Many stratified-randomization designs are special cases of rerandomization.
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In most settings, stratified rerandomization is the most efficient design.
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The choice of designs can be critical for small sample designs (N < 20).
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The number of binary and continuous covariates affects the design choice.
Abstract
Rerandomization is a strategy for improving balance on observed covariates in randomized controlled trials. It has been both advocated and advised against by renowned scholars of experimental design. However, the relationship and differences between stratification, rerandomization, and the combination of the two have not been previously investigated. In this paper, we show that stratified designs can be recreated by rerandomization and explain why, in most cases, stratification on binary covariates followed by rerandomization on continuous covariates is more efficient than rerandomization on all covariates at the same time.
The authors thank Nikolay Angelov, Bength Muthén, Linda Muthén, Mattias Nordin and seminar participants at the Institute for Evaluation of Labour Market and Education Policy (IFAU) and the UppUpp conference, Uppsala University and SLU for helpful comments. Berndt Lundgren is acknowledged for kindly sharing data.