# CHAPTER 8Tests for Nominal Scale Data: Chi-Square and Fisher Exact Tests

## 8.1 Objectives

In this chapter, you will learn the following items:

- How to perform a chi-square goodness-of-fit test.
- How to perform a chi-square goodness-of-fit test using SPSS
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- How to perform a chi-square test for independence.
- How to perform a chi-square test for independence using SPSS.
- How to perform the Fisher exact test.
- How to perform Fisher exact test using SPSS.

## 8.2 Introduction

Sometimes, data are best collected or conveyed nominally or categorically. These data are represented by counting the number of times a particular event or condition occurs. In such cases, you may be seeking to determine if a given set of counts, or frequencies, statistically matches some known, or expected, set. Or, you may wish to determine if two or more categories are statistically independent. In either case, we can use a nonparametric procedure to analyze nominal data.

In this chapter, we present three procedures for examining nominal data: chi-square (*χ*^{2}) goodness of fit, *χ*^{2}-test for independence, and the Fisher exact test. We will also explain how to perform the procedures using SPSS. Finally, we offer varied examples of these nonparametric statistics from the literature.

## 8.3 The *χ*^{2} Goodness-of-Fit Test

Some situations in research involve investigations and questions about relative frequencies and proportions for a distribution. Some examples might include a comparison of the number of women pediatricians ...