Analysis of Simpson’s Paradox and Its Applications

Zhihao Lei

doi:10.54097/315qax57

Authors

Zhihao Lei

DOI:

https://doi.org/10.54097/315qax57

Keywords:

Simpson’s paradox; statistical phenomena; multidimensional data analysis.

Abstract

As a matter of fact, the enigmatic nature and far-reaching consequences of Simpson's Paradox have captivated both scholars and professionals. On this basis, this investigation seeks to offer an exhaustive review of the paradox, examining its historical background, mathematical formulations, and its utilization in diverse sectors. To be specific, the study probes into how the paradox influences the efficacy of healthcare treatments, its contribution to sustaining gender inequality in educational settings like UC Berkeley, and the challenges it presents in analyzing data with multiple dimensions. The research also points out existing gaps in the literature, specifically the absence of methodical solutions for addressing the paradox in intricate, multi-faceted scenarios. Overall, the significance of this study lies in its multi-faceted exploration of Simpson's Paradox. It serves as a foundational text that aims to improve statistical literacy and promote a nuanced understanding of data interpretation, thereby contributing to better decision-making across multiple disciplines.

Downloads

Download data is not yet available.

References

Sharma R, Garayev H, Kaushik M, et al. Detecting Simpson’s Paradox: A Machine Learning Perspective. International Conference on Database and Expert Systems Applications. Cham: Springer International Publishing, 2022: 323-335.

Xu J, Pei J, Cong Z. Finding Multidimensional Simpson's Paradox. ACM SIGKDD Explorations Newsletter, 2022, 24(2): 48-60.

Albers C J. Dutch research funding, gender bias, and Simpson’s paradox. Proceedings of the National Academy of Sciences, 2015, 112(50): E6828-E6829.

Swamy P, Mehta J S, Tavlas G S, et al. Two applications of the random coefficient procedure: Correcting for misspecifications in a small area level model and resolving Simpson's paradox. Economic Modelling, 2015, 45: 93-98.

Bandyopadhyay P S, Raghavan R V, Dcruz D W, et al. Truths about Simpson’s Paradox: Saving the paradox from falsity. Logic and Its Applications: 6th Indian Conference, ICLA 2015, Mumbai, India, January 8-10, 2015. Proceedings 6. Springer Berlin Heidelberg, 2015: 58-73.

Woo E J. Pearls: Simpson’s Paradox—Understanding Numbers That Don’t Seem to Make Sense. Clinical Orthopaedics and Related Research, 2019, 477(11): 2427.

Spanos A. Yule–Simpson’s paradox: the probabilistic versus the empirical conundrum. Statistical Methods & Applications, 2021, 30: 605-635.

Goltz H H, Smith M L. Yule-Simpson's paradox in research. Practical Assessment, Research, and Evaluation, 2010, 15(1): 15.

Rojanaworarit C. Misleading epidemiological and statistical evidence in the presence of Simpson's paradox: an illustrative study using simulated scenarios of observational study designs. Journal of Medicine and Life, 2020, 13(1): 37.

Wang J, He J, Xu W, et al. Learning to Discover Various Simpson's Paradoxes. Proceedings of the 29th ACM SIGKDD Conference on Knowledge Discovery and Data Mining. 2023: 5092-5103.

Rücker G, Schumacher M. Simpson's paradox visualized: the example of the rosiglitazone meta-analysis. BMC medical research methodology, 2008, 8(1): 1-8.

Cani P D, Depommier C. Reply to ‘Simpson’s paradox in proof-of-concept studies’. Nature medicine, 2019, 25(11): 1640-1641.

Ma Y Z. Simpson’s paradox in GDP and per capita GDP growths. Empirical Economics, 2015, 49(4): 1301-1315.

Zhang B, Heng S, MacKay E J, et al. Bridging preference‐based instrumental variable studies and cluster‐randomized encouragement experiments: Study design, noncompliance, and average cluster effect ratio. Biometrics, 2022, 78(4): 1639-1650.

Streiner D L. Statistics Commentary Series. Commentary No. 38: Simpson's Paradox and the Mantel-Haenszel χ2. Journal of Clinical Psychopharmacology, 2020, 40(2): 109-111.

Sarkar P, Bandyopadhyay P S. Simpson's Paradox: A Singularity of Statistical and Inductive Inference. arXiv preprint arXiv:2103.16860, 2021.

Chipman J, Braun D. Simpson's paradox in the integrated discrimination improvement. Statistics in medicine, 2017, 36(28): 4468-4481.

Kock N, Gaskins L. Simpson's paradox, moderation and the emergence of quadratic relationships in path models: an information systems illustration. International Journal of Applied Nonlinear Science, 2016, 2(3): 200-234.

Mittal Y. Homogeneity of subpopulations and Simpson's paradox. Journal of the American Statistical Association, 1991, 86(413): 167-172.

Chu K H, Brown N J, Pelecanos A, et al. Simpson's paradox: A statistician's case study. Emergency Medicine Australasia, 2018, 30(3): 431-433.

Selvitella A. The ubiquity of the Simpson’s Paradox. Journal of Statistical Distributions and Applications, 2017, 4(1): 1-16.

Borenstein M, Hedges L V, T. H J P, et al. Chapter 33: Simpson’s Paradox. Introduction to meta-analysis. Hoboken, NJ: John Wiley & Sons, Inc., 2021.

Nee J, Macfarlane Smith G, Sheares A, et al. Advancing social justice through linguistic justice: Strategies for building equity fluent NLP technology. Equity and Access in Algorithms, Mechanisms, and Optimization. 2021: 1-9.

Lu C. Causal Confirmation Measures: From Simpson’s Paradox to COVID-19. Entropy, 2023, 25(1): 143.

Julious S A, Mullee M A. Confounding and Simpson's paradox. Bmj, 1994, 309(6967): 1480-1481.