13

Analysis of Categorical Data

*The focus of this chapter is on the development of chi-square goodness-of-fit tests used as nonparametric procedures.*

# Topics Covered:

- Chi-square goodness of fit tests to determine if the sample data come from some specified probability model
- The chi-square test of a hypothesis that the two factors cross-classifying a sample (count or frequency) data are independent
- Use of and contingency tables to test a hypothesis that the populations under investigation are homogeneous with respect to certain criteria

# Learning Outcomes:

After studying this chapter, the reader will be able to

- Use the chi-square goodness of fit test to evaluate certain distributional assumptions.
- Test whether or not two classifications of a population are independent.
- Use contingency tables to test whether populations are homogeneous with respect to some characteristics of interest.

# 13.1 Introduction

Often data collected by an investigator through experimentation, observation, or a sample survey are classified into various categories, and frequency counts of observations in each category are recorded. For example, a manager of a manufacturing company may be interested in finding the number of variously sized rods available in stock or the number of defective parts produced during ...