The results obtained were validated for different sample sizes and different numbers of populations.
📌 3 Key Takeaways
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Objective & Hypothesis: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.
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Key Findings & Data: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.
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Conclusion & Impact:The results obtained were validated for different sample sizes and different numbers of populations.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters
Abstract
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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Cite This Article
ALTUNKAYNAK, B., GAMGAM, H. (2022). Selection of one-stage sample size in Chen-Chen-Chang's $tilde{R}$ test and an evaluation of the performance of $tilde{R}$. Hacettepe Journal of Mathematics and Statistics, Cilt: 39 - Sayı: 4, 613–626. https://ajindex.com/articles/530663
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