Testing for Association Using Multiple Response Survey Data: Approximate Procedures Based on the Rao-Scott Approach

This article discusses approximate tests of marginal association in 2-way tables in which one or both response variables admit multiple responses. Although multiple-response questions appear in all fields of research, including sociology, education, and marketing, the development of association tests that can be used with multiple-response data is very recent. A simple test procedure proposed by Agresti and Liu (1999) is extended to tests of association between 2 multiple-response variables, and it is shown that the procedure is a member of the first-order Rao-Scott family of corrected chi-squared statistics. A second-order Rao-Scott version of this procedure is developed. The Type I error control of both first- and second-order procedures is examined through calculation and simulation.