Robustness of Wilcoxon signed-rank test against the assumption of symmetry

摘要

Wilcoxon signed-rank test is one of nonparametric tests which is used to test whether median equals some value in one sample case. The test is based on signed-rank of observations that are drawn from a symmetric continuous distribution population with unknown median. When the assumption about symmetric distribution fails, it can affect the power of test. Our interest in this thesis is to study robustness of the Wilcoxon signed-rank test against the assumption of symmetry. The aim of this study is to investigate changes in the power of Wilcoxon signed-rank test when data sets come from symmetric and more asymmetric distributions through simulations. ududSimulations using Mixtures of Normal distributions find that when the distribution changes from symmetry to asymmetry, the power of Wilcoxon signed-rank test increases. That is, the Wilcoxon signed-rank test is not good and applicable under the asymmetry distribution. Therefore, the second objective is to study the inverse transformation method which is a technique in statistics to make observations from an arbitrary distribution to be a symmetric distribution. Moreover, the effect of the inverse transformation method to the Wilcoxon signed-rank test is also studied to answer whether or not the Wilcoxon signed-rank test is still good and applicable after we apply the inverse transformation method to the test. ud