Abstract

The assumption of normality has a crucial importance in many statistical procedures. Therefore, a number of normality tests are proposed. Also, many investigations are conducted on the performance of these normality tests under a set of alternative distribution. However, there are few studies to compare the performance of the commonly used normality tests in the presence of outliers, but they are not comprehensive. It is important, since the outliers may increase the variability in the data set, they cause the decrease in the statistical power. In this study we show the performance of the commonly used normality tests in the presence of outlier in the data set. An outlier generation method is implied to generate uniform tails and the effects of various magnitude of outliers on the normality tests are obtained in terms of penalized power and Type I error probability. As a result, the most powerful tests are suggested to the researchers for different magnitude of outliers, sample sizes and the contamination ratios. Two real data applications are given to illustrate the importance of choosing the appropriate test.

摘要

正态性假设在许多统计过程中至关重要。因此，提出了许多正态性检验。此外，许多研究都是在一组替代分布下对这些正态性检验的性能进行的。然而，很少有研究比较常用的正态性检验在存在异常值的情况下的性能，但它们并不全面。这很重要，因为异常值可能会增加数据集中的变异性，从而导致统计功效下降。在本研究中，我们展示了数据集中存在异常值时常用的正态性检验的性能。隐含了异常值生成方法来生成均匀的尾部，并且根据惩罚功效和 I 类错误概率获得了不同大小的异常值对正态性检验的影响。因此，建议研究人员针对不同程度的异常值、样本大小和污染率进行最有效的测试。给出了两个真实数据应用来说明选择适当测试的重要性。