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Adjusted chi-squared tests for cross-classified tables of survey data. (English) Zbl 0543.62036
Summary: D. Holt, A. J. Scott and P. D. Ewings [J. R. Stat. Soc., Ser. A 143, 303-320 (1980; Zbl 0461.62014)] propose a modified Pearson \(X^ 2\) statistic for testing independence in a two-way table of survey data. It is shown that the multiplier of \(X^ 2\) needed for this modification is a weighted sum of cell and marginal cell design effects. A similar adjustment of the \(X^ 2\) and \(G^ 2\) statistics is possible whenever log linear models with closed form estimates are fitted to a cross-classified table of survey data.

62G10 Nonparametric hypothesis testing
62H17 Contingency tables
62E20 Asymptotic distribution theory in statistics
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