# 7. Two-Way Tables: Biplots Associated with Correspondence Analysis

1. John Gower1,
2. Sugnet Lubbe2 and
3. Niël le Roux3

Published Online: 3 NOV 2010

DOI: 10.1002/9780470973196.ch7

## Understanding Biplots

#### How to Cite

Gower, J., Lubbe, S. and Roux, N. l. (2011) Two-Way Tables: Biplots Associated with Correspondence Analysis, in Understanding Biplots, John Wiley & Sons, Ltd, Chichester, UK. doi: 10.1002/9780470973196.ch7

#### Author Information

1. 1

The Open University, UK

2. 2

University of Cape Town, South Africa

3. 3

University of Stellenbosch, South Africa

#### Publication History

1. Published Online: 3 NOV 2010
2. Published Print: 7 JAN 2011

#### ISBN Information

Print ISBN: 9780470012550

Online ISBN: 9780470973196

## SEARCH

### Keywords:

• biplot;
• chi-squared distance;
• contingency tables;
• correspondence analysis (CA);
• independent variables;
• Pearson residuals;
• RSA crime data;
• two-way tables

### Summary

In this chapter, the body of a two-way table is still regarded as a dependent variable with the rows and column classifiers treated as independent variables. The dependent variable is no longer restricted to be a numerical variable measured on an interval or ratio scale but is available in the form of counts or frequencies, thus defining contingency tables. Correspondence analysis (CA) is concerned with the analysis and visualization of contingency tables, especially two-way contingency tables. The chapter enables the reader to understand the several variant forms of biplot related to CA without going into great detail about the methodology. The RSA crime data set is used extensively illustrate the different biplots that can be constructed to approximate various aspects of model. In practice the main uses of CA are concerned with approximating chi-squared distance and, to a lesser extent, with approximating the Pearson residuals.

#### Controlled Vocabulary Terms

biplot; Chi-square test; independent variables; two-way tables