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Holt, Scott & Ewings (1980) propose a modified Pearson X2 statistic for testing independence in a two-way table of survey data. It is shown that the multiplier of X2 needed for this modification is a weighted sum of cell and marginal cell design effects. A similar adjustment of the X2 and G2 statistics is possible whenever log linear models with closed form estimates are fitted to a cross-classified table of survey data.
Edward J. Bedrick (Sat,) studied this question.