Seven Proofs of the Pearson Chi-Squared Independence Test and its Graphical Interpretation

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.

Keywords: causality, Pearson correlation coecient, graphical heat map

JEL Classification: 62E10, 62E15