2.8: Data with categorical variables

Supplementary Resource Materials

(ways to test categorical data)

• Chi‑squared Distribution

  • An Introduction to the Chi‑squared Distribution $({{\chi }^{2}})$ (jbstatistics)
  • Using the Chi‑square Table to Find Areas and Percentiles (jbstatistics)

  Chi‑squared Tests

  • Chi‑squared Tests for One‑Way Tables (Goodness‑of‑Fit Tests) (jbstatistics)
  • Chi‑squared Goodness‑of‑Fit Tests for the Binomial Distribution (jbstatistics)
  • Chi‑squared Tests for Two‑Way Tables (Tests of Independence) (jbstatistics)
  • Chi‑squared Tests for Count Data: Finding the p‑value (jbstatistics)

Reference Materials

(Questions to consider when you are reading an article that contains the results of a Chi‑square test)

• Are the variables of interest categorical rather than numerical?
• Are the data given in the article in the form of a frequency table?
• If a two‑way frequency table is involved, is the question of interest one of homogeneity or one of independence?
• What null hypothesis is being tested? Are the results of the analysis reported in the correct context (homogeneity, etc.)?
• Is the sample size large enough to make use of a chi‑square test reasonable? (Are all the expected counts at least 5?)
• What is the value of the test statistic? Is the associated $p$‑value given? Should the null hypothesis be rejected?
• Are the conclusions drawn by the authors consistent with the result of the test?
• How different are the observed and expected counts? Does the result have practical significance as well as statistical significance?

(Introduction to Statistics & Data Analysis, by Peck, Olsen & Devore, Cengage learning, 2014, p. 651)