The Annals of Statistics

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

I. J. Good and Y. Mittal

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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

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

First available: 12 April 2007

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Amalgamation paradox contingency tables homogeneity of subpopulations geometry of contingency tables


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.

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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.