Tests of independence : a state of art

Abstract

The purpose of this project is to investigate the methods used to test the independence between random variables (nominal, ordinal and numerical). For every test, the hypothesis used, the p-value, the assumptions and conditions are stated. The nominal and ordinal variables are illustrated in a contingency table. The independency between categorical variables is considered in the cases of fixed and non-fixed marginals and in the case of multiple response data. The correlation coefficient is used for numerical data in order to test the level of association between two samples. All tests are illustrated by examples. The tests are then applied on a survey done at the University of Balamand (Sabat et al, 2020). The tests used to test the dependency between nominal variables are Pearson’s Chi-Square test, Likelihood Ratio test, Fisher Exact test, McNemar Test and their continuity corrections. As for the ordinal data, Cochran-Armitage and its continuity correction is considered. Moreover, multiple response data is approached by First Order Rao-Scott Chi-Square test. Lastly, Pearson’s correlation and Spearman’s correlation with ranks are studied for numerical data.