We consider hypothesis testing of binary causal queries using observational data. Since the mapping of causal models to the observational distribution that they induce is not one-to-one, in general, causal queries are often only partially identifiable. When binary statistical tests are used for testing partially-identifiable causal queries, their results do not translate in a straightforward manner to the causal hypothesis testing problem. We propose using ternary (three-outcome) statistical tests to test partially-identifiable causal queries. We establish testability requirements that ternary tests must satisfy in terms of uniform consistency and present equivalent topological conditions on the hypotheses. To leverage the existing toolbox of binary tests, we prove that obtaining ternary tests by combining binary tests is complete. Finally, we demonstrate how topological conditions serve as a guide to construct ternary tests for two concrete causal hypothesis testing problems, namely testing the instrumental variable (IV) inequalities and comparing treatment efficacy.

翻译：本文研究利用观测数据对二元因果查询进行假设检验。由于因果模型与其诱导的观测分布之间的映射通常不是一一对应的，因果查询往往仅能部分识别。当使用二元统计检验来测试部分可识别的因果查询时，其检验结果无法直接转化为因果假设检验问题的结论。我们提出采用三元（三结果）统计检验来测试部分可识别的因果查询。我们建立了三元检验在一致一致性方面必须满足的可检验性要求，并给出了假设上等价的拓扑条件。为利用现有的二元检验工具箱，我们证明了通过组合二元检验获得三元检验的方法是完备的。最后，我们通过两个具体的因果假设检验问题——工具变量不等式检验与处理效果比较，展示了如何运用拓扑条件指导构建三元检验。