Lesson 3: Associations in Categorical Data

Property

Patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table.
A two-way frequency table is a convenient way of summarizing such data.
The table is 'two-way' because each bivariate datum is composed of an ordered pair of realizations from two categorical random variables.
The table is a 'frequency' table because the cell entries count the number of subjects that fall into each combination of categories.

Examples

• A survey asks 100 students if they prefer pizza or burgers, and if they prefer soda or water. The results are organized in a $2 \times 2$ table showing how many students fall into each of the four combinations (e.g., Pizza and Soda).
• A clinic records the pet type (Dog, Cat, Bird) and reason for visit (Check-up, Sick). A $3 \times 2$ two-way frequency table is used to count how many dogs came for a check-up, how many cats were sick, etc.
• 8th graders are surveyed on their favorite school subject (Math, English, Science) and their after-school activity (Sports, Music, None). The data is tallied in a $3 \times 3$ table to see if there are associations between subject preference and activities.

Explanation

When you have data in categories (like 'male'/'female' or 'cat'/'dog'), you can't make a scatter plot. A two-way table sorts this data into a grid, showing the counts for each combination, which helps you spot patterns.

Property

To construct a segmented bar graph from a conditional relative frequency table:

1. Choose one variable for the horizontal axis. Each category of this variable will become a bar.
2. Draw a bar for each category, with the total height of each bar representing $100\%$.
3. Within each bar, create segments corresponding to the categories of the second variable. The height of each segment is equal to its conditional relative frequency.
4. Include a legend to identify which segment corresponds to which category.

Examples