Definition: A two-way table shows how often each combination of two categorical variables occurs, with rows for one variable and columns for the other.
What is a two-way table?
It organizes data about two categories at once. Each cell counts the people or items with a given pair of traits.
How do you read one?
Mathbot surveys 80 students about pets and music.
| Likes pop | Likes rock | Total | |
|---|---|---|---|
| Has a pet | 28 | 12 | 40 |
| No pet | 16 | 24 | 40 |
| Total | 44 | 36 | 80 |
What are relative frequencies?
Divide by a row or column total. Among pet owners, 28 / 40 = 70 percent like pop. Among non-owners, 16 / 40 = 40 percent do.
What does that suggest?
A difference in the percents suggests an association between owning a pet and liking pop. If the percents matched, there would be no association.
What is a common mistake?
Dividing by the wrong total. To compare groups fairly, divide each cell by its own group total, not the grand total of 80.
Example: In the table, 24 of 36 rock fans, which is two thirds, have no pet.