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.

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

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Background
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Mun, J., Bang, S., & Kim, J. (2024) · Computational Statistics & Data Analysis · doi:10.1016/j.csda.2024.108078 · Cited by 10
A Survey on Bias in Machine Learning Research
Mikołajczyk, A., & Grochowski, M. (2025) · IEEE Access · doi:10.1109/access.2025.3649998 · Cited by 10
The Evolution of Small Insertions and Deletions in the Coding Genes of Drosophila melanogaster
Chong, Z., Zhai, W., Li, C., Gao, M., Gong, Q., Ruan, J., Li, J., Jiang, L., Lv, X., Hungate, E. A., et al. (2013) · Molecular Biology and Evolution · doi:10.1093/molbev/mst167 · Cited by 9
“It is interesting to note that the expected value of FI is not 1 when data from multiple loci are pooled (Simpson 1951).”
Background
Experimental investigation of quantum Simpson's paradox
Li, Y., Tang, J., Wang, Y., Wu, Y.-C., Han, Y.-J., Li, C., Guo, G., Yu, Y., Li, M.-F., Zha, G., et al. (2013) · Physical Review A · doi:10.1103/physreva.88.015804 · Cited by 9
Association between Hyperbilirubinemia and Hearing Screen Failure in the Neonatal Intensive Care Unit in Infants Born Preterm
Singh, A., Francis, H. W., Smith, P. B., Clark, R. H., & Greenberg, R. G. (2021) · The Journal of Pediatrics · doi:10.1016/j.jpeds.2020.12.059 · Cited by 9
Trends in maternal characteristics and perinatal outcomes among Japanese pregnant women with type 1 and type 2 diabetes from 1982 to 2020
Shingu, K. F., Waguri, M., Takahara, M., Katakami, N., & Shimomura, I. (2022) · Journal of Diabetes Investigation · doi:10.1111/jdi.13841 · Cited by 9
Mothers with higher twinning propensity had lower fertility in pre-industrial Europe
Rickard, I. J., Vullioud, C., Rousset, F., Postma, E., Helle, S., Lummaa, V., Kylli, R., Pettay, J. E., Røskaft, E., Skjærvø, G. R., et al. (2022) · Nature Communications · doi:10.1038/s41467-022-30366-9 · Cited by 9
“…by performing the same analysis without aggregating data (i.e. at the level of each birth) to reveal the unbiased biological relationship between twinning and fertility, its sign ﬂ ipped from positive to negative — an extreme effect of data aggregation known as “ Simpson ’ s paradox ” 51,52 .”
Warmer Temperature and Spatiotemporal Dynamics during Primary Succession on Tropical Coastal Dunes
Martínez, M. L., Pérez-Maqueo, O., Vázquez, G., & Landgrave, R. (2022) · Plants · doi:10.3390/plants11223029 · Cited by 10
“The pattern in which a trend appears in several groups but disappears or reverses when the groups are combined is known as Simpson’s paradox [48].”
Background
Domain Adaptive Decision Trees: Implications for Accuracy and Fairness
Álvarez, J. M., Scott, K. M., Berendt, B., & Ruggieri, S. (2023) · ACM Conference on Fairness, Accountability, and Transparency (FAccT) · doi:10.1145/3593013.3594008 · Cited by 9
“This situation, in fact, is an instance of Simpson’s paradox [27].”
Background
Evolution of cooperation in deme-structured populations on graphs
Moawad, A., Abbara, A., & Bitbol, A. (2024) · Physical review. E · doi:10.1103/physreve.109.024307 · Cited by 9
A spatial analysis of plant phenophase changes and the impact of increases in urban land use
Comber, A., & Brunsdon, C. (2014) · International Journal of Climatology · doi:10.1002/joc.4030 · Cited by 9
“…more pronounced in some areas that have experienced urbanization than in others, indicating the possible effects of other factors – an example of Simpson’s Paradox (Simpson, 1951; Appleton et al., 1996) of the problems of ignoring an explanatory covariate that is correlated to an outcome variable.”
Background
Improved Profitability of a Pulping Mill through Progressive Controller Structure Expansion
Nobakhti, A. (2010) · Proceedings of the Institution of Mechanical Engineers Part I Journal of Systems and Control Engineering · doi:10.1243/09596518jsce877 · Cited by 9
Inferring Ancestries Efficiently in Admixed Populations with Linkage Disequilibrium
Bercovici, S., & Geiger, D. (2009) · Journal of Computational Biology · doi:10.1089/cmb.2009.0105 · Cited by 9
Standardized Mortality Ratio for Evaluating Center-Specific Mortality: Assessment and Alternative
He, K., & Schaubel, D. E. (2014) · Statistics in Biosciences · doi:10.1007/s12561-014-9119-z · Cited by 9
Co-expressed gene assessment based on the path consistency algorithm: Operon detention in Escherichia coli
Saito, S., & Horimoto, K. (2009) · Conference proceedings/Conference proceedings - IEEE International Conference on Systems, Man, and Cybernetics · doi:10.1109/icsmc.2009.5346809 · Cited by 9
“As well known in statistics, Simpson’s paradox illustrates the risk for the pseudocorrelation between two variables, when the two variables are correlated with the other variables [14].”
Background
A multi-agent reinforcement learning model of reputation and cooperation in human groups
McKee, K. R., Hughes, E., Zhu, T. O., Chadwick, M. J., Koster, R., Castaneda, A. G., Beattie, C., Graepel, T., Botvinick, M., & Leibo, J. Z. (2021) · arXiv · doi:10.48550/arxiv.2103.04982 · Cited by 5
“4The sign reversal between the individual and group level is conceptually related to Simpson’s paradox, a well-studied statistical phenomenon whereby the direction of an association at the population-level reverses within the subgroups comprising that population (as described in [88]; see also [89, 90]).”
Background

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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