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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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“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
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Items 701–800 of 1,004
Mai, T. P. T., Hardner, C. M., Alam, M. M., Henry, R. J., & Topp, B. L. (2021) · Agriculture · doi:10.3390/agriculture11070680 · Cited by 20
“Nevertheless, we examined the distribution of predicted values and did not find evidence for Simpson’s paradox, a statistical phenomenon in which a trend appears in several different groups of data but disappears in combined data [41].”
BackgroundRationing of a scarce life‐saving resource: Public preferences for prioritizing COVID‐19 vaccination
Luyten, J., Tubeuf, S., & Kessels, R. (2021) · Health Economics · doi:10.1002/hec.4450 · Cited by 20
Integrating LIDAR‐derived canopy structure into cerulean warbler habitat models
Barnes, K. W., Islam, K., & Auer, S. A. (2015) · Journal of Wildlife Management · doi:10.1002/jwmg.995 · Cited by 20
Complex Adaptive System Models and the Genetic Analysis of Plasma HDL-Cholesterol Concentration
Rea, T. J., Brown, C. M., & Sing, C. F. (2006) · Perspectives in biology and medicine · doi:10.1353/pbm.2006.0063 · Cited by 20
“…will ensure failure to ascribe context dependencies to specific disease-risk genotypes and disregard for Simpson’s paradox (the idea that associations found in subpopulations may be different from the population considered as a whole; Simpson 1951) in interpreting statistical relationships.”
BackgroundFitting in: Group effects and the evolution of fundamentalism
Arce, D. G., & Sandler, T. M. (2009) · Journal of Policy Modeling · doi:10.1016/j.jpolmod.2008.07.002 · Cited by 20
Improving Naive Bayes Using Class-Conditional ICA
Bressan, M., & Vitria, J. M. (2002) · Lecture notes in computer science · doi:10.1007/3-540-36131-6_1 · Cited by 20
Peritz, E. (1984) · Journal of Chronic Diseases · doi:10.1016/0021-9681(84)90067-5 · Cited by 20
Minority Contributions to the Sat Score Turnaround: an Example of Simpson’s Paradox
Wainer, H. (1986) · Journal of Educational Statistics · doi:10.3102/10769986011004239 · Cited by 20
Filser, A., Barclay, K. J., Beckley, A. L., Uggla, C., & Schnettler, S. (2020) · Evolution and Human Behavior · doi:10.1016/j.evolhumbehav.2020.10.001 · Cited by 19
“Of particular concern are the ecological fallacy and Simpson ’ s paradox, the fact that associations in aggregate data may be actually reversed at the individual level (Pollet et al., 2017; Simpson, 1951).”
BackgroundFazlul, I., Koedel, C., & Parsons, E. (2023) · Economics of Education Review · doi:10.1016/j.econedurev.2023.102374 · Cited by 19
A Geographical Perspective on Simpson's Paradox
Sachdeva, M., & Fotheringham, A. S. (2023) · Journal of Spatial Information Science · doi:10.5311/josis.2023.26.212 · Cited by 19
Roswell, M., Harrison, T., & Genung, M. A. (2023) · Philosophical Transactions of the Royal Society B Biological Sciences · doi:10.1098/rstb.2022.0186 · Cited by 18
Klotz, D., Gauch, M., Kratzert, F., Nearing, G., & Jakob Zscheischler, A. (2024) · Hydrology and earth system sciences · doi:10.5194/hess-28-3665-2024 · Cited by 26
Trust-Your-Doctor: A Simple Heuristic in Need of a Proper Social Environment
Wegwarth, O., & Gigerenzer, G. (2012) · Oxford University Press eBooks · doi:10.1093/acprof:oso/9780195388435.003.0003 · Cited by 20
Assessing the fraction of short-distance tandem splice sites under purifying selection
Hiller, M., Szafranski, K., Sinha, R., Huse, K., Nikolajewa, S., Rosenstiel, P. C., Schreiber, S., Backofen, R., & Platzer, M. (2008) · RNA · doi:10.1261/rna.883908 · Cited by 19
“The contradictory results of the global and the motifspecific conservation analysis are an example of the abovedescribed Simpson’s paradox (Simpson 1951).”
