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The ubiquity of the Simpson’s Paradox

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  • Alessandro Selvitella

    (Department of Mathematics and Statistics of McMaster University)

Abstract

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 trend). Even if this issue has an elementary mathematical explanation, it has a deep statistical significance. In this paper, we discuss basic examples in arithmetic, geometry, linear algebra, statistics, game theory, gender bias in university admission and election polls, where we describe the appearance or absence of the Simpson’s Paradox. In the final part, we present our results concerning the occurrence of the Simpson’s Paradox in Quantum Mechanics with focus on the Quantum Harmonic Oscillator and the Nonlinear Schrödinger Equation. We discuss how likely it is to incur in the Simpson’s Paradox and give some concrete numerical examples. We conclude with some final comments and possible future directions.

Suggested Citation

  • Alessandro Selvitella, 2017. "The ubiquity of the Simpson’s Paradox," Journal of Statistical Distributions and Applications, Springer, vol. 4(1), pages 1-16, December.
    • Handle: RePEc:spr:jstada:v:4:y:2017:i:1:d:10.1186_s40488-017-0056-5
    DOI: 10.1186/s40488-017-0056-5
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    Cited by:

    1. Sadri, Arash, 2022. "The Ultimate Cause of the “Reproducibility Crisis”: Reductionist Statistics," MetaArXiv yxba5, Center for Open Science.
    2. Haikady N Nagaraja & Shane Sanders, 2020. "The aggregation paradox for statistical rankings and nonparametric tests," PLOS ONE, Public Library of Science, vol. 15(3), pages 1-21, March.
    3. Satya R. Chakravarty & Palash Sarkar, 2021. "An inequality paradox: relative versus absolute indices?," METRON, Springer;Sapienza Università di Roma, vol. 79(2), pages 241-254, August.

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