Chapter 2 · Displaying and Summarizing Categorical Data

Section 2.6Interpreting Contingency Tables

Contingency tables help you investigate relationships between categorical variables by comparing groups within a dataset. In this section, you'll learn how to interpret contingency tables using marginal and conditional distributions to evaluate possible associations and support statistical conclusions.

Summary

Conditional distributionsFocus on a specific category within another variable, showing proportions within a subgroup.

Comparing distributionsComparing conditional distributions helps us identify associations between variables.

AssociationIf percentages vary significantly between groups, an association between the two variables exists.

Conditional distributions are the key tool for moving beyond description to interpretation — they let you ask whether two categorical variables are related.

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.

Read the sectionRead pages 52–55 to reinforce the concepts introduced in the lesson.

Practice what you've learnedComplete the 3 multi-part practice questions on pages 55–56. Check your work using the Answer Key, then review and correct any questions you missed before moving on.

Think like a statisticianExplore Enrichment: Role-Based Statistical Analysis Tasks and the Chapter Dataset to apply statistical thinking in real-world contexts.

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:

Interpreting contingency tables using marginal and conditional distributions to compare groups and identify possible associations (e.g., library membership and reading frequency from a community survey, or participation in tutoring and course completion from a district report).
Writing evidence-based reports that explain whether two categorical variables appear to be associated using percentages from contingency tables (e.g., disaster preparedness by region from an emergency management survey, or employee training participation by certification status from a workplace audit).
Comparing conditional percentages across groups to support recommendations or policy decisions (e.g., recycling participation by housing type from a municipal study, or voter turnout by age group from an election analysis).

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 56) 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.