MAIN POINTS

Although two variables may be associated, they are not necessarily causally related. By using methods that control other factors, researchers are able to obtain evidence about whether an independent variable has a causal influence on a dependent variable.

An association between two variables is not a sufficient basis for an inference that the two are causally related. Other variables must be ruled out as alternative explanations. An association between two unrelated variables is said to be a spurious relation.

Herbert H. Hyman analyzed the various factors that are generally considered conditions for most bivariate association and classified them into three major groups. The first group consists of variables that specify relationships in terms of interests and concerns. The second class of factors specifies associations in terms of time and place. The third class of factors specifies background characteristics of the units of analysis are the last class of factors.

Elaboration analysis involves considering the nature of the effect of a third variable on a bivariate relationship. If the third variable intervenes between the independent and dependent variables, and the original relationship changes under conditions of the third variable, the third variable clarifies how the variables are related. If the third variable precedes both the independent and the dependent variable, and the original relationship changes under conditions of the third variable, the result specifies the condition under which the relationship exists.

Control and elaboration go hand-in-hand with a third function of multivariate analyses: better predictions.

The inclusion of additional variables in multivariate analyses allows researchers to examine multiple types of relationships between them. There are two general types of relationships that concern us in this chapter: moderation and mediation.

A bivariate relationship between two variables is said to be moderated by a third variable when the original bivariate relationship changes after the third variable is introduced into the analysis. In this type of relationship, which is also called an interaction, the researcher specifies the conditions or contingencies necessary for the relationship to occur.

Closely related to the concept of moderation is that of mediation. In contrast to a relationship between two variables that is moderated by a third variable, in this case, a mediating variable is one that helps to explain how social processes work.

In multivariate analyses, statistical techniques substitute for the experimental method of control. These techniques are employed during data analysis rather than at the data collection stage. There are three methods of statistical control: cross-tabulation, partial correlation, and multiple regression.

Cross-tabulation involves the division of the sample into subgroups according to the categories of the controlled variable; thus, a form of control is exerted that provides evidence about the causal influence of the independent variable on the dependent variable. A partial table shows the extent of relationship between two variables within a single category of some third variable. If an original relationship disappears in partial tables based on an antecedent third variable, the relationship is spurious and not meaningful. If the original relationship changes in the partial tables, but does not completely disappear, the relationship is nonspurious and should be examined further to determine the conditions that bring about the relationship. If the original relationship remains in the partial tables, the third variable does not account for the original relationship.

Partial correlation is a statistical method for controlling the effects of a third variable on a bivariate relationship. The partial correlation coefficient measures the extent to which two interval variables are related. This method can be extended to simultaneously remove the effects of several variables if they have been measured and are interval level variables.

Multiple regression is a simple extension of bivariate regression allowing for an assessment of the relationship between two variables while controlling for the effect of others. Because there are usually several determinants for any dependent variable, social scientists often use a method called multiple regression analysis to specify how a set of independent variables in combination influence a dependent variable. To examine the combined effect of all the independent variables, the coefficient of determination, R² is computed. The square root of R² indicates the correlation between all independent variables taken together with the dependent variable; it is thus denoted as the coefficient of multiple correlation.

A technique known as causal modeling has been developed to combine theoretical knowledge of relationships between variables with empirical evidence about these relationships and hence to provide evidence about causal relationships within a set of variables.