BackgroundResultTowards exploratory hypothesis testing and analysis
Liu, G., Feng, M., Wang, Y., Wong, L., Ng, S.-K., Mah, T. L., & Lee, E. J. D. (2011) · IEEE International Conference on Data Engineering (ICDE) · doi:10.1109/icde.2011.5767907 · Cited by 19
“This phenomenon is called Simpson’s Paradox [19], and it is caused by the fact that “stage” has associations with both treatment and response: doctors tend to give treatment”
BackgroundDiscrimination-aware classification
Kamiran, F. (2011) · doi:10.6100/ir717576 · Cited by 19
“The figure with the decision tree results actually illustrates the Simpson’s paradox [79], in which a relation present in different groups is reversed when the groups are combined.”
Result‘The obesity paradox’: a reconsideration of obesity and the risk of preterm birth
Tsur, A., Mayo, J. A., Wong, R. J., Shaw, G. M., Stevenson, D. K., & Gould, J. B. (2017) · Journal of Perinatology · doi:10.1038/jp.2017.104 · Cited by 19
Barnato, A. E., Chang, C. H., Lave, J. R., & Angus, D. C. (2017) · Journal of Palliative Medicine · doi:10.1089/jpm.2016.0557 · Cited by 19
“What might explain these findings? The most likely is Simpson’s paradox: the mathematical phenomenon in which aggregated data reveal one pattern but the same data, when partitioned, reveal another.(28) This phenomenon is relatively common in disparities research(29) and, in fact, can be leveraged to identify policy-re…”
BackgroundModeling Cumulative Biological Phenomena with Suppes-Bayes Causal Networks
Ramazzotti, D., Graudenzi, A., Caravagna, G., & Antoniotti, M. (2018) · Evolutionary Bioinformatics · doi:10.1177/1176934318785167 · Cited by 18
“One of the main reason for this state of affairs is the emergence of statistical paradoxes such as Simpson’s paradox [39,32].”
BackgroundBayesian Classification of Cork Stoppers Using Class-Conditional Independent Component Analysis
Vitria, J. M., Bressan, M., & Radeva, P. I. (2006) · IEEE Transactions on Systems Man and Cybernetics Part C (Applications and Reviews) · doi:10.1109/tsmcc.2006.876043 · Cited by 19
“A frequent mistake is to think that global independence implies conditional independence, being Simpson’s paradox [14] probably the most wellknown counterexample.”
BackgroundJent, J. R., Ryu, H., Toledo‐Hernández, C., Domingo, J. W. S., & Yeghiazarian, L. (2013) · Environmental Science & Technology · doi:10.1021/es304066z · Cited by 19
Simple Heuristics: The Foundations of Adaptive Social Behavior
Hertwig, R., & Hoffrage, U. (2012) · Oxford University Press eBooks · doi:10.1093/acprof:oso/9780195388435.003.0001 · Cited by 20
Model Determination for Categorical Data With Factor Level Merging
Δελλαπόρτας, Π., & Tarantola, C. (2005) · Journal of the Royal Statistical Society Series B (Statistical Methodology) · doi:10.1111/j.1467-9868.2005.00501.x · Cited by 19
“Since our level merging procedure is based on (undirected) graphical models theory, we give here some necessary definitions; for more details see Lauritzen (1996) and Whittaker (1990). Let G= .”
MethodModeling Helicoverpa armigera (Hübner) (Lepidoptera: Noctuidae) Damages on Cotton
Nibouche, S., Gozé, É., Babin, R., Beyo, J., & Brévault, T. (2007) · Environmental Entomology · doi:10.1603/0046-225x(2007)36[151:mhahln]2.0.co;2 · Cited by 19
Simpson's Reversal Paradox and Cost Allocation
Sunder, S. (1983) · Journal of Accounting Research · doi:10.2307/2490944 · Cited by 19
Reply to commentary by Imai, Keele, Tingley, and Yamamoto concerning causal mediation analysis.
Pearl, J. (2014) · Psychological methods · doi:10.1037/met0000022 · Cited by 21
Phage and bacteria diversification through a prophage acquisition ratchetPreprint
Anthenelli, M., Jasien, E., Edwards, R. A., Bailey, B., Felts, B., Katira, P., Nulton, J., Salamon, P., Rohwer, F. L., Silveira, C. B., et al. (2020) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2020.04.08.028340 · Cited by 19
“The purely lytic community model, thus, displays a Simpson’s paradox, where the local sublinear trend observed in communities with fixed richness differs from the global trend when comparing communities across richness (Simpson 1951; Knowles et al. 2017).”
