Outliers and patterns of outliers in contingency tables with Algebraic Statistics

TL;DR

This paper introduces a model-based framework for identifying outliers and their patterns in contingency tables using algebraic statistics, log-linear models, and exact goodness-of-fit tests, with practical examples.

Contribution

It provides a novel, algebraic-statistics-based definition of outliers and their patterns in contingency tables, enhancing clarity and applicability.

Findings

Definitions of outliers and patterns in contingency tables

Application of algebraic statistics techniques

Numerical examples demonstrating the approach

Abstract

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.