Chi–square tests for comparing vectors of proportions for several cluster samples

Abstract

Test statistics are developed for comparing vectors of proportions obtained from several independent two–stage cluster samples. It is assumed that clusters are selected with probability proportional to size for each sample. Wald's general method of constructing quadratic forms is used to obtain a large sample chi–square test. More easily evaluted chi–square tests are derived from the Dirichlet–multinnomial model. Corresponding goodness–of–fit test for the Dirichlet–multinomial model are also derived.

Keywords:

• Pearson chi–square test
• Dirichlet–multinomial model
• Wald statistics