence relationships between the randomization-based and regression-based methods. We theoretically compare the two-stage randomized design with the completely randomized and cluster randomized designs, which represent two limiting designs. Finally, we conduct simulation studies to evaluate the empirical performance of our sample size formulas. For empirical illustration, the proposed methodology is applied to the analysis of the data from a field experiment on a job placement assistance program.
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