Penalized power properties of the normality tests in the presence of outliers

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.

KEYWORDS:

• Contamination
• Normality
• Outlier
• Penalized power
• Uniform tails