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March, 1984 On Chi-Squared Tests for Multiway Contingency Tables with Cell Proportions Estimated from Survey Data
J. N. K. Rao, A. J. Scott
Ann. Statist. 12(1): 46-60 (March, 1984). DOI: 10.1214/aos/1176346391

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, $X^2$ (or the likelihood ratio test statistic, $G^2$) is obtained as a weighted sum of independent $\chi^2_1$ random variables, and the weights are then related to the familiar design effects (deffs) used by survey samplers. A simple correction to $X^2$ (or $G^2$) 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 $X^2$ and some corrected $X^2$ statistics in a three-way table is given, using some data from the Canada Health Survey, 1978-1979.

Citation

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J. N. K. Rao. A. J. Scott. "On Chi-Squared Tests for Multiway Contingency Tables with Cell Proportions Estimated from Survey Data." Ann. Statist. 12 (1) 46 - 60, March, 1984. https://doi.org/10.1214/aos/1176346391

Information

Published: March, 1984
First available in Project Euclid: 12 April 2007

zbMATH: 0622.62059
MathSciNet: MR733498
Digital Object Identifier: 10.1214/aos/1176346391

Subjects:
Primary: 62D05
Secondary: 62H15

Rights: Copyright © 1984 Institute of Mathematical Statistics

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Vol.12 • No. 1 • March, 1984
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