Jizhou Liu, Azeem M. Shaikh, Liang Zhong
arXiv 5 Jul 2026 · Statistics — Methodology
arXiv:2607.04257 · PDF · DOI · OpenAlex · Extracted main text
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.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Basse, G. W., Feller, A. and Toulis, P (2019) Randomization tests of causal effects under interference | 0.961 | 9 | 4 | 89% |
| 2 | Basse, G. and Feller, A (2018) Analyzing two-stage experiments in the presence of interference | 0.874 | 5 | 2 | 100% |
| 3 | Liu, J (2026) Inference for two-stage experiments under covariate-adaptive randomization self | 0.811 | 4 | 2 | 100% |
| 4 | Zhong, L (2024) Unconditional randomization tests for interference self | 0.811 | 4 | 2 | 100% |
| 5 | Imai, K., Jiang, Z. and Malani, A (2021) Causal inference with interference and noncompliance in two-stage randomized experiments | 0.737 | 3 | 2 | 100% |
| 6 | Hudgens, M. G. and Halloran, M. E (2008) Toward causal inference with interference | 0.737 | 3 | 2 | 100% |
| 7 | Cruces, G., Tortarolo, D. and Vazquez-Bare, G (2025) Design of partial population experiments with an application to spillovers in tax compliance | 0.644 | 2 | 2 | 100% |
| 8 | Basse, G., Ding, P., Feller, A. and Toulis, P (2024) Randomization tests for peer effects in group formation experiments | 0.644 | 2 | 2 | 100% |
| 9 | Athey, S., Eckles, D. and Imbens, G. W (2018) Exact p-values for network interference | 0.511 | 2 | 1 | 100% |
| 10 | Aronow, P. M (2012) A general method for detecting interference between units in randomized experiments | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 26 scored citations.