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additive; that is, if one effect accounted for 8 percent of the total variance
and another accounted for 12 percent of the total variance, we could say
that the two effects together accounted for 20 percent of the total variance.
The eta squared value is the proportion of the total variance as indexed
by the sum of squares that is accounted for by the between-groups source of
variance. In the present room color example, it can be seen from Table 3.2
that we obtained an eta squared value of .610 (87
610).
If these were the results of an actual study, we would conclude that the
color of the room in which students took the mood survey accounted for
61percentofthevarianceinthemoodscores.Itisappropriatetouse
the Greek letter for eta (
.
50
÷
143
.
50
=
.
) when reporting it. Thus, the portion of the
F
statement containing eta squared values is written as follows:
η
2
η
=
.
610
.
4.5.4 PARTIAL ETA SQUARED
In some of its procedures, SPSS reports a statistic known as a partial
eta squared value. This is a variation of the eta squared measure already
described, focusing directly on the effect and the error associated with it.
Keeping with the present one-way design as an example, both eta squared
and partial eta squared values use
SS
A
as the numerator. Eta squared uses
the total sum of squares,
SS
To t a l
,asthedenominator;however,tocompute
partial eta squared we use
SS
A
+
SS
S
/
A
as the denominator.
In a one-way between-subjects ANOVA design, where
SS
To t a l
SS
A
+
SS
S
/
A
, the values for eta squared and partial eta squared will be equal.
However, for all of the other designs that we describe in this topic, the
two measures will yield different values for one of both or the follow-
ing reasons. First, there will be additional independent variables whose
variance will contribute to the denominator of eta squared (the total sum
of squares,
SS
To t a l
) but not contribute to the denominator of partial eta
squared. Second, in within-subjects designs described in Chapters 10-12,
we will see that there are several different error terms as a result of the vari-
ance partitioning process. The partial eta squared measure is computed
with the error term (e.g.,
SS
S
/
A
) specific to the effect (e.g.,
SS
A
)repre-
sented in the denominator. Because of these issues, and unlike eta squared
values, partial eta squared values are not additive across the effects, and
the interpretation of this strength of effect measure is therefore somewhat
different than that of eta squared values. We will focus on the eta squared
value rather than the partial eta squared value as the index of strength of
effect that we will use in this topic.
=
4.5.5 COHEN'S
d
Jacob Cohen (1969, 1977, 1988) suggested looking at the potency of the
treatment effect by examining what he called “effect size.” It bears a similar-
ity to the approach used in calculating the
t
test (discussed in Section 4.8).
Cohen proposed that the mean difference can be judged relative to the
