Hypothesis Testing for the Association Between Categorical Variables: Empirical Application of Chi square Test

Abstract

Chi-square test and the logic of hypothesis testing were developed by Karl Pearson. In this article we demonstrate theoretically and empirically the hypothesis testing for the association between categorical variables using Chi‑square Test. In research, there are studies which often collect data on categorical variables that can be summarized as a series of counts. These counts are commonly arranged in a tabular format known as a contingency table. We show in this paper how the chi-square test statistic can be used to evaluate whether there is an association between the rows and columns in a contingency table. We describes in detail what is a chi-square test, on which type of data it is used and the assumptions associated with its application. We consider both theoretical and empirical cases. On empirical case we use the data from the study which was conducted between September 2017 and March, 2018 in two municipalities of Dodoma and Morogoro, Tanzania. We conclude in this article that the Chi-square test,  only tells us the probability of independence of a distribution of data or in simple terms it does only test that whether two categorical variables are associated with each other or not. It does not tell us that how closely they are associated. Therefore, once we got to know that there is a relation between these two variables, we need to explore other methods to calculate the amount of association between them.

Key words: Contingency table, categorical data analysis, Chi-square test, hypothesis testing

DOI: 10.7176/MTM/9-2-02