Most Stringent Test of Independence in W× K Contingency Tables for Nominal Data Using Monte Carlo Simulations

Abstract

Purpose:  This study aims to analyze the performance of tests of independence for nominal data. Tests of independence is one of the most used statistical techniques in econometrics. A principal interest in many studies regarding contingency tables is to test if the variables are independent in contingency table (CT’s). Many standard tests are available for nominal data. However, there is no clarity about choice of tests for various kinds of Data Generating Process (DGP) of nominal data.  Design/Methodology/Approach: This study used stringent criteria (SC) for evaluation of optimal test of independence among a large numbers of tests of independence in w × k contingency tables using Monte Carlo simulations. Findings: The most stringent test of independence is Logarithmic Minimum Square (LMS) in w × k contingency table for nominal data.  Implications/Originality/Value: This Paper gives very clear guidance to practitioner about use of tests of independence for nominal data. Results recommends based on solid estimation of Monte Carlo Simulation and algorithm for a variety of Data Generating Process (DGP) in w × k contingency tables. We came to conclusion and recommended clearly that Logarithmic Minimum Square (LMS) is the optimal and most stringent test, and no other test can beat it for nominal data in w × k contingency tables.