The Annals of Statistics

The Amalgamation and Geometry of Two-by-Two Contingency Tables

I. J. Good and Y. Mittal

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Abstract

If a pair of two-by-two contingency tables are amalgamated by addition it can happen that a measure of association for the amalgamated table lies outside the interval between the association measures of the individual tables. We call this the amalgamation paradox and we show how it can be avoided by suitable designs of the sampling experiments. We also study the conditions for the "homogeneity" of two subpopulations with respect to various measures of association. Some of the proofs have interesting geometrical interpretations.

Article information

Source
Ann. Statist. Volume 15, Number 2 (1987), 694-711.

Dates
First available: 12 April 2007

Permanent link to this document
http://projecteuclid.org/euclid.aos/1176350369

JSTOR
links.jstor.org

Digital Object Identifier
doi:10.1214/aos/1176350369

Mathematical Reviews number (MathSciNet)
MR888434

Zentralblatt MATH identifier
0665.62058

Subjects
Primary: 62H17: Contingency tables
Secondary: 62A99: None of the above, but in this section

Keywords
Amalgamation paradox contingency tables homogeneity of subpopulations geometry of contingency tables

Citation

Good, I. J.; Mittal, Y. The Amalgamation and Geometry of Two-by-Two Contingency Tables. The Annals of Statistics 15 (1987), no. 2, 694--711. doi:10.1214/aos/1176350369. http://projecteuclid.org/euclid.aos/1176350369.


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See also

  • Addendum: I. J. Good, Y. Mittal. Addendum: The Amalgamation and Geometry of Two-by-Two Contingency Tables. Ann. Statist., vol. 17, no. 2 (1989), 947.