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the week that the math test was given; the verbal proficiency score was then
used as a covariate in the analysis.
The
ANCOVA
yielded
a
significant
effect
for
both
the
covariate,
F
(1, 32)
=
87
.
42,
p
<.
05, and the instructional program independent vari-
able,
F
(2, 32)
05; this latter effect accounted for just under
8 percent of the total variance. Bonferroni corrected multiple compari-
son tests indicated that the computer-based (adjusted
M
=
6
.
52,
p
<.
=
11
.
69,
SE
=
0
.
35, 95 percent
CI
=
10
.
98
−
12
.
39) and freeform (adjusted
M
=
11
.
20,
90) programs resulted in higher
math word problem performance than the tradition instructional program
(adjusted
M
SE
=
0
.
35, 95 percent
CI
=
10
.
49
−
11
.
=
10
.
20,
SE
=
0
.
35, 95 percent
CI
=
9
.
49
−
10
.
92) when con-
trolling for the level of verbal proficiency.
CHAPTER 16 EXERCISES
16.1.
Assume we are interested in the effects of teaching method, Factor
A
(
a
1
group discussion),
on the teaching of an Introductory Statistics course. The three independent
groups of students (
n
=
6) are all measured at the end of the semester
on a comprehensive (100-point) final exam. Further assume that students'
statistical aptitude (
X
) was measured with 50 multiple-choice questions
prior to the start of the experiment to be used as a covariate in the analysis.
The data are as follows:
=
lecture,
a
2
=
PowerPoint presentation, and
a
3
=
Teaching method (
A)
Group
Lecture
PowerPoint
discussion
a
1
X
a
2
X
a
3
X
88
25
70
24
60
23
80
28
71
22
64
23
87
30
73
22
66
27
90
20
80
24
69
22
95
24
75
26
70
25
92
26
70
20
61
24
a. Conduct an ANCOVA and any necessary multiple comparisons tests
using SPSS or SAS.
b. If appropriate, perform multiple comparisons to determine which
pair or pairs of group means are significantly different.
16.2.
Assume we are interested in the effect of treatment type (Factor
A
:
a
1
=
brief,
a
2
=
cognitive-behavioral, and
a
3
=
psychoanalytic) on com-
munity mental health clients' (
n
5) GAF at the end of eight weeks of
treatment (Time 2). The covariate for this study would be the clients' GAF
scores at the start of treatment (Time 1). The data are as follows:
=
