This paper considers the problem of making inferences about the effects of a program on multiple outcomes when the assignment of treatment status is imperfectly randomized. By imperfect randomization we mean that treatment status is reassigned after an initial randomization on the basis of characteristics that may be observed or unobserved by the analyst. We develop a partial identification approach to this problem that makes use of information limiting the extent to which randomization is imperfect to show that it is still possible to make nontrivial inferences about the effects of the program in such settings. We consider a family of null hypotheses in which each null hypothesis specifies that the program has no effect on one of many outcomes of interest. Under weak assumptions, we construct a procedure for testing this family of null hypotheses in a way that controls the familywise error rate – the probability of even one false rejection – in finite samples. We develop our methodology in the context of a reanalysis of the HighScope Perry Preschool program. We find statistically significant effects of the program on a number of different outcomes of interest, including outcomes related to criminal activity for males and females, even after accounting for imperfections in the randomization and the multiplicity of null hypotheses.

中文翻译：

---

处理不完美随机化：highscope 佩里学前班计划的推论

本文考虑了当治疗状态的分配不完全随机时，如何推断一个项目对多种结果的影响的问题。不完全随机化是指在初始随机化之后，根据分析师可能观察到或未观察到的特征重新分配治疗状态。我们针对这个问题开发了一种部分识别方法，该方法利用限制随机化不完善程度的信息来表明，在这种情况下仍然可以对程序的效果做出重要的推论。我们考虑一系列零假设，其中每个零假设都指定该程序对许多感兴趣的结果之一没有影响。在弱假设下，我们构建了一个程序来测试这一系列零假设，以控制有限样本中的系列错误率（即使是一个错误拒绝的概率）。我们在重新分析 HighScope Perry 学前班项目的背景下制定了我们的方法。我们发现该计划对许多不同的感兴趣结果（包括与男性和女性犯罪活动相关的结果）具有统计上显着的影响，即使在考虑了随机化的缺陷和零假设的多重性之后也是如此。