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4.5.3 ETA SQUARED
Eta squared is also known as
R
2
(Kirk, 1995) and as the
correlation ratio
(Guilford & Fruchter, 1978). This statistic is descriptive of the data in
the sample rather than being an estimate of some population parameter.
Eta is a correlation coefficient and therefore varies between zero and one.
Because it is based on a correlation coefficient, eta squared (
2
) can be
directly interpreted as the proportion of total variance of the dependent
variable that is accounted for or explained by (or associated with) the
independent variable in the sample data set. Eta squared will typically
yield a value higher than the estimated omega squared value by about .08
or so (Meyers et al., 2006); it is the strength of the effect index that we will
useinthisbook.
Most professional organizations, such as the American Psychological
Association (APA), strongly encourage researchers to report strength of
effect indexes in addition to statistical significance information, and many
journals are now requiring such reporting in the manuscripts that they
review for publication (APA, 2001; Wilkinson et al., 1999). You are there-
forewelladvisedtoalwayssupplythisinformationwhenreportingthe
F
ratio.
The interpretation of whether the eta squared value is “high” or not
is a relative matter, depending on the context of the research. Kirk (1995,
p. 178), citing work done by Jacob Cohen, suggested that, in the absence
of other criteria, omega squared values of .01, .06, and .14 or greater
could be described in the behavioral sciences as small, medium, and large,
respectively. That translates to approximate eta squared values of .09,
.14, and .22 or greater. Kirk (1996) also talked about a concept of
prac-
tical significance
and Thompson (2002) added to that a notion of
clinical
significance.
The point that Kirk and Thompson emphasized was that we
should take into account the context within which we will use the infor-
mation that the independent variable produces a particular effect rather
than exclusively focusing on the statistical significance of the result. In
such a light, it is possible that researchers will be thrilled in one context
with an eta squared value of .10 or less while being disappointed in another
context with an eta squared value of .20. The “potency” of an effect is a
judgment made by researchers; it is therefore a somewhat subjective eval-
uation informed by and relative to the state of theory and research within
the particular topic area representing the research study.
Eta squared is the proportion of total variance attributable to the
independent variable. It is computed as follows:
η
SS
A
SS
To t a l
.
2
η
=
(4.3)
Because it is based on the percentage of total variance in the data set, in
designs containing more than one independent variable the eta squared
values associated with each of the effects partitioned in the ANOVA are
