Applicability of G-test in analyzing categorical variables

The analysis of a single categorical variable generally involves the testing of goodness-of-fit where the testing is about whether the observed category frequencies fit the theoretical expected category frequencies. On the other hand, the analysis of two categorical variables involves the testing of independence of two variables. Chi-square statistic, considered as one of the foundations of modern statistics, is a method widely used in both testing goodness-of-fit and testing of independence. Although another test called G-test, which is based on likelihood ratios, was recommended around the early 1980’s, the Chi-square statistic has remained prominent and popular due its computational ease during the days prior to electronic calculators and computers. Therefore, this study aims to demonstrate the applicability of G-test as an alternative to Chi-square test in the testing for goodness-of-fit and testing for independence for categorical variables. This study uses two secondary datasets to obtain the results of G-test for the testing of goodness-of-fit and another two secondary datasets to obtain the results of G-test for the testing of independence. The obtained results of the G-test are compared with the respective results of Chi-square test, indicating only slight differences of p-values between the two tests for the datasets.