Institute of Statistics, Beijing University of Technology

We consider the test of independence in contengence tables with multiple column responses in this paper. For the case that the alternative hypothesis refers to monotone trends, we propose an approximate $F$ test based on artificial parameter and regression model. The method eliminates the estimation of correlative coefficients, which are hardly to estimate in contingency tables
with multiple column responses. Simulation results show that the true significant level of the test is near to the nominal one, and has good power.