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 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.