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Paired or partially paired two‐sample tests with unordered samples

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  • Yudong Wang
  • Yanlin Tang
  • Zhi‐Sheng Ye

Abstract

In paired two‐sample tests for mean equality, it is common to encounter unordered samples in which subject identities are not observed or unobservable, and it is impossible to link the measurements before and after treatment. The absence of subject identities masks the correspondence between the two samples, rendering existing methods inapplicable. In this paper, we propose two novel testing approaches. The first splits one of the two unordered samples into blocks and approximates the population mean using the average of the other sample. The second method is a variant of the first, in which subsampling is used to construct an incomplete U‐statistic. Both methods are affine invariant and can readily be extended to partially paired two‐sample tests with unordered samples. Asymptotic null distributions of the proposed test statistics are derived and the local powers of the tests are studied. Comprehensive simulations show that the proposed testing methods are able to maintain the correct size, and their powers are comparable to those of the oracle tests with perfect pair information. Four real examples are used to illustrate the proposed methods, in which we demonstrate that naive methods can yield misleading conclusions.

Suggested Citation

  • Yudong Wang & Yanlin Tang & Zhi‐Sheng Ye, 2022. "Paired or partially paired two‐sample tests with unordered samples," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(4), pages 1503-1525, September.
    • Handle: RePEc:bla:jorssb:v:84:y:2022:i:4:p:1503-1525
    DOI: 10.1111/rssb.12541
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    References listed on IDEAS

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    1. Akritas, Michael G. & Antoniou, Efi S. & Kuha, Jouni, 2006. "Nonparametric Analysis of Factorial Designs With Random Missingness: Bivariate Data," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1513-1526, December.
    2. Jing Qin & Biao Zhang, 2005. "Marginal likelihood, conditional likelihood and empirical likelihood: Connections and applications," Biometrika, Biometrika Trust, vol. 92(2), pages 251-270, June.
    3. Tomasz Antczak & Rafał Weron, 2019. "Point of Sale (POS) Data from a Supermarket: Transactions and Cashier Operations," Data, MDPI, vol. 4(2), pages 1-4, May.
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