Goodness-of-Fit Tests and Categorical Data Analysis

  • Jay L. Devore
  • Kenneth N. Berk
Part of the Springer Texts in Statistics book series (STS)


In the simplest type of situation considered in this chapter, each observation in a sample is classified as belonging to one of a finite number of categories (For example, blood type could be one of the four categories O, A, B, or AB). With pi denoting the probability that any particular observation belongs in category i (or the proportion of the population belonging to category i), we wish to test a null hypothesis that completely specifies the values of all the pi’s (such as H0: p1 =.45, p2 =.35, p3 =.15, p4 =.05, when there are four categories). The test statistic will be a measure of the discrepancy between the observed numbers in the categories and the expected numbers when H0 is true. Because a decision will be reached by comparing the computed value of the test statistic to a critical value of the chi-squared distribution, the procedure is called a chi-squared goodness-of-fit test.


  1. Agresti, Alan, An Introduction to Categorical Data Analysis (2nd ed.), Wiley, New York, 2007. An excellent treatment of various aspects of categorical data analysis by one of the most prominent researchers in this area.Google Scholar
  2. Everitt, B. S., The Analysis of Contingency Tables (2nd ed.), Halsted Press, New York, 1992. A compact but informative survey of methods for analyzing categorical data, exposited with a minimum of mathematics.Google Scholar
  3. Mosteller, Frederick, and Richard Rourke, Sturdy Statistics, Addison-Wesley, Reading, MA, 1973. Contains several very readable chapters on the varied uses of chi-square.Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Statistics DepartmentCalifornia Polytechnic State UniversitySan Luis ObispoUSA
  2. 2.Department of MathematicsIllinois State UniversityNormalUSA

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