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:本文用多种处理方法随机控制试验中的推断值, 处理状态是根据“ 匹配的图例” 设计来确定的。 这里, 匹配的图例设计, 我们指的是实验设计, 从感兴趣的人群中抽样单位 i. d., 组成“ 混合的” 区块, 其基数与治疗次数相等, 最后, 在每个区块中, 每种处理都被完全一致地指定为随机的。 我们首先研究一般环境中匹配图例的设计的估算值和推断值, 其匹配的图例设计, 其总设置的参数是线性对比值的矢量对比值 。 这个表格的参数包括用于比较一个治疗对象相对于另一个对象的标准平均处理效果的处理效果, 但也包括可能有兴趣的参数 。 我们首先建立一个样本模拟的基数, 并构建一个一致的测试结果 。 我们的测试结果为两个测试基点的测试基数 。 我们的测试结果为“ 常规的图例设计中, 测试结果为一个常规的基数, 测试结果为一个常规的基数。</s>