A COMPARATIVE STUDY OF THE ACCURACY OF THE CHI-SQUARED APPROXIMATION FOR THE POWER-DIVERGENCE STATISTIC AND PEARSON’S CHI-SQUARED STATISTIC IN SPARSE CONTINGENCY TABLES

Abstract

The Power divergence family of statistics was introduced by Cressie and Read
in 1984. The likelihood ratio statistic and the Pearson’s chi-squared statistic are
examples of the many members of the power divergency family which are linked
through a family parameter . We present here the results of a comparative simulation
study on the accuracy of the chi-squared approximation for two members
of the family ( = 1 and = 2
3 ) when they are used for goodness-of-fit testing in
sparse contingency tables.