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Simpson's paradox and collapsibility are two closely related concepts in the context of data analysis. While the knowledge about the occurrence of Simpson's paradox helps a statistician to draw correct and meaningful conclusions, the…

Statistics Theory · Mathematics 2014-08-19 P. Vellaisamy

Given two sets of data which lead to a similar statistical conclusion, the Simpson Paradox describes the tactic of combining these two sets and achieving the opposite conclusion. Depending upon the given data, this may or may not succeed.…

Applications · Statistics 2008-01-30 Ora E. Percus , Jerome K. Percus

We investigate how Simpson's paradox affects analysis of trends in social data. According to the paradox, the trends observed in data that has been aggregated over an entire population may be different from, and even opposite to, those of…

Computers and Society · Computer Science 2018-01-16 Nazanin Alipourfard , Peter G. Fennell , Kristina Lerman

Observational data about human behavior is often heterogeneous, i.e., generated by subgroups within the population under study that vary in size and behavior. Heterogeneity predisposes analysis to Simpson's paradox, whereby the trends…

Social and Information Networks · Computer Science 2022-12-16 Kristina Lerman

We describe a data-driven discovery method that leverages Simpson's paradox to uncover interesting patterns in behavioral data. Our method systematically disaggregates data to identify subgroups within a population whose behavior deviates…

Computers and Society · Computer Science 2018-05-09 Nazanin Alipourfard , Peter G. Fennell , Kristina Lerman

Well known Simpson's paradox is puzzling and surprising for many, especially for the empirical researchers and users of statistics. However there is no surprise as far as mathematical details are concerned. A lot more is written about the…

Other Statistics · Statistics 2018-04-24 Priyantha Wijayatunga

Simpson's Paradox is a well-known phenomenon in statistical science, where the relationship between the response variable $X$ and a certain explanatory factor of interest $A$ reverses when an additional factor $B_1$ is considered. This…

Statistics Theory · Mathematics 2025-02-19 Guisheng Dai , Weizhen Wang

The primary objective of this paper is to revisit Simpson's paradox using a statistical misspecification perspective. It is argued that the reversal of statistical associations is sometimes spurious, stemming from invalid probabilistic…

Methodology · Statistics 2016-05-16 Aris Spanos

The occurrence of Simpson's paradox (SP) in $2\times 2$ contingency tables has been well studied. The present work comprehensively revisits this problem using a combination of philosophical reflections, causal considerations, and…

Statistics Theory · Mathematics 2021-09-23 Palash Sarkar , Prasanta S. Bandyopadhyay

Real-world observational datasets and machine learning have revolutionized data-driven decision-making, yet many models rely on empirical associations that may be misleading due to confounding and subgroup heterogeneity. Simpson's paradox…

Machine Learning · Computer Science 2026-03-03 Xian Teng , Yu-Ru Lin

Simpson's paradox is an obstacle to establishing a probabilistic association between two events $a_1$ and $a_2$, given the third (lurking) random variable $B$. We focus on scenarios when the random variables $A$ (which combines $a_1$,…

Methodology · Statistics 2024-07-23 A. Hovhannisyan , A. E. Allahverdyan

Complex contagions describe systems where the probability or rate of contagious transmission is a nonlinear function of the exposure to contagious agents. These models were first studied theoretically but have since been used to capture…

The well-known Simpson's Paradox, or Yule-Simpson Effect, in statistics is often illustrated by the following thought experiment: A drug may be found in a trial to increase the survival rate for both men and women, but decrease the rate for…

Quantum Physics · Physics 2012-03-14 Yaoyun Shi

A central challenge in statistical inference is the presence of confounding variables that may distort observed associations between treatment and outcome. Conventional "causal" methods, grounded in assumptions such as ignorability, exclude…

Methodology · Statistics 2025-09-09 Ellis Scharfenaker , Duncan K. Foley

Data based judgments go into artificial intelligence applications but they undergo paradoxical reversal when seemingly unnecessary additional data is provided. Examples of this are Simpson's reversal and the disjunction effect where the…

Artificial Intelligence · Computer Science 2017-09-14 Subhash Kak

Odds ratios and log-linear parameters are not collapsible, meaning that including a variable into the analysis or omitting one from it, may change the strength of association among the remaining variables. Even the direction of association…

Statistics Theory · Mathematics 2014-08-12 Tamas Rudas

There has been a flurry of research in recent years on notions of fairness in ranking and recommender systems, particularly on how to evaluate if a recommender allocates exposure equally across groups of relevant items (also known as…

Information Retrieval · Computer Science 2022-10-17 Flavien Prost , Ben Packer , Jilin Chen , Li Wei , Pierre Kremp , Nicholas Blumm , Susan Wang , Tulsee Doshi , Tonia Osadebe , Lukasz Heldt , Ed H. Chi , Alex Beutel

This paper describes Simpson's paradox, and explains its serious implications for randomised control trials. In particular, we show that for any number of variables we can simulate the result of a controlled trial which uniformly points to…

Methodology · Statistics 2019-12-04 Norman Fenton , Martin Neil , Anthony Constantinou

The belief that numbers offer a single, objective description of reality overlooks a crucial truth: data does not speak for itself. Every dataset results from choices-what to measure, how, when, and with whom-which inevitably reflect…

Other Statistics · Statistics 2025-07-08 Arthur Charpentier

We analyze the mixing properties of growing networks and find that, in some cases, the assortativity patterns are reversed once links' direction is considered: the disassortative behavior observed in such networks is a spurious effect, and…

Statistical Mechanics · Physics 2009-11-11 Andrea Capocci , Francesca Colaiori
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