Further Inference for Categorical Variables

This chapter takes us further into inferential analysis of categorical (that is, nominal and ordinal) data. Up to now, two chapters have concentrated on categorical variables. In Chapter 5 we learned to compute relative frequencies, which we then used to illustrate concepts and rules of probability. In Chapter 8 we focused on dichotomous categorical variables to learn about confidence intervals and hypothesis tests for a single population proportion.

In this chapter we'll consider two basic issues. First, we'll learn some ways to draw inferences about a categorical variable that can take on more than two possible values. Second, we'll see how we can use sample data to infer whether two categorical variables are independent or somehow related. The thread that unifies most of the discussion in this chapter is another family of continuous density functions called chi-square distributions. The tests statistics that we'll encounter in this chapter follow the shape and proportions of a chi-square (χ²) distribution enabling us to calibrate the likelihood of sampling error.