BackgroundResolution of apparent paradoxes in the race-specific frequency of use-of-force by police
Ross, C. T., Winterhalder, B., & McElreath, R. (2018) · Palgrave Communications · doi:10.1057/s41599-018-0110-z · Cited by 36
“Specifically, we draw a parallel to classic findings on Simpson’s Paradox in applied statistics (Simpson, 1951; Bickel et al., 1975; Pearl, 2014), and demonstrate that pooled analyses of encounter-conditional data—as in Fryer (2016)—will fail to find true encounterconditional anti-black racial…”
ResultInfluentialBobko, P., & Roth, P. L. (2004) · Research in Personnel and Human Resources Management · doi:10.1016/s0742-7301(04)23004-3 · Cited by 26
van Smeden, M., & Moons, K. G. M. (2017) · Statistics in Medicine · doi:10.1002/sim.7286 · Cited by 18
“The other IDI manuscript [3] shows the IDI can suffer from Simpson’s paradox [13] even under small deviations from perfect model calibration.”
BackgroundNovel predictions arise from contradictions
Yanai, I., & Lercher, M. J. (2021) · Genome biology · doi:10.1186/s13059-021-02371-6 · Cited by 19
“This is an example of Simpson ’ s paradox [3, 4], where the correlation between two variables changes sign after controlling for another variable.”
BackgroundMembership Inference Attacks and Generalization
Baluta, T., Shen, S., Hitarth, S., Tople, S., & Saxena, P. (2022) · ACM SIGSAC Conference on Computer and Communications Security (CCS) · doi:10.1145/3548606.3560694 · Cited by 21
“This paradox arises because there are confounding factors or confounders [44, 59] wherein different sub-populations of the data have contradictory statistical properties.”
BackgroundFrey, R., Duncan, S. M., & Weber, E. U. (2022) · Journal of Risk and Uncertainty · doi:10.1007/s11166-022-09398-5 · Cited by 28
Peng, J., Wen, L., Mu, X., & Xiao, J. (2023) · Energy Sustainable Development/Energy for sustainable development · doi:10.1016/j.esd.2023.02.002 · Cited by 18
Time series causal relationships discovery through feature importance and ensemble models
Castro, M., Júnior, P. R. M., Soriano-Vargas, A., Werneck, R. D. O., Gonçalves, M. M., Filho, L. L., Moura, R., Zampieri, M. F., Linares, O. C., Ferreira, V. H. D. S., et al. (2023) · Scientific Reports · doi:10.1038/s41598-023-37929-w · Cited by 20
Prevalence of atypical presentations among outpatients and associations with diagnostic error
Harada, Y., Otaka, Y., Katsukura, S., & Shimizu, T. (2023) · Diagnosis · doi:10.1515/dx-2023-0060 · Cited by 19
Why the Causal View of Fitness Survives
Otsuka, J., Turner, T., Allen, C., & Lloyd, E. A. (2011) · Philosophy of Science · doi:10.1086/659219 · Cited by 18
Defectors Can Create Conditions That Rescue Cooperation
Waite, A. J., Cannistra, C., & Shou, W. (2015) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1004645 · Cited by 19
“This phenomenon is described by the Price equation [13,14] and is also known as “Simpson's Paradox” [15,16].”
MethodA Note on Construct Validity of the Anchoring Method in PISA 2012
Stankov, L., Lee, J., & von Davier, M. (2017) · Journal of Psychoeducational Assessment · doi:10.1177/0734282917702270 · Cited by 18
“Methodological Issues in Need of Further Examination A reviewer of the present article has alerted us of the relevance of the “Simpson’s paradox” (Simpson, 1951) for our findings.”
