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.

中文翻译：

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具有无序样本的配对或部分配对两样本检验

在平均相等的配对双样本检验中，经常会遇到无序样本，其中受试者身份未观察到或不可观察，并且不可能将治疗前后的测量联系起来。受试者身份的缺失掩盖了两个样本之间的对应关系，使现有方法不适用。在本文中，我们提出了两种新颖的测试方法。第一个将两个无序样本中的一个拆分为块，并使用另一个样本的平均值来近似总体平均值。第二种方法是第一种方法的变体，其中使用二次抽样来构造一个不完整的U-统计。这两种方法都是仿射不变的，并且可以很容易地扩展到具有无序样本的部分配对双样本测试。推导了所提出的测试统计的渐近零分布，并研究了测试的局部幂。综合仿真表明，所提出的测试方法能够保持正确的大小，并且它们的能力与具有完美配对信息的预言机测试相当。四个真实的例子被用来说明所提出的方法，在这些例子中，我们证明了幼稚的方法会产生误导性的结论。