Cited by 2,301Probability and Statistical ResearchStatistical Methods and ApplicationsStatistical Methods and Bayesian Inference

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The Interpretation of Interaction in Contingency Tables

Simpson, E. H.·1951·Journal of the Royal Statistical Society Series B: Statistical Methodology

DOI 10.1111/j.2517-6161.1951.tb00088.x

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Abstract

Summary The definition of second order interaction in a (2 × 2 × 2) table given by Bartlett is accepted, but it is shown by an example that the vanishing of this second order interaction does not necessarily justify the mechanical procedure of forming the three component 2 × 2 tables and testing each of these for significance by standard methods.

Integrity signals

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Crossref · 10.1111/j.2517-6161.1951.tb00088.x

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Cheng, P. E., Liou, M., & Aston, J. A. D. (2010) · Journal of the American Statistical Association · doi:10.1198/jasa.2010.tm09061 · Cited by 12
“Norton (1945) extended the discussion to finite K tables, and Simpson (1951) supplied interpretations of various interactions.”
Background
Influence of physico-mechanical properties of Indian dimension stones on cutting rate of diamond wire saw
Rajpurohit, S. S., Sinha, R. K., Sen, P., & Singh, S. (2018) · Arabian Journal of Geosciences · doi:10.1007/s12517-018-3913-8 · Cited by 12
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Pachur, T., Schooler, L. J., & Stevens, J. R. (2012) · Oxford University Press eBooks · doi:10.1093/acprof:oso/9780195388435.003.0007 · Cited by 12
Simple Heuristics in a Social Game
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The ABC of pharmaceutical trial design: some basic principles
Julious, S., & Zariffa, N. (2002) · Pharmaceutical Statistics · doi:10.1002/pst.6 · Cited by 11
“This reversal effect is known as Simpson’s paradox [13,14].”
Background
CONFOUNDING, HOMOGENEITY AND COLLAPSIBILITY FOR CAUSAL EFFECTS IN EPIDEMIOLOGIC STUDIES
Geng, Z., Guo, J., Lau, T. S., & Fung, W. (2001) · Cited by 12
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Vellaisamy, P., & Vijay, V. (2007) · Annals of the Institute of Statistical Mathematics · doi:10.1007/s10463-006-0058-4 · Cited by 12
“This paradox, due to Simpson (1951) , known as Simpson’s paradox.”
Background
Survival of the Greenest
van den Bergh, J. C. J. M. (2018) · Cambridge University Press eBooks · doi:10.1017/9781108564922.014 · Cited by 12
Visual Revelations
Wainer, H. (2002) · CHANCE · doi:10.1080/09332480.2002.10554815 · Cited by 12
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Keller, M., Gummerum, M., Canz, T., Gigerenzer, G., & Takezawa, M. (2012) · Oxford University Press eBooks · doi:10.1093/acprof:oso/9780195388435.003.0006 · Cited by 12
Aggregating and Partitioning Populations in Health Care Disparities Research: Differences in Perspective
Asch, D. A., & Armstrong, K. (2007) · Journal of Clinical Oncology · doi:10.1200/jco.2006.09.3336 · Cited by 12
Yule's Association Paradox and Ignored Stratum Heterogeneity in Capture—Recapture Studies
Kadane, J. B., Meyer, M. M., & Tukey, J. W. (1999) · Journal of the American Statistical Association · doi:10.1080/01621459.1999.10474190 · Cited by 12
“Wachter and Speed (1991) questioned the methodology of poststrata, alleging that if within a poststratum there is a group of people resembling "wily trout," relatively difficult to count in the census and relatively difficult to find in the PBS, then a homogeneity assumption within the poststrata would be violated, in…”
Method
Log-linear models, screening and regional industrial surveys
UPTON, G. J. G. (1981) · Regional Studies · doi:10.1080/09595238100185041 · Cited by 12
The Drug Titration Paradox is Simpson’s Paradox
Schamberg, G., & Brown, E. N. (2021) · Clinical Pharmacology & Therapeutics · doi:10.1002/cpt.2280 · Cited by 12
Hirayama, passive smoking and lung cancer: 30 years on and the numbers still don’t lie
SMITH, D. R., & Beh, E. J. (2011) · Public Health · doi:10.1016/j.puhe.2011.02.008 · Cited by 11

Authors: Simpson, E. H.
Corresponding author: Simpson, E. H.
Venue: Journal of the Royal Statistical Society Series B: Statistical Methodology
Publisher: Oxford University Press (OUP)
Published: 1951-07-01
Volume: 13
Issue: 2
Pages: 238-241
ISSN: 1369-7412 (ISSN-L)
1467-9868
DOI: 10.1111/j.2517-6161.1951.tb00088.x
OpenAlex: W2905472553
Cited by: 2,301
References: 6
Citations by year: 2026: 92 · 2025: 136 · 2024: 122 · 2023: 113 · 2022: 116 · 2021: 121 · 2020: 165 · 2019: 101 · 2018: 94 · 2017: 78 · 2016: 87 · 2015: 84 · 2014: 75 · 2013: 57 · 2012: 109
FWCI: 0.00
Type: journal article
Language: en
Open access: closed
Licence: academic.oup.com/journals/pages/open_access/funder_policies/chorus/standard_publication_model (vor)
Locations: Journal of the Royal Statistical Society Series B (Statistical Methodology) (publishedVersion)
Topics: Physical Sciences › Mathematics › Statistics and Probability › Probability and Statistical Research
Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Applications
Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
Keywords: second-order interactions, three-way contingency tables, marginal homogeneity, interaction testing, categorical data analysis

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The Interpretation of Interaction in Contingency Tables

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