Log-Linear Analysis of Contingency Tables: An Introduction for Historians with an application to Thernstrom on the "Floating Proletariat"

Abstract

Suppose a researcher has information on several attributes of a collection of individuals and that the data he has are available only in qualitative (synonyms are categorical, discrete, polytomous, or ordinal- or nominal- level), as opposed to quantitative (continuous or interval-level) form. For instance, imagine that his information is about yes or no votes, occupational classes, or age groups, but none is in the form of, say, the dollar amounts of property held (not broken into categories) or the length of residence, in months or years, at a particular location. Then he might construct tables, such as Table 1, which show how many people have each set of traits; for example, how many young, unskilled, childless men in a sample were found in both the Boston census schedule in 1880 and the city directory in 1890. When there is very little information available, say, data on only two or three variables, commonsensical methods of analysis may suffice. But what should one do when one is confronted by such monsters as the eighty-celled "four-way" Table 1?