Information Technology Reference
In-Depth Information
The outcome of this ANCOVA leads the researchers to very different
conclusions than the outcome of the ANOVA we performed earlier. Based
on the ANOVA it would be concluded that the training programs did not
result in different levels of performance on the math word problem test.
The ANCOVA overrules that conclusion; by statistically controlling for
verbal ability, we find that there is some difference between the training
programs that is statistically significant.
The top portion of Figure 16.18 presents the adjusted (estimated
marginal) means for the three groups. Because these are predicted values,
the most appropriate indication of their stability is the standard error
associated with these predictions. In reporting these means, we report
the standard errors rather than the standard deviations. Note that these
predicted (adjusted) group means are different than the observed means
shown in Figure 16.16. The
F
ratio for the
group
effect evaluated the
differences of these adjusted means.
The bottom portion of Figure 16.18 provides the results of the pairwise
comparisons of the adjusted means. Based on these results, it appears that
Group 1 (Traditional) performed significantly lower on the math test than
Groups 2 (Freeform) and 3 (Software) when verbal ability was controlled;
these latter two groups appeared to perform comparably.
16.10 PERFORMING THE ANOVA IN SAS
The data file that we use to perform our ANCOVA in
SAS Enterprise Guide
is identical to what we used in SPSS. It is shown in Figure 16.19 in an Excel
file just prior to being imported into SAS.
We first perform an ANOVA without taking the covariate into con-
sideration. From the main menu select
Analyze
➜
ANOVA
➜
Linear
Models.
As shown in Figure 16.20, specify
math_dv
as the
Dependent
variable
and
group
as the
Classification variable.
Select
Model
in the navigation panel on the far left of the screen.
Highlight
group
and click the
Main
pushbutton in the middle of the
window. This action will place
group
into the
Effects
panel as shown in
Figure 16.21.
Select
Model Options
in the navigation panel. Select only
Type III
as
shown in Figure 16.22.
We also wish to obtain the observed means for the groups. This can
be accomplished by selecting the
Arithmetic
portion of the
Post Hoc
Tests
window in the navigation panel shown in Figure 16.23. Click
Add
to show the effects in the model and to display the panels in the
Options
for means tests.
Under
Class effects to use
(the first panel on the right
portion of the window), set the
group
effect to
True
(itisinitiallysetto
False
- double-clicking it displays the
True /Fa l s e
menu from which you
select
True
). Click
Run
to perform the analysis.
The output of the ANOVA is shown in Figure 16.24. This matches the
results produced by SPSS.
