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On simple adjustments to chi-square tests with sample survey data. (English) Zbl 0647.62021

Summary: For testing the goodness-of-fit of a log-linear model to a multi-way contingency table with cell proportions estimated from survey data the authors [Ann. Stat. 12, 46-60 (1984; Zbl 0622.62059)] derived a first- order correction, \(\delta\)., 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 \(\delta\). 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 \(\delta\). 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 \(\delta\). 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.

MSC:

62D05 Sampling theory, sample surveys
62H15 Hypothesis testing in multivariate analysis
62G10 Nonparametric hypothesis testing
62H17 Contingency tables

Citations:

Zbl 0622.62059
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