A simple test of association for contingency tables with multiple column responses

Loughin and Scherer (1998, Biometrics 54, 630-637) investigated tests of as sociation in two-way tables when one of the categorical variables allows fo r multiple-category responses from individual respondents. Standard chi-squ ared tests are invalid in this case, and they developed a bootstrap test pr ocedure that provides good control of test levels under the-null hypothesis . This procedure and some others that have been proposed are computationall y involved and are based on techniques that are relatively unfamiliar to ma ny practitioners. In this paper, the methods introduced by Rao and Scott (1 981, Journal of the American Statistical Association 76, 221-230) for analy zing complex survey data are used to develop a simple test based on a corre cted chi-squared statistic.