Information Technology Reference
In-Depth Information
where
a
is the number of groups and
n
is the number of cases contained
in each group.
6.5.4.2 Degrees of Freedom for Between-Groups Variance
The sum of squares for the between-groups variance (
SS
A
) is based on
subtracting the grand mean from each group mean. In our data set, we
have five levels of the independent variable and therefore have five group
means. The degrees of freedom for the between-groups effect are equal to
the number of levels of the independent variable minus one. Expressed as
a formula, our computation is as follows:
df
A
=
a
−
1
=
5
−
1
=
4,
(6.5)
where
a
is the number of groups.
6.5.4.3 Degrees of Freedom for the Within-Groups (Error)
Va r i anc e
The sum of squares for the unexplained portion of the variance (
SS
S
/
A
)-
the variability of the scores within each group - is based on the difference
between each score in a given group and its respective mean. In computing
the degrees of freedom for the unexplained variance we treat each group
in turn. For the zero months group, we have seven scores from which the
mean will be subtracted. That gives us 5
df
. For the two months group,
we also have seven scores from which that mean will be subtracted. That
gives us another 5
df
. Likewise for the four, six, and eight months groups.
All told, the unaccounted for variance has 30
df
associated with it. This
can be written as the following formula:
df
S
/
A
=
−
=
−
=
.
(
a
)(
n
1)
(5)(7
1)
30
(6.6)
Note that we could have figured out the value of the degrees of freedom
for the unexplained or error variance based on what we already had
computed. Given that there are 34
df
in total and that four of them are
associated with the between-groups effect, the rest had to be associated
with the error variance. We could have thus computed this value as the
residual, and this is a common way for researchers to obtain certain
degrees of freedom values in the summary table when they are doing the
calculations by hand. Of course, by performing the analyses in SPSS or
SAS, all of these values are provided to you.
6.5.5 MEAN SQUARES
Mean square values are computed by dividing each sum of squares by
its respective degrees of freedom. We only compute mean squares for the
between-groups (Factor
A
) effect and the within-groups or error variance.
