#### Introduction

The **chi-squared test of independence** is one of the most basic and common hypothesis tests in the statistical analysis of categorical data. Given 2 categorical random variables, $latex X$ and $latex Y$, the chi-squared test of independence determines whether or not there exists a statistical dependence between them. Formally, it is a hypothesis test with the following null and alternative hypotheses:

$latex H_0: X perp Y text{vs.} H_a: X not perp Y$

If you’re not familiar with **probabilistic independence** and how it manifests in **categorical random variables**, watch my video on calculating expected counts in contingency tables using **joint and marginal probabilities**. For your convenience, here is another video that gives a gentler and more practical understanding of calculating expected counts using **marginal proportions** and **marginal totals**.

Today, I will continue from those 2 videos and illustrate how the chi-squared test of independence can be implemented in both R

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