The Power of Optimization Over Randomization in Designing Experiments Involving Small Samples
The Power of Optimization Over Randomization in Designing Experiments Involving Small Samples
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DOI：
10.1287/opre.2015.1361
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发表时间：
2015-07-01
影响因子：
2.7
通讯作者：
Kallus, Nathan
中科院分区：
文献类型：
--
作者：
Bertsimas, Dimitris;Johnson, Mac;Kallus, Nathan
随机分配，通常被视为对照试验的标准，旨在使实验组在治疗前具有统计学等效性。然而，由于样本很小，这在许多学科中都是一个实际的现实，随机分组往往太不相似而没有用处。我们提出了一种基于离散线性优化的方法来创建组，其均值和方差的差异比随机化小几个数量级。我们提供的理论和计算证据表明，通过优化创建的组具有比随机化创建的组指数更低的差异，这允许更强大的统计推断。
Random assignment, typically seen as the standard in controlled trials, aims to make experimental groups statistically equivalent before treatment. However, with a small sample, which is a practical reality in many disciplines, randomized groups are often too dissimilar to be useful. We propose an approach based on discrete linear optimization to create groups whose discrepancy in their means and variances is several orders of magnitude smaller than with randomization. We provide theoretical and computational evidence that groups created by optimization have exponentially lower discrepancy than those created by randomization and that this allows for more powerful statistical inference.