Moving From Statistical to Hypothesis-driven Outliers

In this article, a new approach to outlier analysis in categorical data is proposed. Standard outlier analysis defines outliers in terms of such data characteristics as mutual distances or correlations among data points. This applies to the analysis of continuous and categorical data, and to univariate and multivariate outlier analysis as well as to data mining. In this article, a new specification of outlying data points is proposed, specifically, it is proposed to define outliers as data points that are extreme with respect to substantive hypotheses. It is also proposed to perform two forms of outlier analysis of the same data. The first is standard outlier analysis that inspects data characteristics. The second is Configural Frequency Analysis (CFA). This method defines outliers as extreme cells that contradict a substantive null hypothesis, the CFA base model. A data example is given, in which, first, outliers are identified using cluster analysis (unsupervised classification). Subsequently, the data are analyzed with CFA (supervised classification). Results show that outliers that were identified under unsupervised classification have the potential of distorting results of supervised classification. The mutual relations of unsupervised and supervised classification, both performed on the same data, are discussed. Configural Frequency Analysis and outlier analysis.