Re: Correlation ratio = eta-squared, or eta?


Ray Koopman wrote:
Bruce Weaver wrote:
I remember learning that "correlation ratio" is another name for
eta-squared, where eta-squared = 1 minus (SS_within/SS_Total) in a
one-way ANOVA design. (I just consulted my old Glass & Hopkins and
verified that my memory was not faulty.) However, when I Google on
<correlation ratio>, I get some pages that tell me correlation ratio =
eta, not eta-squared. Can anyone shed any light on this? Has the
definition changed? Do different fields use different terminology?

I ask because I was just revising some class notes, and was going to
write that eta-squared is sometimes called the "correlation ratio".

Cheers,
Bruce
--
Bruce Weaver
bweaver@xxxxxxxxxxxx
www.angelfire.com/wv/bwhomedir

Hays (1963, pp 325 & 547) defines eta-squared = SS_between/SS_total
and calls it the correlation ratio.

Winer, Statistical Principles in Experimental Design, 2nd ed, 1971,
page 115: "The square of the product-moment correlation between Yij and
Mj is given by [formula, basically Variance of expected Y / Variance of
Y]. This squared product-moment correlation is called the correlation
ratio and is denoted by the symbol Eta^2yx"

I'd suggest avoiding the term "correlation ratio" at all costs, since
there seem to be common references on both sides of the issue.

Using "correlation ratio" for Eta^2 doesn't seem to make much sense to
me, since Eta^2 is analogous to R^2, and r is a "correlation", not R^2.

.