Analysis of Categorical Data

This chapter illustrates some of the possible problems in the analysis of categorical data. It presents selected methods of analysis of ordinal aspects of categorical data. The theory of categorical data is a domain with a long tradition, the chi‐square test being one of the oldest examples of statistical procedures that use only frequencies. The chapter also presents one of the oldest and best known statistical tests, chi‐square tests. Chi‐square tests can also be used for testing hypotheses about jointly distributed categorical variables. Chi‐square tests of either independence or homogeneity serve as tests against a general alternative, asserting simply that the null hypothesis is false (such tests are called omnibus tests). The chapter provides a more detailed analysis of types of contingency tables. It considers the simplest case, corresponding to random sampling from a population whose elements are categorized according to some classification system.