This paper studies inference in randomized controlled trials with multiple treatments, where treatment status is determined according to a "matched tuples" design. Here, by a matched tuples design, we mean an experimental design where units are sampled i.i.d. from the population of interest, grouped into "homogeneous" blocks with cardinality equal to the number of treatments, and finally, within each block, each treatment is assigned exactly once uniformly at random. We first study estimation and inference for matched tuples designs in the general setting where the parameter of interest is a vector of linear contrasts over the collection of average potential outcomes for each treatment. Parameters of this form include standard average treatment effects used to compare one treatment relative to another, but also include parameters which may be of interest in the analysis of factorial designs. We first establish conditions under which a sample analogue estimator is asymptotically normal and construct a consistent estimator of its corresponding asymptotic variance. Combining these results establishes the asymptotic exactness of tests based on these estimators. In contrast, we show that, for two common testing procedures based on t-tests constructed from linear regressions, one test is generally conservative while the other generally invalid. We go on to apply our results to study the asymptotic properties of what we call "fully-blocked" 2^K factorial designs, which are simply matched tuples designs applied to a full factorial experiment. Leveraging our previous results, we establish that our estimator achieves a lower asymptotic variance under the fully-blocked design than that under any stratified factorial design which stratifies the experimental sample into a finite number of "large" strata. A simulation study and empirical application illustrate the practical relevance of our results.

翻译：本文研究多元处理的随机对照试验中的推断问题，其中处理状态根据“匹配元组”设计确定。这里，匹配元组设计是指：从目标总体中独立同分布地抽取实验单元，将其分组为基数等于处理数的“同质”区组，并在每个区组内随机均匀分配每种处理恰好一次。我们首先在一般设定下研究匹配元组设计的估计与推断，其中目标参数为各处理平均潜在结果集合上的线性对比向量。此类参数不仅包括用于比较两种处理相对优劣的标准平均处理效应，还涵盖析因设计分析中可能关注的参数。我们首先建立了样本模拟估计量渐近正态的条件，并构造了其对应渐近方差的一致估计量。结合这些结果，可证明基于这些估计量的检验具有渐近精确性。与之对比，我们表明，对于两种基于线性回归t检验的常见检验程序，其中一个检验通常偏保守，另一个通常无效。随后，我们将上述结果应用于研究我们称为“完全区组”的2^K析因设计的渐近性质——这本质上是将匹配元组设计应用于全因子实验。利用前期结果，我们证明在完全区组设计下，我们的估计量达到的渐近方差低于任何将实验样本分层为有限个“大层”的分层析因设计。模拟研究与实证应用进一步说明了我们结果的实际意义。