Selection of one-stage sample size in Chen-Chen-Chang's $tilde{R}$ test and an evaluation of the performance of $tilde{R}$

In this study, in order to determine the one-stage sample size, power comparisons were made in the $tilde{R}$ 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 $tilde{R}$ in terms of effectiveness. The simulation concerning power comparisons showed that it is impossible to randomly select the one-stage sample size represented by $n_0$ in $tilde{R}$ , based on one-stage sampling, and that the one-stage sample size should be as large as possible. In addition, the recently-suggested $tilde{R}$ test statistic for ordered alternatives was compared with J in terms of experimental type-I error and power. Whilst $tilde{R}$ and J yielded almost the same results in terms of experimental type-I error, $tilde{R}$ 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.

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