Work through the list without notes. If you cannot do a statement, follow its link, then come back. Guide = study guide; Practice = practice questions.
Understanding
- I can explain that the chi-square statistic measures the distance between observed and expected counts, relative to the expected counts. (Guide: “What the chi-square statistic measures”; Practice Q4)
- I can explain why larger values of the chi-square statistic are stronger evidence against H₀. (Guide: “What the chi-square statistic measures”; Practice Q4)
- I can describe chi-square distributions: positive values only, skewed right, less skewed as the degrees of freedom increase. (Guide: “Chi-square distributions”, Figure 1; Practice Q1)
Skills
- I can choose between a test for homogeneity and a test for independence from the way the data were collected. (Guide: “Homogeneity or independence?”; Practice Q2, Q7)
- I can write H₀ and Hₐ for a test for homogeneity, naming the variable and the populations or treatments. (Guide: Worked example 1; Practice Q3, Q6)
- I can write H₀ and Hₐ for a test for independence, naming both variables and the population. (Guide: Worked example 2; Practice Q5)
- I can check the randomization and 10% conditions, and know when the 10% condition is not needed. (Guide: “The three conditions”; Practice Q5, Q6)
- I can check the expected counts condition using expected counts, not observed counts. (Guide: both worked examples; Practice Q5, Q6)
Reasoning
- I can explain what to do when the expected counts condition fails, and how combining categories changes the question. (Guide: Worked example 2; Practice Q6)
- I can explain why the same two-way table can call for different tests under different designs. (Practice Q7)
All ticked? Move on to Topic 3.15, Carrying Out a Chi-Square Test for Homogeneity or Independence, or return to the course roadmap.