Test Statistic for Ordered Alternatives based on Wilcoxon Signed Rank

Abstract

This paper proposes a test statistic for ordered alternatives based on the Wilcoxon signed rankstatistic. One of the classical tests, Jonckheere-Terpstra’s J test, and the R test suggested by Chenet al. were used for type I error rate and power comparisons. For data generated from the normaldistribution, all of the tests gave type I error rates close to nominal alpha. When the data weregenerated from chi-square distribution, the proposed G test and J test for type I error gave betterresults than the R test, but the error rates of the J test for Student’s t distribution are better thanthose of the others. Power results of simulation study for normal distributions showed that theproposed G test was superior to all other considered tests. The G and J tests for the data generatedfrom Student’s t distributions performed well. When the data were generated from chi-squaredistributions, the proposed G test is more powerful than the others. The simulation showed thatthe R test was inferior to the other tests for all cases.