# Lesson 45: Contingency Tables

### Introduction

In this lesson, we'll investigate two more applications of the chi-square test. We'll first look at a method for testing whether two or more multinomial distributions are equal. This method is often referred to as the **test for homogeneity**.** ** (Homogenized milk... get it?)

We'll then look at a method for testing whether two or more categorical variables are independent. This test is often referred to as the **test for independence**. It allows us to test for independence of, say, an individual's political affiliation and his/her preference for a particular presidential candidate.

### Objectives

- To learn how to conduct a test for homogeneity.
- To learn how to conduct a test for independence.
- To understand the proofs in the lesson.
- To be able to apply the methods learned in the lesson to new situations.