Seven proofs of the Pearson Chi-squared independence test and its graphical interpretation

TL;DR

This paper revisits the Pearson Chi-squared independence test, providing modern theoretical derivations and introducing a novel graphical interpretation to enhance understanding and visual assessment of independence.

Contribution

It offers a new derivation method and a graphical visualization approach for the Pearson Chi-squared test, improving interpretability and insight.

Findings

New derivation of the test proof

Graphical method for visual interpretation

Enhanced understanding of independence testing

Abstract

This paper revisits the Pearson Chi-squared independence test. After presenting the underlying theory with modern notations and showing new way of deriving the proof, we describe an innovative and intuitive graphical presentation of this test. This enables not only interpreting visually the test but also measuring how close or far we are from accepting or rejecting the null hypothesis of non independence