Statistics and Probability with Applications for Engineers and Scientists, Preliminary Edition

Chapter 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.

The topics covered are:

• 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 2 × 2 and r × s 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 various-sized rods available in stock or the number of defective parts produced during different work shifts. A sociologist may be interested in finding the number of persons of different religious faiths, different political party affiliation, different race, ...