Chapter 13Analysis 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 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 variously 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 affiliations, different races, ...

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