Categorical Data Analysis in Psychology

by

David Rindskopf

• LAST REVIEWED: 12 January 2023
• LAST MODIFIED: 12 January 2023
• DOI: 10.1093/obo/9780199828340-0306

Introduction

Categorical data are data for which at least one dependent (outcome) variable is nominal or ordinal. Nominal variables, such as gender, ethnicity, religion, and graduation (or successful completion of any course of study), have a limited number of possible values. Categorical variables are generally divided into two major classes: dichotomous (binary) variables, which have two values (e.g., success vs. failure), and polytomous, which have more than two categories. Polytomous variables are further divided into ordered (ordinal) or unordered. Ordinal variables may have a limited number of categories (such as Likert scales) or a potentially unlimited number of categories, usually a count (e.g., number of times a student interrupts a class). Historical treatment of such data normally involved what was termed nonparametric statistics (e.g., chi-square tests of independence), and involved simple data structures (often just two variables). These methods have evolved to include a wide variety of extensions, including latent variables, graphical causal models, and tree-based methods.

General Overviews

Categorical data is a very broad topic, so no article or chapter can summarize the whole field. However, several outline large sections. Plackett 1981 is an excellent example of a categorical data text at the beginning of the era of log-linear models (Plackett mentions them, but has no detailed coverage). Sloane and Morgan 1996 discusses log-linear models for contingency tables. Rindskopf 2012 gives an overview of generalized linear models, most of which are categorical data models. Magidson and Vermunt 2004 provides an overview of latent class analysis.

• Magidson, J., and J. K. Vermunt. 2004. Latent class models. In The Sage handbook of quantitative methodology for the social sciences. Edited by D. Kaplan, 175–198. Thousand Oaks, CA: SAGE.

  Overview of latent class models with less technical detail than journal articles.

• Plackett, R. L. 1981. The analysis of categorical data. 2d ed. London: Griffin.

  An excellent view of categorical data just as log-linear models started to develop. Concentrates mostly on lower-dimensional data, including confidence intervals for proportions and measures of association.

• Rindskopf, D. 2012. Generalized linear models. In APA handbook of research methods in psychology. Vol. 3, Data analysis and research publication. Edited by H. Cooper, P. M. Camic, D. L. Long, A. T. Panter, D. Rindskopf, and K. J. Sher, 191–206. Washington, DC: American Psychological Association.

  DOI: 10.1037/13621-009

  Brief overview of generalized linear models. For more detail, see the book-length treatments discussed later.

• Sloane, D., and S. P. Morgan. 1996. An introduction to categorical data analysis. Annual Review of Sociology 22.1: 351–375.

  DOI: 10.1146/annurev.soc.22.1.351

  Good overview of log-linear models in a condensed form.