Information Technology Reference
In-Depth Information
13.4.3 CALCULATING MEAN SQUARES AND
F
RATIOS
We compute five mean squares for this analysis by dividing each sum of
squares by its respective degrees of freedom. The mean square total is not
calculated.
SS
A
df
A
=
70
87
20
.
MS
A
=
=
35.44
(13.7)
SS
S
/
A
df
S
/
A
=
15
00
12
.
MS
S
/
A
=
=
1.25
(13.8)
SS
B
24
30
1
.
MS
B
=
df
B
=
=
24.30
(13.9)
SS
A
×
B
df
A
×
B
=
40
20
2
.
MS
A
×
B
=
=
20.10
(13.10)
SS
B
×
S
/
A
df
B
×
S
/
A
=
3
00
12
=
.
MS
B
×
S
/
A
=
0.25
.
(13.11)
Three
F
ratios are formed in a simple mixed design. The between-
subjects factor is evaluated with the following
F
ratio.
MS
A
MS
S
/
A
=
35
.
44
F
A
=
=
28.35
.
(13.12)
1
.
25
The remaining
F
ratios are a function of the within-subjects variability
in the study and are each evaluated with
MS
B
×
S
/
A
as the error term:
MS
B
MS
B
×
S
/
A
=
24
.
30
F
B
=
=
97.20
(13.13)
.
0
25
MS
A
×
B
MS
B
×
S
/
A
=
20
.
10
F
A
×
B
=
=
80.40
.
(13.14)
0
.
25
We evaluate the between-subjects main effect (
F
A
) with (2, 12) degrees
of freedom (
df
A
,
df
S
/
A
). The critical value of
F
(see Appendix C) at
05
is 3.89. Since our
F
A
exceeds this critical value, we reject the null hypothesis
and conclude that leadership style affects group performance.
The remaining within-subjects
F
values are evaluated with the fol-
lowing degrees of freedom:
F
B
(1, 12)(
df
B
,
df
B
×
S
/
A
) and
F
A
×
B
(2, 12)
(
df
A
×
B
,
df
B
×
S
/
A
). The critical values of
F
at
α
=
.
05 (see Appendix C)
for
F
B
and
F
A
×
B
are 4.75 and 3.89, respectively. Both observed
F
s exceed
these critical values; thus we reject the null and conclude (in the case
of the main effect of Factor
B
) that simple projects produce higher per-
formance evaluations than do complex projects. However, this conclu-
sion is tempered by the statistically significant interaction effect. All of
these calculations are summarized in an ANOVA summary table (see
Table 13.1).
α
=
.