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In-Depth Information
Ta b l e 8 . 1 .
Summary table for two-way between-subjects design
Source
2
SS
df
MS
F
η
Gender (
A
)
1,400.833
1
1,400.833
38.032
∗
.267
Residence (
B
)
1,551.667
2
775.833
21.063
∗
.296
Gender
×
Residence (
A
×
B
)
1,411.667
2
705.833
19.163
∗
.269
Error
S
/
AB
884.000
24
36.833
Total
5,248.167
29
∗
p
<
.05
as
main effects
; we thus evaluate the main effect for gender and the main
effect for residence. There is also an effect representing the combinations
of the levels of these variables. Such an effect is known as an
interaction
;
here, we are dealing with the Gender
Residence interaction. We will
discuss these three effects in a moment. Finally, we have the unaccounted
source of variance known as error variance or within-groups variance.
×
8.3.2 DEGREES OF FREEDOM
The procedure for computing the sums of squares with a hand calculator
will be covered later in this chapter. Degrees of freedom for the total
variance is always computed in the same manner:
df
To t a l
=
total number of observations
−
1
.
Degrees of freedom for the main effects are determined in the same
way as we described in Chapter 6:
df
Main Effect
=
number of levels of the independent variable
−
1
.
Thus, gender (with two levels) is associated with 1
df
(
a
−
1
=
2
−
1
=
1)
and residence (with three levels) is associated with 2
df
(
b
−
2
=
3
−
1
=
2).
Degrees of freedom for the interaction are computed by multiplying
the degrees of freedom for each of the main effects:
df
A
×
B
=
(
df
A
)(
df
B
)
.
In our example, gender has 1
df
and residence has 2
df
.Multiplying
these two values yields 2
df
for the interaction. Subtracting the degrees of
freedom of the two main effects and the interaction from the total degrees
of freedom gives us the degrees of freedom associated with the error term.
8.3.3 MEAN SQUARE,
F
RATIO, AND ETA SQUARED
These values are obtained in the same manner that we described in Chap-
ter 6. The mean square values are computed for each source of variance
by dividing the sum of squares for that source by its degrees of freedom.
F
ratios are computed for the two main effects and the interaction by
dividing the respective mean square values by the mean square value for
