Modern Mathematical Statistics with Applications pp 723-757 | Cite as

# Goodness-of-Fit Tests and Categorical Data Analysis

## Abstract

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 p_{i} 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 p_{i}’s (such as H_{0}: p_{1} =.45, p_{2} =.35, p_{3} =.15, p_{4} =.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 H_{0} 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.

## Bibliography

- 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 - 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 - 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