IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/3351.html
   My bibliography  Save this paper

The 2 x 2 x 2 case in causality, of an effect, a cause and a confounder. A cross-over’s guide to the 2 x 2 x 2 contingency table

Author

Listed:
  • Colignatus, Thomas

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.

Suggested Citation

  • Colignatus, Thomas, 2007. "The 2 x 2 x 2 case in causality, of an effect, a cause and a confounder. A cross-over’s guide to the 2 x 2 x 2 contingency table," MPRA Paper 3351, University Library of Munich, Germany, revised 14 May 2007.
    • Handle: RePEc:pra:mprapa:3351
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/3351/1/MPRA_paper_3351.pdf
    File Function: original version
    Download Restriction: no
    File URL: https://mpra.ub.uni-muenchen.de/3614/1/MPRA_paper_3614.pdf
    File Function: revised version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Colignatus, Thomas, 2007. "Correlation and regression in contingency tables. A measure of association or correlation in nominal data (contingency tables), using determinants," MPRA Paper 3394, University Library of Munich, Germany, revised 07 Jun 2007.
    2. Saari,Donald G., 2001. "Decisions and Elections," Cambridge Books, Cambridge University Press, number 9780521808163, October.
    3. Saari,Donald G., 2001. "Decisions and Elections," Cambridge Books, Cambridge University Press, number 9780521004046, October.
    4. Colignatus, Thomas, 2007. "A measure of association (correlation) in nominal data (contingency tables), using determinants," MPRA Paper 2662, University Library of Munich, Germany, revised 10 Apr 2007.
    5. Colignatus, Thomas, 2007. "A comparison of nominal regression and logistic regression for contingency tables, including the 2 × 2 × 2 case in causality," MPRA Paper 3615, University Library of Munich, Germany, revised 19 Jun 2007.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Aki Lehtinen, 2007. "The Borda rule is also intended for dishonest men," Public Choice, Springer, vol. 133(1), pages 73-90, October.
    2. Colignatus, Thomas, 2017. "Comparing votes and seats with a diagonal (dis-) proportionality measure, using the slope-diagonal deviation (SDD) with cosine, sine and sign," MPRA Paper 80833, University Library of Munich, Germany, revised 17 Aug 2017.
    3. Conal Duddy & Ashley Piggins & William Zwicker, 2016. "Aggregation of binary evaluations: a Borda-like approach," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 46(2), pages 301-333, February.
    4. Shmuel Nitzan, 2010. "Demystifying the ‘metric approach to social compromise with the unanimity criterion’," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 35(1), pages 25-28, June.
    5. Shin Sato, 2012. "On strategy-proof social choice under categorization," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 38(3), pages 455-471, March.
    6. Colignatus, Thomas, 2013. "The performance of four possible rules for selecting the Prime Minister after the Dutch Parliamentary elections of September 2012," MPRA Paper 44158, University Library of Munich, Germany, revised 02 Feb 2013.
    7. Peter Emerson, 2013. "The original Borda count and partial voting," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(2), pages 353-358, February.
    8. Hartvigsen, David, 2006. "Vote trading in public elections," Mathematical Social Sciences, Elsevier, vol. 52(1), pages 31-48, July.
    9. Antoinette Baujard, 2006. "L'estimation des préférences individuelles en vue de la décision publique.. Problèmes, paradoxes, enjeux," Economie & Prévision, La Documentation Française, vol. 0(4), pages 51-63.
    10. Herrade Igersheim, 2006. "Invoking a Cartesian Product Structure on Social States: New Resolutions of Sen's and Gibbard's Impossibility Theorems," UFAE and IAE Working Papers 659.06, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
    11. Colignatus, Thomas, 2017. "Comparing votes and seats with a diagonal (dis-) proportionality measure, using the slope-diagonal deviation (SDD) with cosine, sine and sign," MPRA Paper 80965, University Library of Munich, Germany, revised 24 Aug 2017.
    12. Steven Brams & Michael Hansen & Michael Orrison, 2006. "Dead Heat: The 2006 Public Choice Society Election," Public Choice, Springer, vol. 128(3), pages 361-366, September.
    13. Diana Cheng & Peter Coughlin, 2017. "Using equations from power indices to analyze figure skating teams," Public Choice, Springer, vol. 170(3), pages 231-251, March.
    14. Antoinette Baujard, 2006. "Une critique opérationnelle du welfarisme dans la prise de décision publique," Post-Print halshs-00155130, HAL.
    15. Eric Libby & Leon Glass, 2010. "The Calculus of Committee Composition," PLOS ONE, Public Library of Science, vol. 5(9), pages 1-8, September.
    16. Michael Ackerman & Sul-Young Choi & Peter Coughlin & Eric Gottlieb & Japheth Wood, 2013. "Elections with partially ordered preferences," Public Choice, Springer, vol. 157(1), pages 145-168, October.
    17. Donald G. Saari, 2019. "Arrow, and unexpected consequences of his theorem," Public Choice, Springer, vol. 179(1), pages 133-144, April.
    18. Andrew Neath & Joseph Cavanaugh & Adam Weyhaupt, 2015. "Model evaluation, discrepancy function estimation, and social choice theory," Computational Statistics, Springer, vol. 30(1), pages 231-249, March.
    19. Colignatus, Thomas, 2010. "Single vote multiple seats elections. Didactics of district versus proportional representation, using the examples of the United Kingdom and The Netherlands," MPRA Paper 22671, University Library of Munich, Germany, revised 06 Jul 2007.
    20. Franklin G. Mixon Jr. & Ernest W. King, 2012. "Social Choice Theory in 10,000 Meters: Examining Independence and Transitivity in the Ncaa Cross-Country Championships," The American Economist, Sage Publications, vol. 57(1), pages 32-41, May.

    More about this item

    Keywords

    Experimental economics; causality; cause and effect; confounding; contingency table; Simpson paradox; conditional independence; risk; safety; epidemiology; correlation; regression; Cornfield’s condition; inference;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:pra:mprapa:3351. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Joachim Winter (email available below). General contact details of provider: https://edirc.repec.org/data/vfmunde.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.