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A Powerful and Robust Test Statistic for Randomization Inference in Group-Randomized Trials with Matched Pairs of Groups

Authors

  • Kai Zhang,

    Corresponding author
    1. Department of Statistics, The Wharton School, University of Pennsylvania, Philadelphia, Pennsylvania 19104, U.S.A.
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  • Mikhail Traskin,

    Corresponding author
    1. Department of Statistics, The Wharton School, University of Pennsylvania, Philadelphia, Pennsylvania 19104, U.S.A.
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  • Dylan S. Small

    Corresponding author
    1. Department of Statistics, The Wharton School, University of Pennsylvania, Philadelphia, Pennsylvania 19104, U.S.A.
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email:zhangk@wharton.upenn.edu

email:mtraskin@wharton.upenn.edu

email:dsmall@wharton.upenn.edu

Abstract

Summary For group-randomized trials, randomization inference based on rank statistics provides robust, exact inference against nonnormal distributions. However, in a matched-pair design, the currently available rank-based statistics lose significant power compared to normal linear mixed model (LMM) test statistics when the LMM is true. In this article, we investigate and develop an optimal test statistic over all statistics in the form of the weighted sum of signed Mann-Whitney-Wilcoxon statistics under certain assumptions. This test is almost as powerful as the LMM even when the LMM is true, but it is much more powerful for heavy tailed distributions. A simulation study is conducted to examine the power.

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