Abstract
There exist several methods of testing homogeneity of two marginal distributions of a square contingency table with ordinal categories. In the present paper, some notes on the properties of the test are made and validity and powers are examined by Monte Carlo simulation. A modification of the Koch-Reinfurt test is proposed for achieving better small-sample approximation to the null distribution. Furthermore a cumulative chi-square test is proposed, which is expected to have fairly high power for broad alternatives of location and/or scale shift. Simulation studies indicate that in small or moderate samples, more accurate approximation distributions are worth developing for some of the tests examined. It is also shown that the power of tests is highly dependent on the latent distributional model and the skewness of the marginal probabilities.
