The DOI matches its Crossref record; 6 of the 6 references it cites were found in a registry or an index.
The Interpretation of Interaction in Contingency Tables
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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In the citing paper
“Indeed, the relationship between body composition and BMI represents a clear example of Simpson’s paradox (Simpson, 1951).”
From The degree to which the cultural ideal is internalized predicts judgments of male and female physical attractiveness (2022) · cites this paper as Simpson, 1951
In the citing paper
“The classical example demonstrating the obstacle of causal vocabulary is Simpson's paradox (Simpson, 1951) - a reversal phenomenon that earns its claim to fame only through a causal interpretation of the data (Pearl, 2000a, Chapter 6).”
From Causal inference in statistics: An overview (2009) · cites this paper as Simpson, 1951
In the citing paper
“Our work extends this to the causal domain, showing that models will endorse logical traps (like Simpson's Paradox (Simpson, 1951)) if pressed.”
From Diagnosing and Mitigating Sycophancy and Skepticism in LLM Causal Judgment (2026) · cites this paper as Simpson, 1951
Citations
Cites
The Logic of Inductive Inference
Fisher, R. A. (1935) · Journal Of The Royal Statistical Society · doi:10.2307/2342435 · Cited by 1,308
124: The Logic of Inductive Inference.
Fisher, R. A. (1935) · Adelaide Research & Scholarship (AR&S) (University of Adelaide) · Cited by 881
The Advanced Theory of Statistics.
P., E. S., & Kendall, M. G. (1944) · Journal Of The Royal Statistical Society · doi:10.2307/2981279 · Cited by 687
Contingency Table Interactions
Bartlett, M. S. (1935) · Journal of the Royal Statistical Society Series B (Statistical Methodology) · doi:10.2307/2983639 · Cited by 313
Calculation of Chi-Square for Complex Contingency Tables
Norton, H. W. (1945) · Journal of the American Statistical Association · doi:10.1080/01621459.1945.10501855 · Cited by 66
Chance in Medicine and Research
Norton, H. W. (1939) · BMJ · doi:10.1136/bmj.2.4103.467-a · Cited by 5
Research works printed but not linked: 1
- Snedecor, 1946, Statistical Methods.
Cited by
Sorted by citations
(2005) · Springer eBooks · doi:10.1007/0-387-27255-0_9 · Cited by 20,333
Trapnell, C., Cacchiarelli, D., Grimsby, J., Pokharel, P., Li, S., Morse, M., Lennon, N. J., Livak, K. J., Mikkelsen, T. S., & Rinn, J. L. (2014) · Nature Biotechnology · doi:10.1038/nbt.2859 · Cited by 7,314
“Drawing conclusions from a group of individuals based on the properties of their average is a hazardous practice because the average can mask important trends among the individuals, resulting in phenomena such as Simpson's paradox 14 .”
BackgroundCausal inference in statistics: An overview
Pearl, J. (2009) · Statistics Surveys · doi:10.1214/09-ss057 · Cited by 2,336
“The phenomenon was discovered by statisticians a century ago (Pearson et al., 1899; Yule, 1903) analyzed by statisticians for half a century (Simpson, 1951; Blyth, 1972; Cox and Wermuth, 2003) lamented by statisticians (Good and Mittal, 1987; Bishop et al., 1975) and wrestled with by statisticians…”
BackgroundInfluentialMultimodal population brain imaging in the UK Biobank prospective epidemiological study
Miller, K. L., Alfaro-Almagro, F., Bangerter, N. K., Thomas, D. L., Yacoub, E., Xu, J., Bartsch, A. J., Jbabdi, S., Sotiropoulos, S. N., Andersson, J. L. R., et al. (2016) · Nature Neuroscience · doi:10.1038/nn.4393 · Cited by 2,020
“This may be due to key differences in the HCP and Biobank datasets, including different non-imaging measures, the use of only rfMRI in the HCP analysis, the different cohort profiles (e.g., age range) and the ability to separate more modes from the larger Biobank cohort.”
Conditional Independence in Statistical Theory
Dawid, A. P. (1979) · Journal of the Royal Statistical Society Series B (Statistical Methodology) · doi:10.1111/j.2517-6161.1979.tb01052.x · Cited by 1,507
Metadata
- 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
- 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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