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On Methods for Comparing Contingency Tables

Leo A. Goodman
Journal of the Royal Statistical Society. Series A (General)
Vol. 126, No. 1 (1963), pp. 94-108
Published by: Wiley for the Royal Statistical Society
DOI: 10.2307/2982447
Stable URL: http://www.jstor.org/stable/2982447
Page Count: 15
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On Methods for Comparing Contingency Tables
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Abstract

In this paper we show that the standard error formulae given by Lewis (1962) and others for the Stouffer method of comparison of sets of 2 × 2 tables do not lead, in general, to consistent estimators of the appropriate standard deviations. Simple modifications of these formulae, which do lead to consistent estimators, are presented here. Since the relative difference between the standard errors published earlier and the consistent standard errors can be large, the earlier formulae should be replaced by the modified ones. For the analysis of K 2 × 2 tables (K ⩾ 2), we present here generalizations of the Stouffer method of comparison and also generalizations of the methods of analysis discussed by Berger (1961) for the special case where K = 2. A simple test of zero second-order interaction in a K × 2 × 2 contingency table is presented here. We also present some methods for analysing K I × J tables (describing attitude changes), and some methods of analysis suitable for the situation where the response categories (i.e. the row and column categories in the tables) are ordinally scaled.

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