BackgroundJirschitzka, J., Kimmerle, J., Halatchliyski, I., Hancke, J., Meurers, D., & Creß, U. (2017) · PLoS ONE · doi:10.1371/journal.pone.0178985 · Cited by 18
Plant single-cell biology and abiotic stress tolerance
Tanveer, M., & Yousaf, U. (2020) · Elsevier eBooks · doi:10.1016/b978-0-12-818204-8.00026-6 · Cited by 18
Behavioral economics and the aggregate versus proximal impact of sociality on heavy drinking
Acuff, S. F., Stoops, W. W., & Strickland, J. C. (2021) · Drug and Alcohol Dependence · doi:10.1016/j.drugalcdep.2021.108523 · Cited by 18
“This discordant finding is consistent with an ecological fallacy – specifically, Simpson’s paradox – in which the aggregate, “ecological” correlations do not match the individual, event-level correlations, resulting in inaccurate inferences about the individual based upon the group to which they belong (Kievit et al.,…”
BackgroundResultAlın, A. (2010) · Wiley Interdisciplinary Reviews Computational Statistics · doi:10.1002/wics.72 · Cited by 18
Paradoxical games and a minimal model for a Brownian motor
Astumian, R. D. (2005) · American Journal of Physics · doi:10.1119/1.1801191 · Cited by 18
Mental Mechanisms: Speculations on Human Causal Learning and Reasoning
Chater, N., & Oaksford, M. (2005) · Cambridge University Press eBooks · doi:10.1017/cbo9780511614576.010 · Cited by 18
Bayesian clinical trials at The University of Texas MD Anderson Cancer Center: An update
Tidwell, R. S. S., Peng, S. A., Chen, M., Liu, D. D., Yuan, Y., & Lee, J. J. (2019) · Clinical Trials · doi:10.1177/1740774519871471 · Cited by 18
“Year 2009 57 (27) 155 (73) 212 (21) 2010 57 (26) 162 (74) 219 (21) 2011 57 (28) 146 (72) 203 (20) 2012 52 (28) 132 (72) 184 (18) 2013 60 (30) 142 (70) 202 (20) Site MD Anderson only 189 (56) 146 (44) 335 (33) Multicenter 94 (14) 582 (86) 676 (66) Other sites only 0 (0) 9 (100) 9 (1) Study source Externally peer review…”
Collapsibility of Distribution Dependence
Ma, Z., Xie, X., & Geng, Z. (2005) · Journal of the Royal Statistical Society Series B (Statistical Methodology) · doi:10.1111/j.1467-9868.2005.00536.x · Cited by 18
“This phenomenon is called the Yule-Simpson paradox (Yule, 1903; Simpson, 1951).”
BackgroundDecomposability and selection of graphical models for multivariate time series
Fried, R. (2003) · Biometrika · doi:10.1093/biomet/90.2.251 · Cited by 18
“Such phenomena are known as Simpson's Paradox (Simpson, 1951).”
BackgroundMeiser, T. (2003) · Social Cognition · doi:10.1521/soco.21.2.121.21318 · Cited by 18
The Analysis of Contingency Tables in Archaeology
LEWIS, R. B. (1986) · Elsevier eBooks · doi:10.1016/b978-0-12-003109-2.50009-x · Cited by 18
Averaging Gone Wrong: Using Time-Aware Analyses to Better Understand BehaviorPreprint
Barbosa, S., Cosley, D., Sharma, A. K., & Junior, R. M. C. (2016) · arXiv (Cornell University) · doi:10.48550/arxiv.1603.07025 · Cited by 18
“This is puzzling: when each of the cohorts exhibits a steady increase in their average comment length, how can the overall mean comment length decrease? This anomaly is an instance of the Simpson’s paradox [63], and occurs because we fail to properly condition on different cohorts when computing mean comment length.”
BackgroundNieuwenhuis, R. (2015) · Demographic Research · Cited by 17
Copositive matrices and Simpson's paradox
Hadjicostas, P. (1997) · Linear Algebra and its Applications · doi:10.1016/s0024-3795(96)00536-8 · Cited by 17
Abegaz, F., Lishout, F. V., John, J. M., Chiachoompu, K., Bhardwaj, A., Duroux, D., Gusareva, E. S., Wei, Z., Hakonarson, H. H., & Steen, K. V. (2021) · BioData Mining · doi:10.1186/s13040-021-00247-w · Cited by 17
Qureshi, M. J., Shah, P. S., Abdelgadir, D., Ye, X. Y., Afifi, J. K., Yuen, R., Calderon-Crossman, S., Taylor, B., Mohammad, K., Piedbœuf, B., et al. (2021) · The Journal of Pediatrics · doi:10.1016/j.jpeds.2021.02.073 · Cited by 17
Qian, S. S., Kennen, J. G., May, J. T., Freeman, M. C., & Cuffney, T. F. (2021) · Water Research · doi:10.1016/j.watres.2021.117685 · Cited by 17
Sznitman, S. R., Shochat, T., van Rijswijk, L., Greene, T., & Cousijn, J. (2021) · Cannabis and Cannabinoid Research · doi:10.1089/can.2021.0106 · Cited by 17
“Per Simpson’s Para-dox, 39,40 heavy cannabis or alcohol users may report more sleep difficulties than occasional users due to substance use disorders (between-person association), while sleep may be better among heavy users when they use cannabis or alcohol compared to no-use due to lower withdrawal discomfort (within-…”
Differential Investment Strategies in Leaf Economic Traits Across Climate Regions Worldwide
Ren, L., Huang, Y., Pan, Y., Xiang, X., Huo, J., Meng, D., Wang, Y., & Yu, C. (2022) · Frontiers in Plant Science · doi:10.3389/fpls.2022.798035 · Cited by 17
“Moreover, the results of such subgroup analysis are quite important because it reminds us to avoid deriving the patterns of the world LES under Simpson’s paradox (Simpson, 1951).”
