The paper introduces a \(p\)-value that summarizes the evidence against a rival causal theory that explains an observed outcome in a single case. We show how to represent the probability distribution characterizing a theorized rival hypothesis (the null) in the absence of randomization of treatment and when counting on qualitative data, for instance when conducting process tracing. As in Fisher's \autocite*{fisher1935design} original design, our \(p\)-value indicates how frequently one would find the same observations or even more favorable observations under a theory that is compatible with our observations but antagonistic to the working hypothesis. We also present an extension that allows researchers assess the sensitivity of their results to confirmation bias. Finally, we illustrate the application of our hypothesis test using the study by Snow \autocite*{Snow1855} about the cause of Cholera in Soho, a classic in Process Tracing, Epidemiology, and Microbiology. Our framework suits any type of case studies and evidence, such as data from interviews, archives, or participant observation.

翻译：本文介绍了一种p值，该值总结了在单个案例中，针对一种可解释所观测结果的对立因果理论（即零假设）的证据强度。我们展示了如何在缺乏随机化处理且依赖定性数据（例如进行过程追踪时）的情况下，表征一个理论化的对立假设（零假设）的概率分布。与费舍尔（Fisher）原始设计类似，我们的p值指示了在一种与观测相容但与工作假设相悖的理论下，观察到相同或更有利观测结果的频率。我们还提出了一种扩展方法，使研究者能够评估其结果对确认偏见的敏感性。最后，我们利用斯诺（Snow）关于苏豪区霍乱病因的研究（过程追踪、流行病学和微生物学领域的经典案例）来展示该假设检验的应用。我们的框架适用于任意类型的案例研究与证据，例如来自访谈、档案或参与式观察的数据。