Outliers

Abstract

An outlier is a value of a variable that is inconsistent with the other values. The discussion is restricted to univariate outliers, that is, outliers that are inconsistent with other values of the same variable. A naive strategy is to apply the Z-score method to detect outliers, to remove the outliers, and to analyze the remaining data as usual. The Z-score method is incorrect and should be replaced by other methods, such as, the MAD-score method . Researchers have to check whether outliers are caused by mistake. If mistakes are detected and the correct values are known, the outliers are corrected. If mistakes are detected but the correct values are not known, the outliers are treated as missing data and the data are analyzed with model-based statistical methods that assume MCAR or MAR . If mistakes are not found, two strategies are suitable. First, to study the robustness of the substantive conclusions against outliers. The data are analyzed with and without the outliers using the same statistical methods. The results of the two analyses are compared, and the results of both analyses or the results of the analysis that gives weakest support to the substantive hypothesis are reported. Second, robust statistical methods , such as, bootstrap methods are applied to analyze the data. Finally, whatever method researchers used, they should always report the frequency and handling of the outliers.