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 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.

Keywords

• Ordered alternatives,Wilcoxon signed rank statistic,Simulation,Power

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