Transforming
t= r * sqrt(n-2)
-------------
sqrt(1-r^2)
gives
r^2 = t^2 / (t^2+n-2)
t and r must have the same sign, so taking the square root gives:
r = t / sqrt(t^2+n-2)
Nice and simple.
Regards.
Alan
Dale Glaser wrote:
> 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
>
> This is a multi-part message in MIME format.
> --------------D067C2990B362FB062366649
> Content-Type: text/plain; charset=us-ascii
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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
> --------------D067C2990B362FB062366649
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> org:Department of Educational Psychology;University of Oklahoma
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>
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--
Alan McLean (alan.buseco.monash.edu.au)
Department of Econometrics and Business Statistics
Monash University, Caulfield Campus, Melbourne
Tel: +61 03 9903 2102 Fax: +61 03 9903 2007
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