Date:         Thu, 12 Jun 2003 11:10:53 -0700
Reply-To:     Dale McLerran <stringplayer_2@YAHOO.COM>
Sender:       "SAS(r) Discussion" <SAS-L@LISTSERV.UGA.EDU>
From:         Dale McLerran <stringplayer_2@YAHOO.COM>
Subject:      Re: Proc Corr??
Comments: To: "Ian(freeserve)" <ian@AZORUBINE.FREESERVE.CO.UK>
In-Reply-To:  <000e01c330c2$6fd7ace0$2e56893e@UKsolad281>
Content-Type: text/plain; charset=us-ascii

Ian,

It might be OK for large samples, but does not provide
acceptable confidence limits for the small sample problem
offered in your post.  The Fisher Z confidence limits for
the data you present are (0.448, 0.961), while the mixed
model approach gives confidence limits of (0.649, 1.032).
The MIXED approach assumes that the correlation is normally
distributed, which is only a reasonable assumption for
large samples.

Dale


--- "Ian(freeserve)" <ian@AZORUBINE.FREESERVE.CO.UK> wrote:
> PROC MIXED can be used to find a confidence interval for
> a correlation coefficient.  The idea appeared recently on
> the allstat discussion list, see:
>
> http://www.jiscmail.ac.uk/cgi-bin/wa.exe?A1=ind0306&L=allstat
>
> I have used this to produce a small example below.  The
> Toeplitz covariance parameter and the assoiciated Wald test
> give the estimate of the correlation coefficient and the CI.
>
> data corr;
>   input x y;
>   obs=_n_;
>   cards;
>   12 19
>   10 15
>   15 23
>   16 16
>   19 21
>   23 25
>   25 21
>   27 26
>   31 30
>   36 27
> ;
> proc corr data=corr nosimple;
>   var x;
>   with y;
> /* Rearrange the data so both x and y are contained in
>    the new variable Y1
> */
> proc transpose data=corr out=corrlong name=varname prefix=y;
>   by obs;
> proc mixed data=corrlong alpha=0.05 cl=wald;
>   class varname obs;
>   model y1=varname /notest;
>   repeated varname / type=toeph subject=obs;
> run;
>
> Dale, does this seem reasonable to you?
>
> Ian.
>
> Ian Wakeling
> Qi Statistics.
>
> > Date:    Wed, 11 Jun 2003 17:38:09 -0700
> > From:    Dale McLerran <stringplayer_2@YAHOO.COM>
> > Subject: Re: Proc Corr??
> >
> > Dennis,
> >
> > I don't believe that SAS produces confidence intervals about
> > the correlation.  You will have to compute your own confidence
> > limits by first applying the Fisher Z transformation
> >
> >     Z = 0.5 * log((1+corr)/(1-corr))
> >
> > The variance of Z is 1/(n-3).  Now compute confidence intervals
> > for Z, assuming Z ~ normal.
> >
> >     Z(L) = Z - 1.96*sqrt(1/(n-3))
> >     Z(U) = Z + 1.96*sqrt(1/(n-3))
> >
> > Back transform the confidence limits for Z to confidence limits
> > on rho.
> >
> >    rho(L) = (exp(2*Z(L) - 1) / (1 - exp(2*Z(L)))
> >    rho(U) = (exp(2*Z(U) - 1) / (1 - exp(2*Z(U)))
> >
> > Dale
> >
> >
> > --- "Dennis G. Fisher" <dfisher@CSULB.EDU> wrote:
> > > How does one obtain the confidence intervals for a correlation?
> I
> > > do
> > > not see any mention of it in the version 8 Procedures guide for
> Proc
> > > Corr.  Is there somewhere else I should be looking???  TIA
> > > Dennis fisher
> > >
> > > --
> > > Dennis G. Fisher, Ph.D.
> > > Director
> > > Center for Behavioral Research and Services
> > > 1090 Atlantic Avenue
> > > Long Beach, CA 90813
> > > 562-495-2330
> > > 562-983-1421 fax


=====
---------------------------------------
Dale McLerran
Fred Hutchinson Cancer Research Center
mailto: dmclerra@fhcrc.org
Ph:  (206) 667-2926
Fax: (206) 667-5977
---------------------------------------

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