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the two independent variables (vehicle and alcohol) combine to produce
a statistically significant unique joint effect. We remind the reader that
because the interaction effect is statistically significant, it takes precedence
over the statistically significant main effect of Factor
B
.Wewillbriefly
review the computational details of these analyses.
11.6.5 COMPUTING TWO-FACTOR WITHIN-SUBJECTS
SIMPLE EFFECTS BY HAND
Simple Effects
As we noted in Chapter 8, a statistically significant interaction effect
is typically followed by an analysis of simple effects. Recall that such an
analysis is like conducting a one-way ANOVA with one of the independent
variables held constant. The sums that we use to form our sums of squares
come from the
AB
matrix of sums in Table 11.2. Thus, in the present
example, the simple effects of Factor
A
(type of vehicle) at a particular
level of Factor
B
(amount of alcohol), for example,
b
3
(3 drinks), would
have the following formulas for sums of squares, degrees of freedom, mean
square, and
F
.
SS
A
at
b
3
=
(
AB
j
3
)
2
n
(
B
3
)
2
(
a
)(
n
)
−
df
A
at
b
3
=
a
−
1
(11.12)
SS
A
at
b
3
df
A
at
b
3
MS
A
at
b
3
=
(11.13)
MS
A
at
b
3
F
A
at
b
3
=
MS
A
×
B
×
S
.
(11.14)
This
F
is evaluated with (
df
A
at
b
3
,
df
A
×
B
×
S
).
Likewise, to compute the simple effects of Factor
B
at levels of
A
(e.g.,
level
a
2
), we have the following formula:
SS
B
at
a
2
=
(
AB
2
k
)
2
n
(
A
2
)
2
(
b
)(
n
)
−
df
B
at
a
2
=
b
−
1
(11.15)
SS
A
at
b
2
df
B
at
a
2
MS
B
at
a
2
=
(11.16)
MS
B
at
a
2
MS
A
×
B
×
S
.
F
B
at
a
2
=
(11.17)
This
F
is evaluated with (
df
B
at
a
2
,
df
A
×
B
×
S
).
Simple Comparisons
Following a statistically significant simple effect analysis that has three
or more treatments, paired or simple comparisons can be conducted.
