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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
Published by: Institute of Mathematical Statistics
Stable URL: http://www.jstor.org/stable/2241334
Page Count: 18
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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.
The Annals of Statistics © 1987 Institute of Mathematical Statistics