@article{article_471954, title={Test Statistic for Ordered Alternatives based on Wilcoxon Signed Rank}, journal={Gazi University Journal of Science}, volume={32}, pages={718–735}, year={2019}, author={Altunkaynak, Bülent and Gamgam, Hamza}, keywords={Ordered alternatives,Wilcoxon signed rank statistic,Simulation,Power}, abstract={<p class="MsoNormal" style="text-align:justify;"> <span style="line-height:107%;">This paper
proposes a test statistic for ordered alternatives based on the Wilcoxon signed
rank statistic. One of the classical tests, Jonckheere-Terpstra’s J test, and the R test suggested by Chen et al. were used for type I error rate and
power comparisons. For data generated from the normal distribution, all of the
tests gave type I error rates close to nominal alpha. When the data were
generated from chi-square distribution, the proposed G test and J test for
type I error gave better results than the R
test, but the error rates of the J
test for Student’s t distribution are
better than those of the others. Power results of simulation study for normal
distributions showed that the proposed G
test was superior to all other considered tests. The G and J tests for the
data generated from Student’s t distributions performed well. When the data
were generated from chi-square distributions, the proposed G test is more powerful than the others. The simulation showed that
the R test was inferior to the other
tests for all cases. </span> <span style="font-size:9pt;line-height:107%;font-family:’Times New Roman’, serif;"> <span lang="en-us" xml:lang="en-us"> </span> </span> </p> <p> </p>}, number={2}, publisher={Gazi University}