Statistical inference and power analysis for direct and spillover effects in two-stage randomized experiments.

Area of Science:

• Statistics
• Causal Inference
• Experimental Design

Background:

• Two-stage randomized experiments are increasingly used for causal inference.
• These designs are vital when outcomes are influenced by treatment assignments within clusters.

Purpose of the Study:

• To provide a methodological framework for statistical inference and power analysis in two-stage randomized experiments.
• To develop unbiased estimators for direct and spillover effects and their variance estimators.
• To create hypothesis testing procedures and sample size formulas.

Main Methods:

• Utilized a randomization-based framework for causal inference.
• Developed unbiased estimators for direct effects, average direct effects, and spillover effects.
• Derived conservative variance estimators and sample size formulas.
• Conducted theoretical comparisons with completely randomized and cluster randomized designs.
• Performed simulation studies to validate sample size formulas.

Main Results:

• Established a general framework for statistical inference and power analysis in two-stage randomized experiments.
• Provided unbiased estimators for causal quantities and conservative variance estimators.
• Developed hypothesis testing procedures and derived sample size formulas.
• Demonstrated the utility of the methodology through an empirical illustration on health insurance program evaluation.

Conclusions:

• The proposed methodology offers a robust framework for analyzing two-stage randomized experiments.
• The developed tools facilitate accurate causal inference, hypothesis testing, and sample size determination.
• An open-source software package is available to implement the methodology.