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

I. J. Good and Y. Mittal
The Annals of Statistics
Vol. 15, No. 2 (Jun., 1987), pp. 694-711
Stable URL: http://www.jstor.org/stable/2241334
Page Count: 18
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The Amalgamation and Geometry of Two-by-Two Contingency Tables
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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.

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