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Statistics · AP · Inference for Categorical Data — Chi-Square

What this topic is

In Statistics · AP, this CED topic focuses on: Skills Focus: Selecting an Appropriate Inference Procedure for Categorical Data. In plain terms, students should be able to explain the main idea in their own words and complete a straightforward practice item with justification.

This topic is assessed on the AP Exam.

Why it matters

• Inference write-ups are scored on conditions, mechanics, and contextual conclusions together.
• Chi-square inference handles categorical data beyond simple proportions.
• Students must choose goodness-of-fit vs homogeneity/independence appropriately.
• Expected counts and conditions are part of the plan step.
• Linking components to which categories drive significance is strong FRQ practice.

How you can support

• Walk the four steps: state, plan (conditions), do, conclude in context.
• Ask: “One categorical variable or a relationship between two?”
• Have them write hypotheses about distributions or association in words.
• Praise computing/checking expected counts before trusting the p-value.
• Ask which cells contribute most to χ² and what that means in context.
• Keep the conclusion tied to the original research question.

What not to do

• Do not jump to a calculator p-value without stating hypotheses and conditions.
• Do not use a proportions z-test when the design needs χ².
• Do not skip the expected-count condition.
• Do not confuse homogeneity with independence wording.
• Do not claim causation from a significant χ² alone.