Jason --
t^2 = r^2*(n-2)
-----------
(1-r^2)
is a special case of the more general case of using R^2 to compute
the F statistic in a Prediction/Regression/Linear Models approach to
research studies.
Letting
R^2(Assumed) = R^2 for the ASSUMED MODEL
R^2(Restricted) = R^2 for the RESTRICTED MODEL
NA = number of linearly independent predictor vectors (i.e., the number of
parameters) in the ASSUMED MODEL.
NR = number of linearly independent predictor vectors (i.e., the number of
parameters) in the RESTRICTED MODEL
N = total number of observations (cases)
df1 = NA - NR =numerator degrees of freedom
df2 = N - NA =denominator degrees of freedom
F(df1,df2) = (R^2(Assumed) - R^2(Restricted))/(df1)
-----------------------------------------------
(1 - R^2(Assumed))/(df2)
Now consider the your special case when:
The ASSUMED MODEL CONTAINS ONLY TWO PREDICTORS:
Y = b0*U + b1*X + Ea
and the Hypothesis is "b1 = 0"). Then the RESTRICTED MODEL is:
Y = b0*U + Er
In this special case,
R^2(Restricted) = 0
and then
F(df1,df2) = (R^2(Assumed)/(df1)
-----------------------------------------------
(1 - R^2(Assumed))/(df2)
and you can easily solve for R^2 if desired.
R^2(Assumed) = F*(df1)
-------------------
(df2) + F*(df1)
and in your special case of only ONE predictor (in addition to, U),
sometimes called "simple regression".
df1 = 2 - 1 = 1
and
df2 = N - 2
R^2(Assumed) = r^2 = F
------------
N - 2 + F
but since
t^2(df2) = F(1,df2)
then we have
r^2 = t^2
-----------------
N - 2 + t^2
which is what you obtain from Bob's
suggestion --
> > 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?
> >
> Try squaring both sides and re-arranging. ( Joe Ward's comment "GOOD
SUGGESTION BY BOB")
>
> Bob
>
> --
> Bob O'Hara
> Metapopulation Research Group
> Division of Population Biology
> Department of Ecology and Systematics
> PO Box 17 (Arkadiankatu 7)
> FIN-00014 University of Helsinki
> Finland
>
> tel: +358 9 191 7382 fax: +358 9 191 7301
> email: [EMAIL PROTECTED]
> To induce catatonia, visit:
> http://www.helsinki.fi/science/metapop/
----- Original Message -----
From: "Anon." <[EMAIL PROTECTED]>
To: <[EMAIL PROTECTED]>
Sent: Saturday, June 24, 2000 7:20 AM
Subject: Re: Stupid question on relationship of r and t
> "Jason Osborne, Ph.D." wrote:
> >
> > 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?
> >
> Try squaring both sides and re-arranging.
>
> Bob
>
> --
> Bob O'Hara
> Metapopulation Research Group
> Division of Population Biology
> Department of Ecology and Systematics
> PO Box 17 (Arkadiankatu 7)
> FIN-00014 University of Helsinki
> Finland
>
> tel: +358 9 191 7382 fax: +358 9 191 7301
> email: [EMAIL PROTECTED]
> To induce catatonia, visit:
> http://www.helsinki.fi/science/metapop/
>
> I have yet to see any problem, however complicated, which, when you
> looked at it in the right way, did not become still more complicated. -
> Poul Anderson
>
>
>
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