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On Chi-Squared Tests for Multiway Contingency Tables with Cell Proportions Estimated from Survey Data

J. N. K. Rao and A. J. Scott
The Annals of Statistics
Vol. 12, No. 1 (Mar., 1984), pp. 46-60
Stable URL: http://www.jstor.org/stable/2241033
Page Count: 15
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On Chi-Squared Tests for Multiway Contingency Tables with Cell Proportions Estimated from Survey Data
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Abstract

The impact of survey design on standard multinomial-based methods for a multiway contingency table is studied, under nested loglinear models. The asymptotic null distribution of the Pearson chi-squared test statistic, X2 (or the likelihood ratio test statistic, G2) is obtained as a weighted sum of independent χ2 1 random variables, and the weights are then related to the familiar design effects (deffs) used by survey samplers. A simple correction to X2 (or G2) is also obtained which requires the knowledge of only the cell deffs and the deffs for collapsed tables (marginals), whenever the model admits a direct solution of likelihood equations under multinomial sampling. Finally, an example on the relative performance of X2 and some corrected X2 statistics in a three-way table is given, using some data from the Canada Health Survey, 1978-1979.

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