Modified Wilcoxon procedure for dependent group - Ahad, Nor Aishah; Abdullah, Suhaida; Md Yusof, Zahayu; Syed Yahaya, Sharipah Soaad; Lim, Yai Fung (Universiti Utara Malaysia, 2014)
Nonparametric methods require no or very limited 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 step to compute the statistic W considered 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.The result shows that this test produced liberal Type I error rates under skewed distribution.The use of the indicator positive, zero and negative differences influence the result of the Wilcoxon statistic.These finding was demonstrated using an example data.