3: Two-Way Tables: Independence and Association

Overview Section

This lesson is about the analysis of two-way tables. We begin with the structure of the simplest two-way table, a \(2\times 2\) table, and its corresponding joint distribution. We then consider how to extend the goodness-of-fit tests that we saw in Lesson 2. More specifically, we will learn the Chi-squared test of independence for two discrete binary random variables, and basic measures of associations such as odds-ratios and relative risk that will describe the strength of association between two binary random variables. We will then extend these concepts to an \(I \times J\) table, to analyze two discrete random variables with \(I\) and \(J\) categories.

Upon completion of this lesson, you should be able to:

  Objective 3.1

Interpret measures of association, such as relative risk and odds ratio, between two categorical variables.

  Objective 3.2

Carry out a statistical test for association in a two-way table and interpret the results.

  Objective 3.3

Explain the difference between a retrospective and a prospective study and why one would be carried out instead of the other.