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