Suppressor Variables

[Podcast]

(Taken from the work of Kristin
Woolley)

"Most researchers determine the worth of a
predictor variable by its correlation with the dependent variable. However,
sometimes a variable can raise the total R^{2}
even though it has a negligible correlation with the dependent variable and a
strong correlation with the other predictor variables (Hinkle, Wiersma & Jurs,
1994; Pedhazur, 1982). A variable that when added as another predictor increases
the total R^{2} is called a suppressor
variable. Horst (1966, p. 363) explained:

A suppressor variable may be defined as those predictor variables which do not measure variance in the criterion measures, but which do measure some of the variance in the predictor measures which is not found in the criterion measure. They measure invalid variance in the predictor measures and serve to suppress this invalid variance. "

There may be cases when you select a predictor that does
not have a relationship with the outcome variable (DV) but increases the
multiple *R*.

Suppose that both *IV1 and IV2 *are
positively correlated with *DV*. That means that
if either of those variables increases, we expect to see *Y* increase. But
suppose that the regression equation comes out as

*Y* = 12.78 + 1.3*X*_{1}
- 2.4*X*_{2}

[Taken from the work of David Howell]

"Cohen's classic example (Maybe it was Darlington), is of
a speeded test of history. We want to predict knowledge of historical facts. We
give a test which supposedly tests that. But some people will do badly just
because they read very slowly, and don't get through the exam. Others read very
quickly, and do all of the questions. We don't think that reading speed has
anything to do with how much history you know, but it does affect your score. We
want to "adjust" scores for reading speed, which is like saying "The correlation
between true historical knowledge and test score, *controlling for* reading
speed."

**Suppression
Examples**

__Practice__

X1=Amount of psychotherapy

X2=Degree of depression

Y=Number of prior suicide attempts

Classical Suppressor Example [Dataset] X1 is the suppressor

Two Practical Examples of Suppressor Variables can be found here.