This chapter covers some basic methods for analyzing categorical data. The simplest case is where there are only two categories, which are usually called success and failure. Assuming random sampling, such situations can be analyzed using the binomial distribution, which was introduced in Chapter 4. Contingency tables, also introduced in Chapter 4, refer to situations where there are two or more categories. The main goal here is to describe some additional methods for analyzing such data.
There are many methods for analyzing categorical data beyond those covered in this chapter (e.g., Agresti, 1990, 1996; Andersen, 1997; Lloyd, 1996; & Powers & Xie, 1999; Simonoff, 2003; Agresti, 1990; Fienberg, 1980). The focus here is on the more basic techniques that might be used.
13.1 One-Way Contingency Tables
A one-way contingency table represents a situation where each participant can be classified into one of mutually exclusive categories. The probabilities associated with these categories are denoted by . The immediate goal is to test
the hypothesis that ...