1. What are the levels of measurement for those variables used in the χ² test? Explain when the χ² test is used in hypothesis testing.

2. Explain what is meant by a positive relationship between two variables and a negative relationship between two variables. Describe examples of situations in which one would expect to find a positive relationship and when one would expect to find a negative relationship. Can one assign direction when both variables in a table are dichotomous?

3. Discuss how the concept of statistical independence underlies statistical hypothesis testing in general. Based on statistical analysis, are we justified in asserting that two variables are statistically dependent? Why or why not? Explain why researchers typically focus on statistical independence rather than statistical dependence.

4. Does the utility of χ² decline as we begin to compare variables with more and more groups? For example, imagine we are interested in comparing religious affiliation against political persuasion in the United States. There is a plethora of categories designed to capture information about each variable of interest. How useful is χ² in telling us anything substantive about the relationship between these two variables?

5. Suppose you were using the percentage difference method discussed in chapter 9 to determine the relationship between two variables of interest arranged in a bivariate table. Are there any instances where you might find a very large percentage difference yet fail to find statistically significant results after conducting a χ² test? If so, what factors would explain this?

6. What are we calculating when we calculate expected frequencies? What is the reason for calculating expected frequencies the way we do? In layman’s terms, what do expected frequencies tell us?

7. Compare and contrast symmetrical and asymmetrical measures. Is it generally good practice to rely on symmetrical measures of association? Why or why not?

8. The calculation of γ relies on the comparison of same ordered and inverse ordered pairs. The calculation of τ-b relies on the additional concept of tied pairs. What is a tied pair? How do such pairs differ from same ordered and inverse ordered pairs? Which of these measures is preferable and why?

9. When conducting χ² analyses, what do we gain from reporting PRE measures or from discussing the strength of significant relationships? Discuss an example in which it would be important to report not only significance but also strength.