Variance identification and efficiency analysis in randomized experiments under the matched-pair design.

Area of Science:

• Statistics
• Experimental Design
• Econometrics

Background:

• Neyman's 1923 work introduced randomization-based inference for estimating average treatment effects (ATE) in completely randomized designs.
• Standard estimators rely solely on the treatment assignment mechanism for variance inference.

Purpose of the Study:

• Extend Neyman's randomization-based inference to matched-pair designs.
• Analyze the relative efficiency of matched-pair versus completely randomized designs for ATE estimation.
• Provide methods for empirical evaluation of design efficiency.

Main Methods:

• Randomization-based inference under matched-pair design.
• Variance identification for standard ATE estimators.
• Efficiency analysis comparing matched-pair and completely randomized designs.
• Empirical evaluation using experimental data.

Main Results:

• Identified variance for standard ATE estimators in matched-pair experiments.
• Quantified the relative efficiency gains of matched-pair designs over completely randomized designs.
• Developed methods for empirical assessment of design efficiency.

Conclusions:

• Matched-pair designs offer potential efficiency improvements for ATE estimation.
• Randomization-based analysis minimizes reliance on modeling assumptions.
• The findings are illustrated with numerical and empirical examples.