Performance of the modified Wilcoxon signed rank test

• Main Authors: Ahad Nor Aishah, Yahaya Sharipah Soaad Syed, Zahayu, MdYusof, Suhaida, Abdullah, Fung Lim Yai
• Format: Conference Proceeding
• Language: English
• Subjects: Computer simulation; Monte Carlo simulation; Null hypothesis; Rank tests; Statistical analysis; Statistical tests
• ISSN: 0094-243X; 1551-7616
• DOI: 10.1063/1.4903657

Nonparametric methods require only few assumptions to be made about the format of the data, and they may therefore be preferable when the assumptions required for parametric methods are not valid. The Wilcoxon signed rank test applies to matched pairs studies. For two tail test, it tests the null hypothesis that there is no systematic difference within pairs against alternatives that assert a systematic difference. The test is based on the Wilcoxon signed rank statistic W, which is the smaller of the two ranks sums. The steps to compute W consider the positive and negative differences and omit all the zero differences. In this study, we modify the Wilcoxon signed rank test using the indicator function of positive, zero and negative differences to compute the Wilcoxon statistic, W. The empirical Type I error rates of the modified statistical test was measured via Monte Carlo simulation. These rates were obtained under different distributional shapes, sample sizes, and number of replications. The modified Wilcoxon signed rank test was found to be robust under symmetric distributions even though the values are quite conservative. The finding also demonstrated that different number of replication does not influence the result because there is not much difference in the value of the Type I error rates obtained.