In this tutorial, you're going to learn about two-way tables, also called contingency tables. Specifically you will focus on:
Two-way tables area way of showing the relationship between two categorical variables.
Suppose you had 335 students in different parts of the country and they were asked the question, if you had to pick one thing about school that's most important to you: getting good grades, being popular, or being good at sports? The distribution looked like this.
This means that 57 rural students said the grades were the most important thing. Six urban students said that being popular was the most important thing to them. We can see the relationship between school location and goal.
One of the things that we can look at with a two-way table, one of its most important features, is called the marginal distributions. They are called that because they're written in the margins. They are the row totals and column totals for the particular categories that you have.
This shows that there were 149 rural students in this study, whereas there were only 35 urban students in this study. It shows you that 168 students said that grades were the most popular thing, regardless of where they live. And 98 students said that being popular was the most important thing at school.
We also can add up all these cell values and obtain the grand total. This means there were 335 students in the study, which we knew at the beginning, based on the way the problem was posed. This allows us to answer some pretty interesting probability problems.
Two-way tables help you to understand the relationships between two different events, or two different categories. Use two-way tables to answer some pretty interesting probability questions. Oftentimes, you use those marginal distributions, the row totals or column totals, or even the grand total.
Good luck.
Source: This work adapted from Sophia Author Jonathan Osters.
A way of presenting data such that we can see the relationships between two categorical variables.