Type I Error of the Modified Wilcoxon Signed Rank Test under Leptokurtic Distribution
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Nor Aishah Ahad, Sharipah Soaad Syed Yahaya, Suhaida Abdullah, Lim Yai Fung and Zahayu Md Yusof
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Abstract. Group comparisons are at the heart of many research questions addressed by researchers. Making inferences and drawing conclusions through statistical hypothesis testing on the differences between groups is actively adopted by researchers in many disciplines. When the groups are dependent, and violation of normality assumption occurred, the most commonly used method like paired t-test, usually produced doubtful result which will lead to misleading conclusions. As alternative, researchers tend to choose nonparametric Wilcoxon signed rank test for the purpose. The computation of this statistic involves ranking the absolute difference of each pair of observations and any pair with 0 differences will be discarded. In this study, the statistic was modified by including the 0 differences in the ranking. The empirical Type I error rates of the modified statistical test was measured via Monte Carlo simulation. These rates were obtained under the combination of leptokurtic distributional shapes with various sample sizes and number of replications. The modified Wilcoxon signed rank test was found to be more robust under symmetric leptokurtic with conservative values as compared to the skewed leptokurtic distribution. The finding also indicated that different number of replications had no effect on Type I error.