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Statistica Sinica 27 (2017), 1319-1345

MORE POWERFUL MULTIPLE TESTING IN RANDOMIZED
EXPERIMENTS WITH NON-COMPLIANCE
Joseph J. Lee1, Laura Forastiere2, Luke Miratrix1 and Natesh S. Pillai1
1Harvard University and 2University of Florence

Abstract: Two common concerns raised in analyses of randomized experiments are (i) appropriately handling issues of non-compliance, and (ii) appropriately adjusting for multiple tests (e.g., on multiple outcomes or subgroups). Although simple intention-to-treat (ITT) and Bonferroni methods are valid in terms of type I error, they can each lead to a substantial loss of power; when employing both simultaneously, the total loss may be severe. Alternatives exist to address each concern. Here we propose an analysis method for experiments involving both features that merges posterior predictive 𝒫-values for complier causal effects with randomization- based multiple comparisons adjustments; the results are valid familywise tests that are doubly advantageous: more powerful than both those based on standard ITT statistics and those using traditional multiple comparison adjustments. The operating characteristics and advantages of our method are demonstrated through a series of simulated experiments and an analysis of the United States Job Training Partnership Act (JTPA) Study, where our methods lead to different conclusions regarding the significance of estimated JTPA effects.

Key words and phrases: Causal inference, hypothesis testing, multiple comparisons, posterior predictive p-value, principal stratifiation, randomization-based inference.

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