Analysis of Covariance - Analysis of Variance Designs - page 463

Software, respectively. The variable named math_dv indicates the number
of math word problems solved correctly; we have used the letters dv in
the ending of the name to help you remember that this is the dependent
variable. The variable named verb_cov indicates the score on the verbal
proficiency test (higher scores indicate greater verbal proficiency); we have
used the letters cov in the ending of the name to help you remember that
this variable is used as the covariate.
16.6.2 OUR DATA ANALYSIS STRATEGY
We will perform the data analysis for this numerical example by using
SPSS and then by using SAS, foregoing the hand calculations for the sake
of space. The analysis will proceed as follows:
First, we will run the simplified ANOVA design, using group as the
independent variable and math_dv as the dependent variable. This
will establish a context for the covariance analysis to show us what
we would have obtained without the covariate in the analysis.
Second, in preparation for the covariance analysis, we will evaluate
the data to ensure that the assumptions of linearity and homogeneity
of regression are met.
Third, we will perform the ANCOVA, using group as the indepen-
dent variable, math_dv as the dependent variable, and verb_cov as
the covariate.
16.7 PERFORMING THE ANOVA IN SPSS
From the main SPSS menu select Analyze ➜ General Linear Model ➜
Univariate . Selecting this path will open the dialog window shown in
Figure 16.3. We have configured it with group as the fixed factor and
math_dv as the dependent variable. Because the only information of
interest in this analysis is the main effect of group ,weclick OK to run the
basic ANOVA.
The summary table for the ANOVA is shown in Figure 16.4. As can
be seen from the output, the F ratio associated with group is not statis-
tically significant. Based only on this information, it would ordinarily be
concluded that the educational training programs do not differ in their
effectiveness of teaching math word problem solving; that is, there are no
significant differences between the means of the three groups.
16.8 EVALUATING THE ANCOVA ASSUMPTIONS IN SPSS
16.8.1 LINEARITY OF REGRESSION
Thefirstassumptionwewillevaluateisthelinearityofregression.The
goal here is to view the scatterplot of the covariate (verbal proficiency)
and the dependent variable (number of math problems correctly solved).