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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 = .
 
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