Abstract
In two-sample problems for ordered response categories, we discuss the performances of F-test and "accumulated chi-square test" in the accumulating nethod based on the Monte Carlo evaluation. First, we investigate the degrees of approximation of distribution for above test statistics to their null asymptotic distributions. Next, we evaluate their powers by comparing them with those of Wilcoxon's rank-sum tests and of Pearson's chi-squase test. The type I error probabilities exceed nominal levels if we make use of so called "conventional degrees of freedom" in the F-test, while use of "actual degrees of freedom" has tendency to give slightly lower levels than nominal ones. The power of the accumulated chi-square test is essentially the same as that of the F-test with the actual degrees of freedom. Wilcoxon's rank-sum test and Pearson's chi-square test are favorable to location-shift and scale-shift alternatives respectively, though the accumulating method has high powers against broad alternatives, including location-shift alternatives.
