Outlier Detection Using the Range Distribution

Abstract

Detecting outliers is a major issue that has been studied in various applications and research domains. Statistical analysis procedures are affected by the presence of outliers in the data. They can decrease normality of the distribution, increase the error variance, and reduce the power of many statistical tests. To date, many researchers continue to design techniques that would provide solutions to detect outliers efficiently. In this chapter, we explore the use of the range statistic to identify outliers in univariate data. We examine the performance of the range statistics standardized by the interquartile range (IQR) in detecting outliers and compare the results to the results obtained by the standardized range with respect to standard deviation, σ. The numerical experiments with real data sets have demonstrated that the performance of the range statistic in detecting outliers can become more robust when standardized with respect to the IQR instead of the standard deviation, which itself is influenced by outliers.