arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2008.01029stat.ME
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随机试验中的条件假设分析

Conditional As-If Analyses in Randomized Experiments

Nicole E. Pashley, Guillaume W. Basse, Luke W. Miratrix

摘要:

“分析你随机化的方式”这一命令对统计学家来说是众所周知的,因为费舍尔主张将随机化作为推断的基础。然而,即使是那些相信基于随机化的推理的优点的人,也很少严格遵守这一禁令。伯努利随机化实验经常被分析为完全随机化实验,而完全随机化实验被分析为好像它们已经分层;更一般地说,分析一个实验就好像它已经被不同地随机化并不罕见。本文在一个基于随机化的框架内研究了这种做法背后的理论基础。具体地说,我们要问的是,什么时候可以合法地分析一个根据一种设计随机化的实验,就好像它是根据其他设计随机化的一样。我们表明,这种类型的分析是有效的一个充分条件是,用于分析的设计是来自原始设计的适当形式的条件。我们用我们的理论来证明某些现有的方法,质疑他人,并最终提出新的方法论见解,如条件近似协变量平衡。

英文摘要:

The injunction to `analyze the way you randomize' is well-known to statisticians since Fisher advocated for randomization as the basis of inference. Yet even those convinced by the merits of randomization-based inference seldom follow this injunction to the letter. Bernoulli randomized experiments are often analyzed as completely randomized experiments, and completely randomized experiments are analyzed as if they had been stratified; more generally, it is not uncommon to analyze an experiment as if it had been randomized differently. This paper examines the theoretical foundation behind this practice within a randomization-based framework. Specifically, we ask when is it legitimate to analyze an experiment randomized according to one design as if it had been randomized according to some other design. We show that a sufficient condition for this type of analysis to be valid is that the design used for analysis be derived from the original design by an appropriate form of conditioning. We use our theory to justify certain existing methods, question others, and finally suggest new methodological insights such as conditioning on approximate covariate balance.

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