A class of Rasch model tests is proposed, all of them based on the Manter-Haenszel chi-squared statistic. All tests make use of the 'sufficient statistics' property the Rasch model possesses. One element of our general class, the test for item bias developed by Holland and Thayer, has been discussed extensively in the psychometric literature. Three applications of the general procedure are presented, two on unidimensionality and one on item dependence in educational testing. In each case, simulation results are reported. Our procedure is also applied to real data