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：本文研究多处理随机对照试验中的推断问题，其中处理状态依据"匹配元组"设计确定。所谓匹配元组设计，是指从目标总体中独立同分布抽样得到实验单元，将其分组为基数等于处理数量的"同质"区组，最后在每个区组内，每种处理均匀随机分配恰好一次。我们首先研究匹配元组设计在一般设定下的估计与推断问题，其中目标参数为各类处理平均潜在结果集合上的线性对比向量。此类参数既包含用于比较不同处理相对效应的标准平均处理效应，也涵盖析因设计分析中可能关注的参数。我们首先建立样本类比估计量渐近正态的条件，并构造其相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。相比之下，我们证明基于线性回归构造t检验的两种常见检验程序中，一种通常偏保守，另一种则通常无效。进一步，我们将结果应用于研究所谓"完全区组"2^K析因设计的渐近性质——该设计实质上是将匹配元组设计应用于全因子实验。利用前述结论，我们证明在完全区组设计下，我们的估计量所能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展示了我们结果的实际价值。