Information Technology Reference
In-Depth Information
Ta b l e 6 . 2 .
Summary table for one-way between-subjects design
Between-subjects effects
Source
SS
df
MS
F
η
2
43.47
∗
Study time (
A
)
230,496.57
4
57,624.14
.853
Error (
S
/
A
)
39,772.00
30
1325.73
Total (
T
)
270,268.57
34
∗
p
<.
05
.
deviation of 100. To give you a sense for how to interpret these values,
a score of 400 is 1
SD
below the mean and is not really competitive in
the acceptance model of most college programs, whereas a score of 650 is
1.5
SD
above the mean and is considered to be quite competitive in most
programs.
The scores of each participant in our example, organized by group,
are shown in the top portion of Table 6.1. This table also contains some
computational results that we will discuss in Section 6.5. The trend of
the data, stated informally, appears to be that greater periods of study
generally seem to have resulted in better performance on the SAT.
6.3 PARTITIONING THE TOTAL VARIANCE INTO ITS SOURCES
We have already computed the ANOVA for our numerical example, and
the results are shown in the summary table in Table 6.2. In Sections 6.5
and later, we will outline how the ANOVA is performed; for now, our
focus is on the results. Because it is a one-way design, the summary
table is structured exactly as we have already talked about in Chapter 3.
The numbers were calculated by hand and so will differ slightly (from
rounding effects) from the output of SPSS and SAS. Briefly, here are the
highlights.
The total variance (
SS
T
) is associated with 34
df
(
df
T
). This is because
there are thirty-five observations (elements of data) in the data set (five
groups with seven observations in each) and the
df
T
is calculated as one
minus the total number of observations.
Study time
is the source of variance representing the independent
variable. It is composed of five levels (groups) and so its
df
A
=
1
or 4. Its mean square (
MS
A
) as shown in the summary table in Table 6.1
was computed by hand to be 57624.14. This was obtained by dividing
the study time sum of squares by the study time degrees of freedom
(230496
5
−
.
57
÷
4
=
57624
.
286).
A
is short for the within-groups source of variance. It rep-
resents variability within each group despite the fact that all the students
in a particular group studied for the same length of time, and has 30
df
S
/
A
.
This is because each group has seven cases and therefore 6
df
.Sincethere
are five groups, there are 6
Error or
S
/
×
5
=
30
df
for
df
S
/
A
.
