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Yule-Simpson's paradox: the probabilistic versus the empirical conundrum

机译：yule-simpson的悖论：概率与经验难题

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The current literature views Simpson's paradox as a probabilistic conundrum by taking the premises (probabilities/parameters/ frequencies) as known. In such a context, it is shown that the paradox arises within a very small subset of the relevant parameter space, rendering the paradox unlikely to occur in real data. The problem, however, is that the probabilistic perspective, ignores certain crucial empirical (data, statistical) issues raised by the original Pearson and Yule papers on 'spurious' association reversals. Placing the paradox in a broader empirical framework that begins with the raw data z(0) and an appropriately selected statistical model M-theta(x), the discussion elucidates the original Yule-Pearson conundrum by formalizing its notion of 'spurious or fictitious associations' into 'statistically untrustworthy associations' stemming from a misspecified M-theta(x); invalid probabilistic assumptions imposed on z(0). It is shown that several empirical examples used to illustrate Simpson's paradox in the current literature constitute examples of the Yule-Pearson untrustworthy association reversals. The empirical perspective is used to revisit the causal explanation of the paradox and make a case that several widely accepted causal claims are questionable on statistical adequacy grounds. It is also used to propose a procedure to detect and account for the 'third entity' in the paradox, as well as (reliably) select among different potential causal explanations, such as collider, mediator or confounder, on empirical grounds.
机译：目前的文献通过以已知的房屋（概率/参数/频率）作为概率难题的观点来观看SIMPSON的悖论。在这样的上下文中，示出了悖论在相关参数空间的一个非常小的子集中出现，渲染在实际数据中不太可能发生的悖论。然而，该问题是概率的角度，忽视原始Pearson和Yule论文提出的某些至关重要的经验（数据，统计）问题对“虚假”协会逆转。 Placing the paradox in a broader empirical framework that begins with the raw data z(0) and an appropriately selected statistical model M-theta(x), the discussion elucidates the original Yule-Pearson conundrum by formalizing its notion of 'spurious or fictitious associations '进入“统计上不值得信任的关联”源于误操作的M-THETA（X）;在Z（0）上施加无效的概率假设。结果表明，用于说明当前文献中的辛普森的悖论的若干经验例子构成了尤拉尔逊不值得信任的关联逆转的例子。经验主义的观点用于重新审视悖论的因果解释，并在统计充分理由上进行若干广泛接受的因果索赔是值得怀疑的案例。它还用于提出一种方法来检测和占悖论中的“第三实体”，以及（可靠地）在实证地面上的不同潜在因果解释中选择不同的潜在因果解释。

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