Two-sample tests have been one of the most classical topics in statistics with wide application even in cutting edge applications. There are at least two modes of inference used to justify the two-sample tests. One is usual superpopulation inference assuming the units are independent and identically distributed (i.i.d.) samples from some superpopulation; the other is finite population inference that relies on the random assignments of units into different groups. When randomization is actually implemented, the latter has the advantage of avoiding distributional assumptions on the outcomes. In this paper, we will focus on finite population inference for censored outcomes, which has been less explored in the literature. Moreover, we allow the censoring time to depend on treatment assignment, under which exact permutation inference is unachievable. We find that, surprisingly, the usual logrank test can also be justified by randomization. Specifically, under a Bernoulli randomized experiment with non-informative i.i.d. censoring within each treatment arm, the logrank test is asymptotically valid for testing Fisher's null hypothesis of no treatment effect on any unit. Moreover, the asymptotic validity of the logrank test does not require any distributional assumption on the potential event times. We further extend the theory to the stratified logrank test, which is useful for randomized blocked designs and when censoring mechanisms vary across strata. In sum, the developed theory for the logrank test from finite population inference supplements its classical theory from usual superpopulation inference, and helps provide a broader justification for the logrank test.

翻译：两次模版测试是统计中最古老的话题之一, 甚至在尖端应用中也广泛应用。 在本文中, 至少有两种模式用来证明两次模版测试的合理性。 一种是通常的超人口推论, 假设单位是独立的, 某些超人口样本分布相同( i.d.) ; 另一种是有限的人口推论, 取决于单位随机分配到不同组。 当实际应用随机化时, 后者具有避免对结果进行分布假设的优势。 在本文中, 我们将侧重于受审查结果的有限人口推论, 这在文献中探索得较少。 此外, 我们允许审查时间以处理任务为依据, 假设单位的精确变异性推论是无法实现的。 我们发现, 奇怪的是, 通常的校正测试测试也可以通过随机化实验进行。 具体地说, 在每个治疗臂内进行检查时, 校正测试对于测试结果的逻辑值是有效的, 更精确性测试的逻辑是更精确性的, 在任何单位里程中, 也要求更精确的逻辑的逻辑推算。