BackgroundSimpson's Paradox: An Example in a New Zealand Survey of Jury Composition
Westbrooke, I. (1998) · CHANCE · doi:10.1080/09332480.1998.10542093 · Cited by 17
“What is Simpson’s Paradox Simpson’s paradox occurs when combining data sets gives a misleading overall picture. The name originates from a paper by Simpson in 1951. Let’s have a look at what happens in this case, as it is a good case study for the more general problem. A genuine example in fact - virtually all the exa…”
BackgroundStuijver, D. J. F., Romualdi, E., van Zaane, B., Bax, L., Buller, H. R., Gerdes, V. E. A., & Squizzato, A. (2014) · Internal and Emergency Medicine · doi:10.1007/s11739-014-1168-2 · Cited by 17
Roflumilast for asthma: Safety findings from a pooled analysis of ten clinical studies
Chervinsky, P., Meltzer, E. O., Busse, W., Ohta, K., Bardin, P. G., Bredenbröker, D., & Bateman, E. D. (2015) · Pulmonary Pharmacology & Therapeutics · doi:10.1016/j.pupt.2015.11.003 · Cited by 17
Higdem, J. L., Kostal, J. W., Kuncel, N. R., Sackett, P. R., Shen, W., Beatty, A. S., & Kiger, T. B. (2016) · Educational Measurement Issues and Practice · doi:10.1111/emip.12103 · Cited by 16
Juhlin, K., Star, K., & Norén, G. N. (2017) · Pharmacoepidemiology and Drug Safety · doi:10.1002/pds.4285 · Cited by 17
“This would have been an example of Simpson 0 s paradox, 13 where it would be incorrect to infer that patients are more likely than others to report medication error.”
BackgroundSilverman, J. M., & Schmeidler, J. (2017) · Medical Hypotheses · doi:10.1016/j.mehy.2017.10.022 · Cited by 17
“Such an apparent contradiction of higher survival rates for high risk than low risk survivors is an example of Simpson’s paradox [11].”
BackgroundFamilywise decompositions of Pearson’s chi-square statistic in the analysis of contingency tables
Lombardo, R., Takane, Y., & Beh, E. J. (2019) · Advances in Data Analysis and Classification · doi:10.1007/s11634-019-00374-7 · Cited by 17
An Empirical Analysis of Virtual Goods Permission Rights and Pricing Strategies
Ke, D., Ba, S., Stallaert, J., & Zhang, Z. (2012) · Decision Sciences · doi:10.1111/j.1540-5915.2012.00384.x · Cited by 17
La causalité dans la philosophie contemporaine
Kistler, M. (2004) · Intellectica Revue de l Association pour la Recherche Cognitive · doi:10.3406/intel.2004.1711 · Cited by 17
“En revanche, il n'y a aucune corréla- 59 D'après Simpson (1951).”
