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8.5 Setting Up a Chi-Square Test for Homogeneity or Independence

Part of Inference for Categorical Data: Chi-Square in AP® Statistics. Read the opening section, then create a free account for the full interactive lesson, practice, and progress tracking.

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Writing Hypotheses for Two-Way Chi-Square Tests

Test for Homogeneity:

  • H0{H_0}: The distribution of [variable] is the same for all [populations/groups]
  • Ha{H_a}: The distribution of [variable] is NOT the same for all [populations/groups]

Test for Independence:

  • H0{H_0}: There is no association between [variable 1] and [variable 2] in the population
  • Ha{H_a}: There is an association between [variable 1] and [variable 2] in the population

Conditions for both tests:

  1. Random: Data from random samples or randomized experiment
  2. Independence:
    • 10% condition (if sampling without replacement)
    • For homogeneity: samples from different populations are independent of each other
  3. Large Counts: All expected counts Eij≥5{E_{ij} \geq 5}
Degrees of freedom:
df=(r−1)(c−1)df = (r-1)(c-1)
where r{r} = number of rows, c{c} = number of columns (not counting totals)

In this unit

6 lessons

  1. 8.1Introducing Statistics: Are My Results Unexpected?Preview lesson
  2. 8.2Setting Up a Chi-Square Goodness of Fit TestPreview lesson
  3. 8.3Carrying Out a Chi-Square Test for Goodness of FitPreview lesson
  4. 8.4Expected Counts in Two-Way TablesPreview lesson
  5. 8.5Setting Up a Chi-Square Test for Homogeneity or IndependenceThis lesson
  6. 8.6Carrying Out a Chi-Square Test for Homogeneity or IndependencePreview lesson

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