Measures of association for cross-classifications under complex sampling designs

Molina-Cuevas, Emiro Antonio (1982) Measures of association for cross-classifications under complex sampling designs. University of Southampton, Doctoral Thesis.

Abstract

This thesis is concerned with the effect that the sample design has on the measurement and comparison of the association between the rows and columns of two-way contingency tables. We concentrate on a family of measures defined by Altham in 1970. The measures are functions of the cross-ratins of the table and are designed to compare the inherent association in two different contingency tables. In addition, the measures have a physical interpretation in terms of metrics. We also investigate the measures with operational meaning discussed by Goodman and Kruskal in 1954.Under simple random sampling, Altham's measures are distributed as non-central chi-square random variables. It is shown that under complex sampling, this distribution changes to a mixture, and ignoring the design may lead to misleading results. Measures are defined that are adequate for most standard designs and which have a simple distribution theory. As a result a test of independence emerges which seems easier to apply than the modified Wald statistic currently in use. It is shown that this approach may also be used to investigate Goodman and Kruskal's measures, and similar results are obtained. Finally the approach is extended to the measurement of quasi-association and association in three-way tables.

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