Introduction to Categorical Data Analysis

CHAPTER 11
A Historical Tour of Categorical
Data Analysis ∗
We conclude by providing a historical overview of the evolution of methods for
categorical data analysis (CDA). The beginnings of CDA were often shrouded in
controversy. Key figures in the development of statistical science made groundbreaking
contributions, but these statisticians were often in heated disagreement with one
another.
11.1 THE PEARSON–YULE ASSOCIATION CONTROVERSY
Much of the early development of methods for CDA took place in the UK. It is fitting
that we begin our historical tour in London in 1900, because in that year Karl Pearson
introduced his chi-squared statistic (X 2 ). Pearson’s motivation for developing the chisquared
test included testing whether outcomes on a roulette wheel in Monte Carlo
varied randomly and testing statistical independence in two-way contingency tables.
Much of the literature on CDA in the early 1900s consisted of vocal debates
about appropriate ways to summarize association. Pearson’s approach assumed that
continuous bivariate distributions underlie cross-classification tables. He argued that
one should describe association by approximating a measure, such as the correlation,
for the underlying continuum. In 1904, Pearson introduced the term contingency as
a “measure of the total deviation of the classification from independent probability,”
and he introduced measures to describe its extent and to estimate the correlation.
George Udny Yule (1871–1951), an English contemporary of Pearson’s, took an
alternative approach in his study of association between 1900 and 1912. He believed
that many categorical variables are inherently discrete. Yule defined measures, such
as the odds ratio, directly using cell counts without assuming an underlying continuum.
Discussing one of Pearson’s measures that assumes underlying normality,
An Introduction to Categorical Data Analysis, Second Edition. By Alan Agresti
Copyright © 2007 John Wiley & Sons, Inc.
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