ABSTRACT
In the first few chapters of this book we studied various statistics that describe a set of data. Those measures of centrality and dispersion were applied to a single-variable, or univariate, data set. We saw, for example, ways of computing mean family income or modal religious preference. As important as such univariate descriptive measures are, their utility is clearly limited, since so many sociological problems usually call for a type of analysis far more complex than that which can be provided by the simple description of a single variable. Such analyses must also tell us how two or more variables are related to each other. In this chapter and Chapters 10-12 we will examine some of the many measures that sociologists use to assess the relationships between two variables. Such measures are called measures of relationship, association, or correlation. In generat we shall say that "two qualities are associated when the distribution of values of the one differs for different values of the other" (Weiss 1968: 158). In statistical language, the opposite of association is independence. We can illustrate these concepts of association and independence by using the data from Tables 9.1 and 9.2. In Table 9.1, the variables of sex and preference for Brand X are independent, or not associated: Proportionately as many males as females prefer Brand X. However, in Table 9.2 the variables are associated: As we go from the category male to the category female, the proportion of people preferring Brand Y changes from 40 percent to 10 percent. This example illustrates another way by which we define association and
Sex
Male Female
Yes t 40 40 Prefer Brand X No 60 60 Totals 100 100
Prefer Brand Y Yes
No
Totals
Sex
Male Female
40 10
60 90
100 100
There are a great many things in the world that seem to be related to or associated with each other. As we noted earlier, height and weight are generally related so that in any population the tall people tend to weigh more than the short people. (The word tend is used to emphasize the point that the relationship is not perfect-some tall person may indeed weigh less than some short person.) Intelligence and academic success also are related to one another, as are religious preference and suicide rates, and a host of other variables.
