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March, 1987 On Simple Adjustments to Chi-Square Tests with Sample Survey Data
J. N. K. Rao, A. J. Scott
Ann. Statist. 15(1): 385-397 (March, 1987). DOI: 10.1214/aos/1176350273

Abstract

For testing the goodness-of-fit of a $\log$-linear model to a multi-way contingency table with cell proportions estimated from survey data, Rao and Scott (1984) derived a first-order correction, $\delta\ldot$, to Pearson chi-square statistic, $X^2$ (or the likelihood ratio statistic, $G^2$) that takes account of the survey design. It was also shown that $\delta\ldot$ requires the knowledge of only the cell design effects (deffs) and the marginal deffs provided the model admits direct solution to likelihood equations under multinomial sampling. Simple upper bounds on $\delta\ldot$ are obtained here for models not admitting direct solutions, also requiring only cell deffs and marginal deffs or some generalized deffs not depending on any hypothesis. Applicability of an $F$-statistic used in GLIM to test a nested hypothesis is also investigated. In the case of a logit model involving a binary response variable, simple upper bounds on $\delta\ldot$ are obtained in terms of deffs of response proportions for each factor combination or some generalized deffs not depending on any hypothesis. Applicability of the GLIM $F$-statistic for nested hypotheses is also studied.

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J. N. K. Rao. A. J. Scott. "On Simple Adjustments to Chi-Square Tests with Sample Survey Data." Ann. Statist. 15 (1) 385 - 397, March, 1987. https://doi.org/10.1214/aos/1176350273

Information

Published: March, 1987
First available in Project Euclid: 12 April 2007

zbMATH: 0647.62021
MathSciNet: MR885744
Digital Object Identifier: 10.1214/aos/1176350273

Subjects:
Primary: 62D05
Secondary: 62H15

Rights: Copyright © 1987 Institute of Mathematical Statistics

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Vol.15 • No. 1 • March, 1987
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