Abstract
In the present paper, the conditions under which Simpson’s paradox does not occur are discussed for various cases. These conditions are first obtained from the descriptive point of view and then on the assumption of prior probability distributions of parameters. The robustness of the results is discussed with respect to the prior probability distributions. Practically, the result is given as the magnitude of odds ratio (or relative risk), i.e., Simpson’s paradox does not occur if the odds ratio is more or less than a certain values, depending on various cases.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Geng, Z.H.I. (1992). Collapsibility of relative risk in contingency tables with a response variable, J R Statist Soc B, 54, 585–593.
Hand, D.J. (1994). Deconstruction statistical questions, J R Statist Soc, A157, 317–356.
Hayashi, C. (1993). Treatise on behaviormetrics (in Japanese), Asakura-Syoten, 108–122.
Hintsman, D.L. (1993). On variability, Simpson’s paradox, and the relation between recognition and recall: reply to Tulving and Flexser, Psychol Rev, 100, 143–148.
Miettinen, O.S. (1976). Stratification by multivariate confounder score, Am J Epidemiol, 104 (6), 609–620.
Shapiro, S.H. (1982). Collapsing contingency tables: a geometric approach. Am Statistn, 36, 43–46.
Simpson, E.H. (1951). The interpretation of interaction in contingency tales, J R Statist Soc, B13, 238–241.
Vogt, A. (1995). Simpson’s paradox revisited, Student, 1, 2, 99–108.
Weinberg, C.R. (1993). Toward a clear definition of confounding, Am J Epidemiol, 137, 1, 1–8.
Wermuth, N. (1989). Moderating effects of subgroups in linear models, Biometrika, 76, 81–92.
Yamaoka, K. (1996). Beyond Simpson’s Paradox: A descriptive approach, Data Analysis and Stochastic Models, 12, 23 9–253.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1998 Springer-Verlag Berlin · Heidelberg
About this paper
Cite this paper
Hayashi, C., Yamaoka, K. (1998). Beyond Simpson’s Paradox: One Problem in Data Science. In: Rizzi, A., Vichi, M., Bock, HH. (eds) Advances in Data Science and Classification. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-72253-0_9
Download citation
DOI: https://doi.org/10.1007/978-3-642-72253-0_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-64641-9
Online ISBN: 978-3-642-72253-0
eBook Packages: Springer Book Archive