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

Basil Msuha ,Tiberio Mdendemi

doi:10.7176/mtm/9-2-02

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

Highlights

The logic of hypothesis testing was first invented by Karl Pearson (1857–1936), a renaissance scientist and famous statistician in Victorian London in 1900
4.0 Empirical Results and Discussion The chi-square tests were conducted to ascertain whether the two categorical variables under the study are independent or not
The chi-square test of association between keeping cattle and environmental pollution rejected the null hypothesis of independence at 5% level of significance on pollution variables except one, implying that keeping cattle could result into noise, heaps of waste, odour, and plant destruction

Summary

Introduction

The logic of hypothesis testing was first invented by Karl Pearson (1857–1936), a renaissance scientist and famous statistician in Victorian London in 1900. Pearson’s Chi-square distribution and the Chi-square test known as test for goodness of fit and test of independence are his most important contribution to the modern theory of statistics. The importance of this distribution is that one should not depend much on only the normal distribution only for inferencing about the data and hypothesis. Karl Pearson invented the Chi square distribution mainly to address the needs of economists, biologists and psychologists (Magnello, 2006). His paper in 1900 published in Philosophical www.iiste.org magazine elaborates the invention of Chi-square distribution and goodness of fit test (Pearson, 1992; Plackett, 1983)

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