1. Control Tables
March 7, 2011

2. Objectives By the end of this meeting, you should be able to:
Explain the concept of statistical control.
Differentiate intervening (mediator) and interacting (moderator) variables.
Appropriately choose control variables in data analysis.
Compute a control table.

3. Think About
When analyzing the relationship between variables, what does it mean to “control” for a variable?
We cannot always use experimental data in political science.

4. Control Variables
Frequently when we observe a relationship between two variables, causally there may be a third variable acting as well.
Therefore we must statistically ‘control’ for that variable to see if a relationship continues between our initial two variables.
Imagine that we believe that ideology leads to vote choice. Does that finding still hold if partisanship is controlled?

5. Intervening and Interacting Variables
An intervening variable is one where the third variable occurs between the independent and the dependent variable.
An interacting variable is one that moderates, in a casual sense, the effect of the independent variable on the dependent variable. The effects of interacting variables can be very different.
Sometimes an effect may be negative for one value but positive for another
Sometimes an effect may be stronger (but in the same direction) for one value of the variable than another.

6. Intervening and Interacting Variables
In the previous example with ideology and vote choice, what type of variable is partisanship?
There are two general ways to answer that question.
Theoretically
Empirically

7. Antecedent Variables
It is also important to identify if the control variable is antecedent to the independent variable, i. e. does it occur before.
If the control variable is antecedent and including it in the model eliminates the effect of the independent variable then the initial relationship must be considered spurious.

8. Spuriousness
While control variables may help us eliminate relationships that are spurious, it is important to look for relationships that are specified by the control variable.
In these cases, there is a relationship between the independent and dependent variable but it only occurs at one level of the control variable.
For instance, you might discover that the relationship between race and turnout is spurious when education is considered except for Native Americans.

9. How Many Control Variables to Use?
Parsimony vs. accuracy
Achen and the rule of three
The medical field: rule of thirty
Make sure to use only those that have a relationship with both the independent and dependent variable.
If the variable does not have a relationship with both the independent and dependent variable, then it is a poor control.

10. How Many Control Variables to Use?
When testing for spuriousness only look at those variables that precede both the independent and dependent variable
Remember if a control occurs between the independent and dependent variable (i.e. is intervening) then it cannot render the initial relationship spurious.
When in doubt follow the trend of the literature.

11. For Next Time Read WKB chapter 14, pp. 298-313
Answer questions 1, 2, & 3 on page 324.