Randomization Tests in Randomized Saturation Designs

2026-07-05

AI Summary

This study addresses the challenge of testing spillover effects in clustered populations by proposing a finite-sample valid randomization inference method tailored for randomized saturation designs. It develops both conditional and unconditional randomization test frameworks that enable exact hypothesis tests for sharp nulls at both individual and average levels, and, for the first time, provides an unconditional finite-sample valid test for monotonicity assumptions across multiple saturation levels. The approach integrates conditional relabeling distributions, studentized test statistics, and pairwise imputation techniques to accommodate sharp nulls, bounded null hypotheses, and weak average spillover effects. Simulations and an empirical application to a cash transfer experiment in Zimbabwe demonstrate the method’s finite-sample validity and practical feasibility.

Abstract

Randomized saturation designs are widely used to study spillover effects in clustered populations. In these designs, clusters are first assigned to treatment saturation levels, and units are then randomized within clusters according to the assigned saturation. This paper develops randomization tests for such experiments under several null hypotheses that arise naturally in spillover analysis. For a fixed pair of saturation levels, we first study two individual-level hypotheses: a partially sharp null of no spillover effect for every untreated unit and a bounded null that restricts individual spillover effects by a prespecified constant. Both hypotheses can be tested using a common conditional randomization framework, with finite-sample validity obtained by combining the same focal-unit relabeling distribution with null-specific statistics. We then study weak average-spillover nulls and show that, although these nulls do not yield finite-sample exact conditional tests, studentized relabeling statistics deliver asymptotically valid randomization-based inference. Finally, for multiple ordered saturation levels, we develop a finite-sample valid unconditional pairwise-imputation test for global monotonicity of spillover effects. Simulations and an application to the Zomba Cash Transfer experiment illustrate the finite-sample behavior and practical implementation of the methods.

Problem

• randomization tests
• spillover effects
• randomized saturation designs
• null hypotheses
• finite-sample validity

Innovation

• randomization test
• spillover effects
• randomized saturation design
• finite-sample inference
• monotonicity test