Distribution of Variables by Method of Outlier Detection

The presence of outliers can very problematic in data analysis, leading statisticians to develop a wide variety of methods for identifying them in both the univariate and multivariate contexts. In case of the latter, perhaps the most popular approach has been Mahalanobis distance, where large values suggest an observation that is unusual as compared to the center of the data. However, researchers have identified problems with the application of this metric such that its utility may be limited in some situations. As a consequence, other methods for detecting outlying observations have been developed and studied. However, a number of these approaches, while apparently robust and useful have not made their way into general practice in the social sciences. Thus, the goal of this study was to describe some of these methods and demonstrate them using a well known dataset from a popular multivariate textbook widely used in the social sciences. Results demonstrated that the methods do indeed result in datasets with very different distributional characteristics. These results are discussed in light of how they might be used by researchers and practitioners.