OK....I'm going out on a limb here and I'm sure there will be much
castigation for my strategy but here goes........
On page 67 in Cohen's (1988) power analysis text, equation 2.5.3 offers the
standardized mean difference:
(d subscript s) = t * sqrt ((n1 + n2)/(n1*n2)), so I decided to work
backwards given the following:
r = .5
n1 = 40 (sample size for group1)
n2 = 40 (sample size for group2)
then t = (.5*sqrt (80-2))/(sqrt 1 - .25) = 4.41588/.866 = 5.099168
So, given Cohen's formula: d subscript s = 5.099168*sqrt(( 40 + 40)/(40 *
40)) = 1.1402
I then turn to page 22 and refer to Table 2.2.1 (Equivalents of d) and
notice that when d = 1.1402 (interpolation necessary!) then the fifth column
(i.e., r), r = .482 when d = 1.1 and r = .514 when d = 1.2, so that comes
rather close to .5................
So you can indeed derive r from t but you will need to know the sample sizes
for each of the groups..............hope this helps.........dale glaser
Dale Glaser, Ph.D.
Senior Statistician, Pacific Science & Engineering Group
Adjunct faculty/lecturer, SDSU/USD/CSPP
San Diego, CA
-----Original Message-----
From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED]]
On Behalf Of Jason Osborne, Ph.D.
Sent: Friday, June 23, 2000 2:33 PM
To: [EMAIL PROTECTED]
Subject: Stupid question on relationship of r and t
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I am working on a power analysis project- we are reviewing old journal
articles to calculate observed effect sizes and power. Some of these
articles, for example reporting t-test results, only give means and
t-test, no standard deviation. thus, no effect size calculation is
possible. I was hoping to estimate an effect size by converting a t to
an r. I seem to remember a formula that relates the two, but am having
a dickens of a time tracking one down. The one I did track down, for
calculating t from r, is not that helpful:
t= r * sqrt(n-2)
-------------
sqrt(1-r^2)
I want to be able to calculate r from t. I tried algebraically
manipulating the formula, but never quite got it to where I could do
this. Any advice?
Alternatively, a formula for converting t or F to eta-squared, which is
roughly analogous to r-squared, would also be helpful (I know they are
not exactly analogous).
Thanks in advance,
Jason
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