The Power of Optimization Over Randomization in Designing Experiments Involving Small Samples

• 成果类型: Article
• 署名作者: Bertsimas, Dimitris; Johnson, Mac; Kallus, Nathan
• 署名单位: Massachusetts Institute of Technology (MIT); Massachusetts Institute of Technology (MIT)
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.2015.1361
• 发表日期: 2015
• 页码: 868-876
• 关键词: propensity score

摘要

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.