A general definition of causality is introduced and then specialized to become operational. By considering simple examples a number of advantages, and also difficulties, with the definition are discussed. Tests based on the definitions are then considered and the use of post-sample data emphasized, rather than relying on the same data to fit a model and use it to test causality. It is suggested that a bayesian viewpoint should be taken in interpreting the results of these tests. Finally, the results of a study relating advertising and consumption are briefly presented.

THE PROBLEM AND A DEFINITION

Most statisticians meet the concept of causality early in their careers as, when discussing the interpretation of a correlation coefficient or a regression, most textbooks warn that an observed relationship does not allow one to say anything about causation between the variables. Of course this warning has much to recommend it, but consider the following special situation: Suppose that X and Y are the only two random variables in the universe and that a strong correlation is observed between them. Further suppose that God, or an acceptable substitute, tells one that X does not cause Y, leaving open the possibility of Y causing X. In the circumstances, the strong observed correlation might lead to acceptance of the proposition that Y does cause X. This possibility occurs because of the extra structure imposed on the situation by the knowledge that X does not cause Y.