In prior work we have introduced an asymptotic threshold of sufficient randomness for causal inference from observational data. In this paper we extend that prior work in three main ways. First, we show how to empirically estimate a lower bound for the randomness from measures of concordance transported from studies of monozygotic twins. Second, we generalize our methodology for application on a finite population and we introduce methods to implement finite population corrections. Third, we generalize our methodology in another direction by incorporating measured covariate data into the analysis. The first extension represents a proof of concept that observational causality testing is possible. The second and third extensions help to make observational causality testing more practical. As a theoretical and indirect consequence of the third extension we formulate and introduce a novel criterion for covariate selection. We demonstrate our proposed methodology for observational causality testing with numerous example applications.

翻译：在先前的工作中，我们引入了从观测数据进行因果推断所需充分随机性的渐近阈值。本文从三个主要方面扩展了该研究。首先，我们展示了如何利用从同卵双胞胎研究中迁移得来的一致性度量，对随机性的下界进行经验性估计。其次，我们将方法论推广至有限总体的应用场景，并介绍了实现有限总体校正的方法。第三，我们通过将已测量的协变量数据纳入分析，从另一方向对方法论进行了推广。第一个扩展体现了观察性因果检验可行的概念验证。第二和第三项扩展则有助于提升观察性因果检验的实用性。作为第三项扩展的理论性间接成果，我们提出并引入了新的协变量选择准则。通过大量实例应用，我们展示了所提出的观察性因果检验方法论。