Introducing a Third Variable - Causal Relationships
Introducing a Third Variable - Causal Relationships
Causation, strictly speaking, means that a change in one variable will produce a change in another. In this context, the definition will be broadened somewhat to include the concept of a precondition influencing a variable of interest. Thus, we could conceive that credit-card usage is partly determined by a persons' sex. In this case, sex could be conceptualized as causal in nature, despite the fact that it would be impossible to take a group of people and change their sex to observe if a change in credit-card usage was "produced." The weaker term, "influence," often will be used when it is more appropriate than the term "cause," but the logic of the analysis normally will remain the same.
Given the causation concept, that a change in one variable will produce a change in another, it is reasonable to conclude that, if two variables are causally linked, they should be associated. Thus, an obvious data analysis procedure to identify or confirm causation is to measure the association between two variables. If association provides evidence of causation, then, conversely, the lack of association suggests the absence of causation. Thus, an association between attitude (A) and behavior (B) is evidence of:
A Causal Relationship
A —> B
If a third variable is introduced into the analysis, however, at least five other causal explanations for the association become possible. The association could be due spuriously to a third variable, C (such as income—a high-income explains a person's attitude toward the Republican party's positions and the person's voting behavior):
Spurious Association Between A and B A B
But there are other possibilities as well. Three of the most interesting are:
Intervening Variable
Additive
Effect on B
A-» C
B
A~>B
C
The first is that the third variable intervenes in the causal link between variables A and B. The second is that variable C is an independent cause of variable B. The third is that there is an interactive effect of variables A and C on variable B.
Even when a third variable is not involved in the analysis, the direction of causation could still be in doubt. It could be that we have:
A Causal Relationship in the Reverse Direction
B-h> A
In the following five sections, each of the five causal interpretations will be discussed. It should be noted that the discussion could apply to any association measurement introduced in Chapter 13.
Causation, strictly speaking, means that a change in one variable will produce a change in another. In this context, the definition will be broadened somewhat to include the concept of a precondition influencing a variable of interest. Thus, we could conceive that credit-card usage is partly determined by a persons' sex. In this case, sex could be conceptualized as causal in nature, despite the fact that it would be impossible to take a group of people and change their sex to observe if a change in credit-card usage was "produced." The weaker term, "influence," often will be used when it is more appropriate than the term "cause," but the logic of the analysis normally will remain the same.
Given the causation concept, that a change in one variable will produce a change in another, it is reasonable to conclude that, if two variables are causally linked, they should be associated. Thus, an obvious data analysis procedure to identify or confirm causation is to measure the association between two variables. If association provides evidence of causation, then, conversely, the lack of association suggests the absence of causation. Thus, an association between attitude (A) and behavior (B) is evidence of:
A Causal Relationship
A —> B
If a third variable is introduced into the analysis, however, at least five other causal explanations for the association become possible. The association could be due spuriously to a third variable, C (such as income—a high-income explains a person's attitude toward the Republican party's positions and the person's voting behavior):
Spurious Association Between A and B A B
But there are other possibilities as well. Three of the most interesting are:
Intervening Variable
Additive
Effect on B
A-» C
B
A~>B
C
The first is that the third variable intervenes in the causal link between variables A and B. The second is that variable C is an independent cause of variable B. The third is that there is an interactive effect of variables A and C on variable B.
Even when a third variable is not involved in the analysis, the direction of causation could still be in doubt. It could be that we have:
A Causal Relationship in the Reverse Direction
B-h> A
In the following five sections, each of the five causal interpretations will be discussed. It should be noted that the discussion could apply to any association measurement introduced in Chapter 13.
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