# How Likely Is Simpson’s Paradox?

@article{Pavlides2009HowLI, title={How Likely Is Simpson’s Paradox?}, author={Marios G. Pavlides and Michael D. Perlman}, journal={The American Statistician}, year={2009}, volume={63}, pages={226 - 233} }

What proportion of all 2×2×2 contingency tables exhibit Simpson’s Paradox? An exact answer is obtained for large sample sizes and extended to 2×2×ℓ tables by Monte Carlo approximation. Conditional probabilities of the occurrence of Simpson’s Paradox are also derived. If the observed cell proportions satisfy a Simpson reversal, the posterior probability that the population parameters satisfy the same reversal is obtained. This Bayesian analysis is applied to the well-known Simpson reversal of…

## 56 Citations

A First Inquiry into Simpson's Paradox with Belief Functions

- EconomicsIPMU
- 2014

This paper explores what happens if data are considered in the framework of belief functions instead of classical probability theory, and the co-occurrence of the paradox with both the probabilistic approach and belief function approach is studied.

How Likely is Simpson's Paradox in Path Models?

- EconomicsInt. J. e Collab.
- 2015

It is suggested that Simpson's paradox is likely to occur in empirical studies, in the field of e-collaboration and other fields, frequently enough to be a source of concern.

The ubiquity of the Simpson’s Paradox

- Physics
- 2017

The Simpson’s Paradox is the phenomenon that appears in some datasets, where subgroups with a common trend (say, all negative trend) show the reverse trend when they are aggregated (say, positive…

Yule–Simpson’s paradox: the probabilistic versus the empirical conundrum

- Philosophy
- 2020

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…

The quantification of Simpson’s paradox and other contributions to contingency table theory

- MathematicsPloS one
- 2022

The analysis of contingency tables is a powerful statistical tool used in experiments with categorical variables. This study improves parts of the theory underlying the use of contingency tables.…

Simpson's paradox

- Mathematics, Environmental Science
- 2010

Simpson's paradox occurs when an observed association between two variables is reversed after considering the third variable. Having two different conclusions makes this phenomenon paradoxical. In…

Judicious Judgment Meets Unsettling Updating: Dilation, Sure Loss and Simpson’s Paradox

- Computer Science
- 2017

These findings show that unsettling updates reflect a collision between the rules' assumptions and the inexactness allowed by the model itself, highlighting the invaluable role of judicious judgment in handling low-resolution information, and the care the user must take when applying learning rules to update imprecise probabilities.

Simpson's paradox, moderation and the emergence of quadratic relationships in path models: an information systems illustration

- Geology
- 2016

While Simpson's paradox is well-known to statisticians, it seems to have been largely neglected in many applied fields of research, including the field of information systems. This is problematic…

Simpson’s paradox in GDP and per capita GDP growths

- Economics
- 2015

Simpson’s paradox occurs frequently in economic data analysis, wherein aggregation is a common practice. Yet, this paradox is not well known among researchers in economy. In this article, we present…

Viewing Simpson's Paradox

- Philosophy
- 2014

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…

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