ABSTRACT
Many of the data sets used to illustrate the chi-square test in introductory statistics textbooks originate in complex surveys. This chapter is concerned with the effects of clustering on hypothesis tests and models for categorical data, since clustering usually decreases precision. A. Agresti and J. S. Simonoff are good references on the analysis of categorical data in non-survey situations. The chapter outlines some of the basic approaches for testing independence with data from a complex survey. R. E. Fay references a number of studies demonstrating that the simple random sample -based test statistics “may give extremely erroneous results when applied to data arising from a complex sample design.” In complex surveys, though, unlike in multinomial and product multinomial sampling, the tests for independence and homogeneity of proportions are not necessarily the same. D. Holt et al. note that often clustering has less effect on tests for independence than on tests for goodness of fit or homogeneity of proportions.
