Simpson’s paradox (SP) is a statistical phenomenon where the association between two variables reverses, disappears, or emerges, after conditioning on a third variable. It has been proposed (by, e.g., Judea Pearl) that SP should be analyzed using the framework of graphical causal models (i.e., causal DAGs) in which SP is diagnosed as a symptom of confounding bias. This paper contends that this confounding-based analysis cannot fully capture SP: there are cases of SP that cannot be explained away in terms of confounding. Previous works have argued that some cases of SP do not require causal analysis at all. Despite being a logically valid counterexample, we argue that this type of cases poses only a limited challenge to Pearl’s analysis of SP. In our view, a more powerful challenge to Pearl comes from cases of SP that do require causal analysis but can arise without confounding. We demonstrate with examples that accidental associations due to genetic drift, the use of inappropriate aggregate variables as causes, and interactions between units (i.e., inter-unit causation) can all give rise to SP of this type. The discussion is also extended to the amalgamation paradox (of which SP is a special form) which can occur due to the use of non-collapsible association measures, in the absence of confounding.

辛普森悖论 (SP) 是一种统计现象，其中两个变量之间的关联在以第三个变量为条件后逆转、消失或出现。已经建议（例如，Judea Pearl）应该使用图形因果模型（即因果 DAG）的框架来分析 SP，其中 SP 被诊断为混杂偏差的症状。本文认为，这种基于混杂的分析无法完全捕获 SP：有些 SP 的情况无法用混杂来解释。之前的研究认为，某些 SP 案例根本不需要因果分析。尽管这是一个逻辑上有效的反例，但我们认为此类案例对 Pearl 对 SP 的分析仅提出了有限的挑战。我们认为，Pearl 面临的更强大的挑战来自 SP 案例，这些案例确实需要因果分析，但可以在不混淆的情况下出现。我们通过例子证明，由于遗传漂变而导致的偶然关联、使用不适当的聚合变量作为原因以及单元之间的相互作用（即单元间因果关系）都可以产生这种类型的SP。讨论还扩展到合并悖论（其中 SP 是一种特殊形式），在没有混杂的情况下，由于使用不可折叠关联措施而可能发生合并悖论。