Evaluating a Control Variable
By Daniel Palazzolo, Ph.D.

We need to go through a few steps to assess the effects of a control variable.

1. Test a bivariate relationship—referred to as the “original relationship.” It must be statistically significant and at least reasonably strong to begin with. Record all the relevant information associated with a bivariate analysis. Also, check the case processing box to be sure there are sufficient cases. If there are fewer than 1,000 cases, it will be very difficult to test a control variable.

2. Consider a control variable, either by theory or deductive logic, that seems to provide an alternative explanation for the original relationship. By introducing the control variable, you will get a crosstab table for each value of the control variable. In order to do get the output you need, first run a crosstab with the dependent variable in the row and the independent variable in the column, and select column percentages for the cells and the relevant statistics. Then go back and run the crosstab again, but this time add the control variable in the third box (labeled previous and next).

3. Assess the impact of the control variable. This involves comparing the results for each value of the control variable with the original relationship. Thus for each value of the control variable we should compare the crosstab, the strength measure, the significance, and the row percentages. Four things can happen (see scenario’s below).

4. Write the results in clear, commonsense terms, i.e. identifying the effects of the control variable but relating the values of the control with the values of the independent and dependent variables.

Scenario 1: Spurious. The control variable renders the original relationship insignificant.
Column %: Column percentages grow closer together for all values of the control variable, to the point that there no longer appears to be a difference between the values of the independent variable in the original relationship.

Strength Measure: Measures are much weaker, approximating zero for all values of the control variable.

Significance: The relationships for all values of the control variable are no longer significant.

Scenario 2: No change or Enhanced. We see no major changes in the original relationship when we inspect the values of the control variable.

Column %: In this case the column percentages for each value of the control variable remain roughly the same, and differences in the column percentages remain roughly the same.

Strength Measure: Remains roughly the same; a small change may occur, but nothing substantial.

Significance: Relationship remains significant for all values of the control variable.

In the case of an “enhanced” result, while the control variable does not alter the original relationship, it may be directly related to the dependent variable. In this case, we will see a difference in the row % totals between the original and the control variables. The way to affirm this is to run a separate crosstab between the control and the dependent variable.

Scenario 3: Specified (or Conditional). The control variable has differential effects on the original relationship, i.e. the original remains the same for at least one value of the control variable, but changes for at least one value of the control variable.

Column %: The column percentages remain the same for some of the values of the control variable, but they either grow closer together or further apart for one or more values of the control variable.

Strength Measure: Roughly the same for at least one value of the control variable, but lower or higher for at least one value of the control variable.

Significance: Significant for at least one value of the control variable, but not significant for at least one value of the control variable.

Scenario 4: Exaggerated/Suppressed. In some instances, the original relationship changes for all values of the control variable; showing either a weakening of the original relationship, in which case we say it was exaggerated, or a strengthening of the original relationship, in which we say it was suppressed. This is different from a spurious relationship (in which the control variable renders the original relationship insignificant), or an enhanced relationship (where the original relationship stays in tact and the control has an independent effect on the dependent variable), or a specified relationship (where the results of the control differ with different values of the control variable).

Column %: In this case the column percentages for each value of the control variable are closer together (exaggerated) or further apart (suppressed).

Strength Measure: Lower for all values of the control variable (exaggerated) or higher for all values of the control variable (suppressed).

Significance: Normally relationships for all values of the control remain statistically significant, even though the relationship is weaker.

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Copyright 2010