ANALYSIS OF QUANTITATIVE DATAreligious upbringing because one’s gender is fixed
at birth. The explanation pattern changes how a
researcher explains the results. It implies that the
initial bivariate relationship is spurious.
The suppressor variable patternoccurs when
the bivariate tables suggest independence but a rela-
tionship appears in one or both of the partials. For
example, religious upbringing and abortion attitude
are independent in a bivariate table. Once you intro-
duce the control variable region of the country, you
see that religious upbringing is associated with
abortion attitude in the partial tables. The control
variable suppressed the true relationship, and the
true relationship appears in the partials.
Multiple Regression Analysis
Multiple regression is a popular statistical tech-
nique whose calculation is beyond the level of this
book. Although by using appropriate statistics soft-
ware you can compute multiple regression quickly,
a background in statistics is needed to prevent you
from making errors in its calculation and interpre-
tation. Multiple regression requires interval- or
ratio-level data.
Multiple regression’s great advantage is its
ability to adjust for several control variables (i.e.,
alternative explanations) simultaneously. With per-
centaged tables, you can rarely use more than one
control variable at a time. In addition, multiple
regression is widely used, and you are likely to
encounter it when reading research reports or
articles. Multiple regression results tell the reader
two things. First, it tells the overall predictive
power of the set of independent and control variable
on the dependent variable. A statistic, R-squared
(R^2 ), tells us how well a set of variables “explains”
a dependent variable. Explainhere means making
fewer errors when predicting the dependent vari-
able scores on the basis of information about the
independent variables. A good model with several
variables might account for, or explain, a large per-
centage of variation in a dependent variable. For
example, an R^2 of 0.50 means that knowing the
independent and control variables improves the
accuracy of predicting the dependent variable by
50 percent and that you would make one-half as
many errors in predicting the dependent variable
with the variable as you would not knowing about
the independent and control variables.
Second, multiple regression results give the
direction and size of the effect of each variable on a
dependent variable. The effect is measured precisely
with a numerical value. The higher the value, the
larger the effect of a variable on predicting the
dependent variable. The sign (positive or negative)
of the effect tells you the direction of the impact on
the dependent variable. For example, you can see
how five independent or control variables simulta-
neously affect a dependent variable with all vari-
ables controlling for the effects of one another. This
is especially valuable for testing theories that state
that multiple independent variables cause one
dependent variable.
We measure effect of an independent or control
variable on the dependent variable by using a stan-
dardized regression coefficient or the Greek letter
beta (ß). It is similar to a correlation coefficient, and
ranges from zero to 0.99 or –0.99 with zero mean-
ing no effect. We can perform statistical tests to deter-
mine the statistical significance (discussed later in
this chapter) of a coefficient. The beta coefficient for
two variables equals the correlation coefficient.
We use the beta regression coefficient to deter-
mine whether control variables have an effect. For
example, the bivariate correlation between Xand Yis
0.75. Next, we statistically add four control variables.
If the beta remains at 0.75, the four control variables
have no effect. However, if the beta for Xand Y
becomes smaller (e.g., drops to 0.20), the control
variables have an effect on the dependent variable.
Consider an example of regression analysis with
age, income, education, and region as independent
variables. The dependent variable is a score on a polit-
ical ideology index. The multiple regression results
show that income and religious attendance have large
effects, education and region minor effects, and age
no effect. All independent variables together have a
38 percent accuracy in predicting a person’s politicalSupressor variable pattern Occurs when the bivari-
ate tables suggest independence but a relationship
appears in one or both partials.