Chi-squared tests in dual frame surveys

In order to obtain better coverage of the population of interest and cost less, a number of surveys employ dual frame structure, in which independent samples are taken from two overlapping sampling frames. This research considers chi-squared tests in dual frame surveys when categorical data is encountered. We extend generalized Wald's test (Wald 1943), Rao-Scott first-order and second-order corrected tests (Rao and Scott 1981) from a single survey to a dual frame survey and derive the asymptotic distributions. Simulation studies show that both Rao-Scott type corrected tests work well and thus are recommended for use in dual frame surveys. An example is given to illustrate the usage of the developed tests.