1/n - Proportional Correction to Tests of Independence

Abstract

It is known that both the Pearson and G-test of independence have the same asymptotic distribution, namely χ 2 with ( K − 1 ) ( M − 1 ) degrees of freedom, where K and M are the number of levels, respectively, of two attributes. However, when extending the accuracy ot this approximation by 1 n -proportional terms, the resulting corrections differ quite dramatically. The purpose of this article is to derive each of these corrections and demonstrate their use in practical application.