TITLE:
1/n - Proportional Correction to Tests of Independence
AUTHORS:
Jan Vrbik
KEYWORDS:
Test of Independence, Asymptotic Distribution, Chi-Square Test, Contingency Tables, G-Test, Kronecker Product
JOURNAL NAME:
Applied Mathematics,
Vol.16 No.3,
March
27,
2025
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.