# Introduction

Link to Video Transcript in a Word file

The previous module focused on using t-tests to comparie continuously distributed outcomes, such as body mass index, but how can you compare categorical outcomes?

This module will introduce the chi-square test of independence to test associations between categorical exposures and categorical outcomes. After completing this section you should be able to perform the chi-square test of independence by hand or using the R statistical package.

The chi-square test of independence can be used to test for differences with several types of variables that were introduced in module 1:

1. Categorical variables: Variables that fall into two or more categories that do not have any inherent ranking or ordering, such as race and ethnicity (e.g., white, black, Hispanic, Asian, etc.)
2. Dichotomous variables: Variables that have just two possible values (e.g., male or female; occupational exposure to asbestos: Yes or No; death: Yes or No; developed coronary heart disease: Yes or No)
3. Ordinal variables: Categorical variables that have more than two ranked or ordered values (e.g., physical activity: <30 minutes/week, 30-180 minutes/week, >180 minutes/week; amount of current smoking: none, <10/day, 10-20/day, 21-30/day, >30/day); or number of past heart attacks: 0, 1, 2, 3, etc.)

Essential Questions

1. How do we test the statistical significance of associations between exposures and categorical outcomes?
2. How do we determine whether an exposure increases or decreases the risk of a particular health outcome?
3. When is it most appropriate to assess data categorically?

# Learning Objectives

After completing this module, you will be able to:

• Identify situations in which a chi-square test is appropriate
• Perform chi-square tests by hand and using the R computing package
• Interpret results of chi-square tests correctly
• Identify the appropriate hypothesis testing procedure for evaluating categorical data
• Communicate the results of chi-square tests for a non-technical/lay audience