top of page

Relationships Between Two Categorical Variables (Lesson 3.1)

Chapter 3 - Day 1

Learning Targets
  • Distinguish between explanatory and response variables.
  • Make a segmented bar chart to display the relationship between two categorical variables.

  • Determine if there is an association between two categorical variables and describe the association if it exists.

Activity: How are Your Favorite Classes Related? 

Experience First

Students will need access to a computer or a phone with Internet access in order to make a segmented bar graph with the 2 Categorical Variables” applet.


When collecting class data, be sure that each student only records one tally in the two-way table. You might want to prep them by asking them to have a quick chat in their small groups about their favorite core class (they must choose between Math and English) and their favorite elective class (several choices here). 

Formalize Later

The idea of explanatory and response variables is first introduced in this lesson but will also be needed for the next lesson when we look at relationships between two quantitative variables. 


Be sure to make a close connection between the percents that students calculate in question 4 with the stacked bars in the segmented bar graph. 


At the end of the activity, you might ask students “What would the segmented bar graph look like if there was NO association?” The answer is that every segment for Math would be exactly the same size as the segment for English (equal percents). In this case, knowing that someone preferred math would not help us at all to predict what their favorite elective class might be. 


Much later in the course, students will use a chi-square test for association to determine if sample data provides convincing evidence of an association for two categorical variables for some population.

bottom of page