Information Technology Reference
In-Depth Information
Dependent Variable: satscore satscore
Sum of
Squares
Source
DF
Mean Square
F Value
Pr
>
F
SS
S/A
Model
43.47
<
.0001
4
30
34
230497.1429
39771.4286
270268.5714
57624.2857
1325.7143
Error
Corrected Total
satscore Mean
R-Square
Coeff Var
Root MSE
0.852845
6.800227
36.41036
535.4286
SS
A
Source
DF
Mean Square
F Value
Pr
>
F
Type III SS
group
4
230497.1429
57624.2857
43.47
<.0001
Figure 6.19
TheoutputoftheANOVA.
The middle portion of Figure 6.19 presents what SAS calls
R-Square
;
this is what we have been labeling as
eta squared
(
2
) and is equivalent to
our hand-calculated value. It is keyed to the
Model
sum of squares and
is the proportion of the total sum of squares accounted for by the model.
In designs with more than a single independent variable, we will wish
to compute the separate eta squared values associated with each of the
statistically significant effects.
In addition to the
RSquare
, SAS provides three other pieces of infor-
mation in that middle table. The
Coeff Var
is the
coefficient of variation;
it
is the ratio of the standard deviation of the sample as a whole to the mean
of the sample as a whole and can be useful in comparing the variability
of different distributions. The
Root MSE
,the
root mean squared error
,is
the square root of the mean square associated with the error variance (i.e.,
the square root of 1325.7143 is 36.41036).
Satscore Mean
is the overall or
grand mean of the sample as a whole.
η
6.10 COMMUNICATING THE RESULTS
Based on the omnibus ANOVA, we know that the independent variable
is associated with a statistically significant and substantial effect size. This
portion of the results can be communicated in a simple sentence:
The amount of preparation for the SAT in which students engaged appeared
to
significantly
affect
their
performance
on
the
test,
F
(4, 30)
=
43
.
47,
2
p
<.
05,
η
=
.
853.
Note that we cannot address the issue of which means differ from
which other means with the information obtained from the omnibus
analysis. In Chapter 7, we will consider a variety of ways to assess mean
differences.
