In mixed methods approaches, statistical models are used to identify “nested” cases for intensive, small-n investigation for a range of purposes, including notably the examination of causal mechanisms. This article shows that under a commonsense interpretation of causal effects, large-n models allow no reliable conclusions about effect sizes in individual cases—even if we choose “onlier” cases as is usually suggested. Contrary to established practice, we show that choosing “reinforcing” outlier cases—where outcomes are stronger than predicted in the statistical model—is appropriate for testing preexisting hypotheses on causal mechanisms, as this reduces the risk of false negatives. When investigating mechanisms inductively, researchers face a choice between “onlier” and reinforcing outlier cases that represents a trade-off between false negatives and false positives. We demonstrate that the inferential power of nested research designs can be much increased through paired comparisons of cases. More generally, this article provides a new conceptual framework for understanding the limits to and conditions for causal generalization from case studies.

在混合方法方法，统计模型被用来识别“嵌套”的情况下进行密集，小ñ用于各种目的，包括因果机制特别是考试的调查。这篇文章表明，在因果效应的常识性解读，large- ñ即使对于通常情况下我们选择的“较新的”案例，这些模型也无法得出有关单个案例效果大小的可靠结论。与已建立的惯例相反，我们表明选择“加强”异常情况（其结果比统计模型中的预测要强）适合于检验因果机制中先前存在的假设，因为这减少了假阴性的风险。在归纳研究机制时，研究人员面临着“异常”和强化异常情况之间的选择，这代表了假阴性和假阳性之间的权衡。我们证明，通过案例的成对比较，可以大大提高嵌套研究设计的推理能力。更普遍，