BackgroundOn meta-analyses of imaging data and the mixture of records
Ramsey, J. D., Spirtes, P., & Glymour, C. (2010) · NeuroImage · doi:10.1016/j.neuroimage.2010.07.065 · Cited by 17
The relationship between career mobility and occupational expertise
HEIJDEN, B. I. J. M. V. D. (2003) · Employee Relations · doi:10.1108/01425450310453535 · Cited by 17
“The reason was to take into account the danger of Simpson's paradox ( Simpson, 1951”
BackgroundDowning, A., Harrison, W. J., West, R. M., Forman, D., & Gilthorpe, M. S. (2009) · Journal of Epidemiology & Community Health · doi:10.1136/jech.2008.085852 · Cited by 17
“This leads to concerns regarding the interpretability of any findings due to the reversal paradox,”
BackgroundMethods for computational causal discovery in biomedicine
Ma, S., & Statnikov, A. (2017) · Behaviormetrika · doi:10.1007/s41237-016-0013-5 · Cited by 16
“For example, when studying the effect of two different treatments on the outcome of a disease, omitting the selection variable disease severity , which influences the choice of the treatment, may lead to discovering the causal relation between treatment and disease outcome (Simpson 1951).”
BackgroundThe Accuracy of Hamilton–Perry Population Projections for Census Tracts in the United States
Baker, J., Swanson, D. A., & Tayman, J. (2020) · Population Research and Policy Review · doi:10.1007/s11113-020-09601-y · Cited by 17
“Having reductions in each age group and an increase in the overall MAPE for females is an example of the Simpson-Yule paradox (Simpson 1951; Yule 1903) and is due to the differences in the size of the age groups.”
BackgroundRoss, C. T., & Winterhalder, B. P. (2015) · American Journal of Human Biology · doi:10.1002/ajhb.22757 · Cited by 16
“…dynamics of human parasite systems, and risks capturing spurious correlations created by averaging data at national levels [Simpson’s paradox (Simpson, 1951) and the ecological inference fallacy (Freedman, 1999)], the discarding of variance information (Draper, 1995), the file drawer effect…”
BackgroundFactor Structure of the Rahim Leader Power Inventory (Rlpi) with Clinical Female Student Supervisees
Hess, C. W., & Wagner, B. T. (1999) · Educational and Psychological Measurement · doi:10.1177/00131649921970314 · Cited by 17
“However, the combining of data across distinct groups can potentially induce Simpson’s paradox (Simpson, 1951), a type of aggregation error (Nunnally & Bernstein, 1994).”
BackgroundJoint Tests of Linkage and Association for Quantitative Traits
Allison, D. B., & Neale, M. C. (2001) · Theoretical Population Biology · doi:10.1006/tpbi.2001.1544 · Cited by 16
“This is an example of what is referred to as ‘‘Simpson’s paradox’’ (Simpson, 1951) and is illustrated in Fig.”
Good, I. J. (1988) · Springer eBooks · doi:10.1007/978-94-009-2863-3_2 · Cited by 17
MacCann, R. G. (1995) · Australian Journal of Education · doi:10.1177/000494419503900205 · Cited by 17
Log-Linear Models in Geography
UPTON, G. J. G., & Fingleton, B. (1979) · Transactions of the Institute of British Geographers · doi:10.2307/621927 · Cited by 17
Gabbay, D. M., & Woods, J. (2003) · A practical logic of cognitive systems · doi:10.1016/s1874-5075(03)80008-6 · Cited by 17
Environmental Change, If Unaccounted, Prevents Detection of Cryptic Evolution in a Wild Population
Potter, T., Bassar, R. D., Bentzen, P., Ruell, E. W., Torres‐Dowdall, J., Handelsman, C. A., Ghalambor, C. K., Travis, J., Reznick, D. N., & Coulson, T. N. (2020) · The American Naturalist · doi:10.1086/711874 · Cited by 16
“Both statistical problems that we have discussed are potential examples of the Yule-Simpson effect—a change in the magnitude or sign of a covariance conditional on a third variable (Yule 1903; Simpson 1951).”
BackgroundA comparison of misinformation feature effectiveness across issues and time on Chinese social media
Ji, J., Zhu, Y., & Chao, N. (2022) · Information Processing & Management · doi:10.1016/j.ipm.2022.103210 · Cited by 21
Publication bias in psychology: A closer look at the correlation between sample size and effect size
Linden, A. H., Pollet, T. V., & Hönekopp, J. (2024) · PLoS ONE · doi:10.1371/journal.pone.0297075 · Cited by 20
Macêdo, M., Ransom, N., Feng, Y., Hurst, J., & Wurtele, E. S. (2013) · BMC Bioinformatics · doi:10.1186/1471-2105-14-214 · Cited by 16
“The “Simpson’s paradox” [6], which refers to contradictory statistical results obtained when analysis is performed within versus across groups of data [7], is an example of mishandling of data.”
