**Evaluating a Control Variable**

By Daniel Palazzolo, Ph.D.

(printable version here)

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.