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n
ˆ
ψ
2
57
)
2
7
(
−
78
.
SS
A
comp
2
=
=
=
21,606.36
(7.18)
c
2
2
SS
A
comp
2
1
MS
A
comp
2
=
=
21,606.36
MS
A
comp
2
MS
S
/
A
21, 606
.
36
F
A
comp
2
=
=
=
16.30
.
(7.19)
.
1, 325
73
Evaluate at 1 and
df
S
/
A
(1, 20),
p
05. We conclude that students who
prepare for four months perform significantly higher on the SAT than do
students who study for two months.
<.
7.27.3 HYPOTHESIS 3
The third hypothesis contrasts students who study from two to four
months with those who study from six to eight months. The coefficients
forthiscomparisonareasfollows:
011
−
1
−
1
.
Thus,
ˆ
ψ
3
=
(
c
1
)(
Y
1
)
+
(
c
2
)(
Y
2
)
+
(
c
3
)(
Y
3
)
+
(
c
4
)(
Y
4
)
+
(
c
5
)(
Y
5
)
=
(0)(412
.
86)
+
(1)(474
.
29)
+
(1)(552
.
86)
+
(
−
1)(614
.
29)
+
(
−
1)(623
.
86)
= −
211.00
(7.20)
n
(
ˆ
)
2
00)
2
ψ
7(
−
211
.
SS
A
comp
3
=
=
=
77,911,75
(7.21)
c
2
4
SS
A
comp
3
1
MS
A
comp
3
=
=
77,911.75
MS
A
comp 3
MS
S
/
A
77, 911
.
75
=
=
73
=
.
F
A
comp
3
58.77
(7.22)
1, 325
.
.05. We conclude that
students who prepare for six to eight months score higher on the SAT than
do students who study only two to four months.
These computed
F
values correspond directly to the
t
values that
SPSS produces when it conducts
Contrast Tests
as shown later in Figure
7.26. Recall from our disc
us
sion in Chapter 6 that the
t
and
F
statistics
are related:
t
2
Again, we evaluate at 1 and
df
S
/
A
(1, 30),
p
<
F
and
√
F
t
. Thus, when we square the three SPSS-
produced
t
values, in the
Assume equal variances
section of Figure 7.26
(
=
=
630), we produce
F
values (99.16, 16.30, 58.22) that
are equivalent to the
F
values we obtained, less some minor rounding
error.
−
9
.
958,
−
4
.
037,
−
7
.