BackgroundTransitive reasoning distorts induction in causal chains
von Sydow, M., Hagmayer, Y., & Meder, B. (2015) · Memory & Cognition · doi:10.3758/s13421-015-0568-5 · Cited by 16
“For example, the Simpson paradox (Simpson, 1951) describes how statistical dependencies can vanish or even be reversed when moving from populations to subpopulations.”
BackgroundSimpson's paradox in the integrated discrimination improvement
Chipman, J., & Braun, D. (2016) · Statistics in Medicine · doi:10.1002/sim.6862 · Cited by 16
“In this paper, we investigate instances where Simpson’s paradox – where the conclusion of the overall metric contradicts the conclusions when stratified by a key covariate [19] – occurs in the IDI and whether it simultaneously occurs in other metrics, including AUC, Brier score, and R2.”
MethodA Statistical Guide for the Ethically Perplexed
Hubert, L. J., & Wainer, H. (2015) · Routledge eBooks · doi:10.4324/9780203840023.ch4 · Cited by 16
Gorman, K. (2010) · Scholarly Commons (University of Pennsylvania) · Cited by 16
A new group-selection model for the evolution of homosexuality
Kirby, J. (2003) · Biology & Philosophy · doi:10.1023/a:1026321628276 · Cited by 16
“Simpson, who first wrote about it in the early 1950’s, is to consider a hypothetical example ( Simpson, 1951: 238–241).”
BackgroundEdward Simpson: Bayes at Bletchley Park
Simpson, E. (2010) · Significance · doi:10.1111/j.1740-9713.2010.00424.x · Cited by 16
Self-citationLafont, S., Amoros, E., Gadegbeku, B., Chiron, M., & Laumon, B. (2007) · Accident Analysis & Prevention · doi:10.1016/j.aap.2007.05.010 · Cited by 16
Female Faculty Role Models and Student Outcomes: A Caveat about Aggregation
Johnson, I. Y. (2014) · Research in Higher Education · doi:10.1007/s11162-014-9331-1 · Cited by 16
“The problems that arise with aggregation are known in probability and statistics as Simpson’s paradox (Simpson 1951), in which a correlation is reversed when data are grouped.”
BackgroundA Formal Framework of Aggregation for the OLAP-OLTP Model
Lenz, H.-J., & Thalheim, B. (2009) · doi:10.3217/jucs-015-01-0273 · Cited by 16
STATISTICAL TECHNIQUES FOR TEXT CLASSIFICATION BASED ON WORD RECURRENCE INTERVALS
Berryman, M. J., Allison, A., & Abbott, D. (2003) · Fluctuation and Noise Letters · doi:10.1142/s021947750300104x · Cited by 16
“On closer inspection of the raw data we found that the cause is a Simpson reversal, also known as Simpson’s paradox [19], [20].”
MethodHighly multiplexed single-cell quantitative PCR
VanInsberghe, M. A., Zahn, H., White, A. K., Petriv, O. I., & Hansen, C. L. (2018) · PLoS ONE · doi:10.1371/journal.pone.0191601 · Cited by 16
Robinson, M. D., & Sedikides, C. (2020) · Cambridge University Press eBooks · doi:10.1017/9781108264822.031 · Cited by 18
Exploratory basis pursuit classification
Brown, M., & Costen, N. P. (2005) · Pattern Recognition Letters · doi:10.1016/j.patrec.2005.03.012 · Cited by 16
“2005 Published by Elsevier B.V. Keywords: Feature selection; Sparse classification; Regularization”
BackgroundMethodLocal Linear Discriminant Analysis (LLDA) for group and region of interest (ROI)-based fMRI analysis
McKeown, M. J., Li, J., Huang, X., Lewis, M. M., Rhee, S., Truong, K. N., & Wang, Z. J. (2007) · NeuroImage · doi:10.1016/j.neuroimage.2007.04.072 · Cited by 16
“While it is difficult to analytically determine why this would be so, a possible and intuitive explanation is the " Simpson paradox " (Simpson, 1951).”
Current Controlled Trials in Cardiovascular Medicine
Lièvre, M. M., Cucherat, M., & Leizorovicz, A. (2002) · Cited by 16
Hood, S. L., & Dinsmore, S. J. (2007) · Digital Commons - University of South Florida (University of South Florida) · Cited by 16
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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