Outliers and patterns of outliers in contingency tables with Algebraic Statistics

In this paper we provide a definition of pattern of outliers in contingency tables within a model-based framework. In particular, we make use of log-linear models and exact goodness-of-fit tests to specify the notions of outlier and pattern of outliers. The language and some techniques from Algebraic Statistics are essential tools to make the definition clear and easily applicable. Some numerical examples show how to use our definitions.