2024/03/01 by A. A. Hovhannisyan, Hovhannisyan, A., A. E. Allahverdyan +1 · 1 citation
Arts and Humanities · Computer Science · Mathematics · #Applications (stat.AP) #Artificial Intelligence (cs.AI) #Benford’s Law and Fraud Detection #Data Analysis #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #Methodology (stat.ME) #Philosophy and History of Science #Probability (math.PR) #Rough Sets and Fuzzy Logic #Statistics and Probability (physics.data-an)
paper · pdf · doi:10.48550/arxiv.2403.00957
openalex publication_date 2024/03/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Simpson's paradox is an obstacle to establishing a probabilistic association between two events a1 and a2, given the third (lurking) random variable B. We focus on scenarios when the random variables A (which combines a1, a2, and their complements) and B have a common cause C that need not be observed. Alternatively, we can assume that C screens out A from B. For such cases, the correct association between a1 and a2 is to be defined via conditioning over C. This setup generalizes the original Simpson's paradox: now its two contradicting options refer to two particular and different causes C. We show that if B and C are binary and A is quaternary (the minimal and the most widespread situation for the Simpson's paradox), the conditioning over any binary common cause C establishes the same direction of association between a1 and a2 as the conditioning over B in the original formulation of the paradox. Thus, for the minimal common cause, one should choose the option of Simpson's paradox that assumes conditioning over B and not its marginalization. The same conclusion is reached when Simpson's paradox is formulated via 3 continuous Gaussian variables: within the minimal formulation of the paradox (3 scalar continuous variables A1, A2, and B), one should choose the option with the conditioning over B.