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Association Detector Visualization

Run Association Detector in Fullscreen

You can include this MicroSim on your website using the following iframe:

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<iframe src="https://dmccreary.github.io/statistics-course/sims/association-detector/main.html" height="522px" width="100%" scrolling="no"></iframe>

Description

This MicroSim helps students understand association between categorical variables by comparing conditional distributions visually. When we have a two-way table (also called a contingency table), one key question is: "Does the distribution of one variable depend on the value of the other variable?"

The visualization displays:

  • Two horizontal 100% stacked bar charts: Each bar represents the conditional distribution for one level of the row variable (e.g., Freshmen/Sophomores vs. Juniors/Seniors)
  • Color-coded segments: Each segment shows the percentage of responses in that category (e.g., Fall, Winter, Spring, Summer)
  • Difference indicators: Visual arrows highlight the largest difference between the two distributions

How to Use

  1. Observe the default data: The initial display shows Season preference by Grade Level with a moderate association
  2. Compare the bars: If the bars look nearly identical, there is little evidence of association. If they look quite different, the variables may be associated
  3. Use presets: Click "Strong," "None," or "Moderate" to see examples of different association strengths
  4. Edit the data: Click on any cell in the two-way table to enter your own values
  5. Toggle options: Use the "Show %" button to display/hide percentage labels, and "Highlight" to show/hide difference indicators

Key Concepts

  • Conditional Distribution: The distribution of one variable for a specific value of another variable
  • Association: Two variables are associated if the conditional distribution of one variable changes depending on the value of the other
  • No Association: If conditional distributions are nearly identical across all levels, the variables are independent

Lesson Plan

Learning Objectives

By the end of this lesson, students will be able to:

  1. Compare conditional distributions displayed as 100% stacked bar charts
  2. Differentiate between data showing strong, moderate, and no association
  3. Interpret percentage differences as evidence for or against association
  4. Explain in their own words what it means for two categorical variables to be associated

Target Audience

  • AP Statistics students
  • Introductory college statistics students
  • Grade level: 10-12 and undergraduate

Prerequisites

  • Understanding of categorical variables and two-way tables
  • Ability to calculate and interpret percentages
  • Familiarity with bar charts

Duration

20-30 minutes

Activities

Warm-Up (5 minutes)

  1. Display the MicroSim with "No association" preset
  2. Ask: "If you didn't know whether a student was a Freshman or Senior, would knowing their grade level help you predict their favorite season?"
  3. Guide students to notice that the bars look identical when there's no association

Exploration (10-15 minutes)

  1. Switch to "Strong association" preset
  2. Discussion questions:
  3. "How are these bars different from the 'No association' example?"
  4. "Which season shows the biggest difference between grade levels?"

  5. "If I told you a student's favorite season was Summer, could you guess their grade level?"

  6. Have students experiment with "Moderate" association and describe the differences

  7. Challenge: "Create your own data where Freshmen prefer Spring and Seniors prefer Fall"

Analysis (10 minutes)

  1. Students enter their own data scenarios and analyze results
  2. Journal prompt: "Describe in your own words what makes two categorical variables 'associated' versus 'independent'"
  3. Group discussion: Share real-world examples where association between categorical variables matters

Assessment Suggestions

Formative Assessment

  • Observe student explanations during pair discussions
  • Check journal responses for understanding of key concepts

Summative Assessment

Present students with a new two-way table (without the visualization) and ask them to:

  1. Sketch what the 100% stacked bars would look like
  2. Predict whether there is strong, moderate, or no association
  3. Explain their reasoning using percentage comparisons

References

  1. Wikipedia: Contingency Table - Background on two-way tables and tests for independence

  2. Khan Academy: Two-way Tables - Video lessons on analyzing categorical data relationships

  3. OpenStax Statistics: Contingency Tables - College-level treatment of association and chi-square tests

  4. AP Statistics Course Framework - College Board standards for exploring categorical data (Unit 1)