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

CED focus

Introducing Statistics: Are My Results Unexpected?

This topic is assessed on the AP Exam.

Multiple-choice tips

  • Match procedure to parameter and design before calculating.
  • Match χ² GOF vs homogeneity vs independence from the table setup.
  • Eliminate expected-count violations in MC.
  • Check whether a proportions z-test is inappropriate.
  • Identify which cells drive a large χ² in MC.

Free-response tips

  • Use State–Plan–Do–Conclude with conditions and context throughout.
  • State hypotheses about distributions or association in words.
  • Show expected counts or use calculator χ² output with labels.
  • Conclude about the population in context.
  • Link conclusion back to the research question.

Common traps

  • ‘Accept H₀’ wording or skipping conditions
  • Using a z-test when χ² is required
  • Skipping expected-count condition
  • Confusing homogeneity and independence wording

Quick checklist

  • [ ] Can choose the correct χ² procedure
  • [ ] Can check expected counts
  • [ ] Can conclude about association in context

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