In this study, in order to determine the one-stage sample size, power comparisons were made in the (R) over tilde test suggested by Chen et al. for ordered alternatives, and the Jonckheere-Terpstra J test, which is one of the classic test statistics, was compared with (R) over tilde in terms of effectiveness. The simulation concerning power comparisons showed that it is impossible to randomly select the one-stage sample size represented by no in (R) over tilde, based on one-stage sampling, and that the one-stage sample size should be as large as possible. In addition, the recently-suggested (R) over tilde test statistic for ordered alternatives was compared with J in terms of experimental type-I error and power. Whilst (R) over tilde and J yielded almost the same results in terms of experimental type-I error, (R) over tilde was found to give a worse performance than J with regard to power. The results obtained were validated for different sample sizes and different numbers of populations.