Colignatus, Thomas (2007): The 2 x 2 x 2 case in causality, of an effect, a cause and a confounder. A crossover’s guide to the 2 x 2 x 2 contingency table.
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Abstract
Basic causality is that a cause is present or absent and that the effect follows with a success or not. This happy state of affairs becomes opaque when there is a third variable that can be present or absent and that might be a seeming cause. The 2 x 2 x 2 layout deserves the standard name of the ETC contingency table, with variables Effect, Truth and Confounding and values {S, S}, {C, C}, {F, F}. Assuming the truth we can find the impact of the cause from when the confounder is absent. The 8 cells in the crosstable can be fully parameterized and the conditions for a proper cause can be formulated, with the parameters interpretable as regression coefficients. Requiring conditional independence would be too strong since it neglects some causal processes. The Simpson paradox will not occur if logical consistency is required rather than conditional independence. The paper gives a taxonomy of issues of confounding, a parameterization by risk or safety, and develops the various cases of dependence and (conditional) independence. The paper is supported by software that allows variations. The paper has been written by an econometrician used to structural equations models but visiting epidemiology hoping to use those techniques in experimental economics.
Item Type:  MPRA Paper 

Institution:  Thomas Cool Consultancy & Econometrics 
Original Title:  The 2 x 2 x 2 case in causality, of an effect, a cause and a confounder. A crossover’s guide to the 2 x 2 x 2 contingency table 
Language:  English 
Keywords:  Experimental economics; causality; cause and effect; confounding; contingency table; Simpson paradox; conditional independence; risk; safety; epidemiology; correlation; regression; Cornfield’s condition; inference 
Subjects:  C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C10  General 
Item ID:  3351 
Depositing User:  Thomas Colignatus 
Date Deposited:  29. May 2007 
Last Modified:  18. Feb 2013 10:07 
References:  Colignatus is the name of Thomas Cool in science. Cool, Th. (1999, 2001), “The Economics Pack, Applications for Mathematica”, http://www.dataweb.nl/~cool, ISBN 9080477419, JEL990820 Colignatus, Th. (2007d), “Correlation and regression in contingency tables. A measure of association or correlation in nominal data (contingency tables), using determinants", http://mpra.ub.unimuenchen.de/3226/01/MPRA_paper_3226.pdf, Retrieved from source Colignatus, Th. (2007e), “Elementary statistics and causality”, work in progress, http://www.dataweb.nl/~cool/Papers/ESAC/Index.html Fisher, R.A. (1958a), “Lung Cancer and Cigarettes? Letter to the editor”, Nature, vol. 182, p. 108, 12 July 1958 [Collected Papers 275], see Lee (2007), http://www.york.ac.uk/depts/maths/histstat/fisher275.pdf, Retrieved from source Fisher, R.A. (1958b), “Cancer and Smoking? Letter to the editor”, Nature, vol. 182, p. 596, 30 August 1958 [Collected Papers 276], see Lee (2007), http://www.york.ac.uk/depts/maths/histstat/fisher276.pdf, Retrieved from source Kleinbaum, D.G., K.M. Sullivan and N.D. Barker (2003), “ActivEpi Companion texbook”, Springer Lee, P.M. (2007), “Life and Work of Statisticians”, http://www.york.ac.uk/depts/maths/histstat/lifework.htm, Revised 24 April 2007 Pearl, J. (1998), “Why there is no statistical test for confounding, why many think there is, and why they are almost right”, UCLA Cognitive Systems Laboratory, Technical Report (R256), January 1998 Pearl, J. (2000), “Causality. Models, reasoning and inference”, Cambridge Saari, D.G. (2001), “Decisions and elections”, Cambridge Schield, M. (1999, 2003), “Simpson’s paradox and Cornfield’s conditions”, Augsburg College ASAJSM, http://web.augsburg.edu/~schield/MiloPapers/99ASA.pdf, 07/23/03 Updated, Retrieved from source 
URI:  http://mpra.ub.unimuenchen.de/id/eprint/3351 
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 The 2 x 2 x 2 case in causality, of an effect, a cause and a confounder. A crossover’s guide to the 2 x 2 x 2 contingency table. (deposited 29. May 2007) [Currently Displayed]