Test Statistic for Ordered Alternatives based on Wilcoxon Signed Rank

Year 2019, Volume: 32 Issue: 2, 718 - 735, 01.06.2019

Bülent Altunkaynak , Hamza Gamgam

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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