# Exact tests to compare contingency tables under quasi-independence and quasi-symmetry

## TL;DR

This paper develops exact statistical tests using Markov bases for comparing multiple square contingency tables under quasi-independence and quasi-symmetry models, with applications demonstrated through real data examples.

## Contribution

It introduces a novel framework for exact testing of multiple tables under specific models using Markov bases, expanding the tools for contingency table analysis.

## Key findings

- Markov bases are characterized for the models.
- An exact test procedure is proposed.
- Applications demonstrate practical utility.

## Abstract

In this work we define log-linear models to compare several square contingency tables under the quasi-independence or the quasi-symmetry model, and the relevant Markov bases are theoretically characterized. Through Markov bases, an exact test to evaluate if two or more tables fit a common model is introduced. Two real-data examples illustrate the use of these models in different fields of applications.