Chapter 2 · Displaying and Summarizing Categorical Data
Section 2.4Introduction to Contingency Tables
Section 2.4: Introduction to Contingency Tables
Contingency tables organize data from two categorical variables, making it easier to compare groups and identify potential relationships. In this section, you'll learn how to construct and interpret contingency tables, calculate marginal distributions, and use them to summarize and analyze categorical data.
Summary
Contingency tables are a powerful tool for organizing and comparing two categorical variables at once, revealing patterns that would be invisible in separate frequency tables.
The Real World Statistics Learning Progression
Each section follows the same learning progression: understand the concept, practice the skill, think like a statistician, then apply your learning to authentic data.
Learn This Section
Whether learning independently or teaching a class, the learning path below is designed to help students master the concepts in this section. Page references correspond to the Real World Statistics instructional system.
Need Extra Support? If you'd like additional guidance while working through the practice questions, explore the Worked Solutions Manual for step-by-step solutions and explanations.
From Learners to Statisticians
Examples of authentic statistical work supported by this section include:
- Organizing two categorical variables into contingency tables (e.g., survey responses on breakfast habits and energy levels, employee hiring records by department and hiring source, or student participation by grade level and activity type).
- Analyzing relationships between categorical variables using marginal distributions and percentages (e.g., customer satisfaction by membership status, transportation method by neighborhood, or volunteer participation by age group).
- Writing evidence-based reports that interpret patterns in contingency tables using proportions to support conclusions (e.g., course enrollment by grade level, patient outcomes by treatment type, or voting preference by age group).
You may use these ideas to design your own investigations or explore the Real World Statistics System.
Enrichment: Role-Based Statistical Analysis Tasks
Enrichment tasks place students in the role of a statistician working on real research problems, where they evaluate data, justify decisions, and communicate findings clearly. Each section includes multiple enrichment tasks, including one with a model response that demonstrates statistical reasoning in context, showing how evidence is evaluated, decisions are justified, and conclusions are communicated. This serves as a bridge to working with authentic datasets and independent statistical investigation within each chapter.
Available in the Interactive eBook at the end of the section (page 46) and in the Appendix of the Print Book (page 401).
Teaching with Real World Statistics?
These structured learning paths — including Enrichment tasks and Chapter Datasets — can be adapted or copied directly into Canvas, Google Classroom, Schoology, and other learning management systems to simplify lesson planning and student assignments.
Part of the Real World Statistics instructional system — bringing together print, interactive learning, videos, datasets, enrichment, worked solutions, and teacher resources.