Date: Wed, 24 Jan 2001 15:27:25 -0500
Reply-To: ahutson@BIOSTAT.UFL.EDU
Sender: "SAS(r) Discussion" <SAS-L@LISTSERV.UGA.EDU>
From: Alan Hutson <ahutson@BIOSTAT.UFL.EDU>
Organization: University of Florida, Dept. of Statistics
Subject: Re: Confidence Intervals For Proportions
Content-Type: text/plain; charset=us-ascii
I would suggest reading
Agresti, A and Coull, B
Approximate is better than "exact" for interval
estimation of binomial proportions. Amer. Statist. 52 (1998), no. 2,
119--126.
A simple modification of the approximate interval will provide
much more accurate confidence intervals than the "exact" method
Best
Alan
John Jones wrote:
>
> This macro will calculate the exact confidence interval not the normal
> approximation.
>
> jj
>
> /*************************************************************************
> * %CI_Prop(Alpha=, N=, M=, ds=) where,
> *
> * Alpha = Area outside the confidence region
> * N = Denominator; number at risk (variable)
> * M = Numerator; number of events (variable)
> * ds = Dataset to calculate confidence intervals
> *
> * Example: %CI_Prop(Alpha=.05, N=N, M=M, ds=ds)
> *
> * Reference: Handbook of Tables for Probability and
> * Statistics, 2nd Edition, pages 219-237
> * William H. Beyer
> ******************************************************************************/
> %Macro ci_prop(alpha=, N=, M=,ds=);
>
> *--{UPPER LIMIT: estimation}--;
> data Upper;
> retain cntr 0;
> set &ds ;
> cntr+1;
> *--{2 SIDED: confidence interval}--;
> cutoff=input(symget('alpha'),8.)/2;
> *--{INTERATE: over the parameter space}--;
> do ul=0 to 1 by .0001;
> if (ul<=1) then alpha=ProbBnml(ul,&N,&M);
> *--{ALL: alpha estimates that are less than equal to the limit}--;
> if (alpha<=cutoff) then output;
> end;
> run;
> proc sort; by cntr cutoff alpha; run;
>
> *--{UPPER LIMIT: that closest estimates the cutoff}--;
> data Upper;
> set Upper;
> by cntr cutoff alpha;
> if (last.cutoff=1);
> drop alpha;
> run;
>
> *--{LOWER LIMIT: estimation}--;
> data Lower;
> retain cntr 0;
> set &ds ;
> cntr+1;
> *--{2 SIDED: confidence interval}--;
> cutoff=input(symget('alpha'),8.)/2;
> *--{INTERATE: over the parameter space}--;
> do ll=0 to 1 by .0001;
> if (ll<=1) then alpha=ProbBnml(ll,&N,&N)-ProbBnml(ll,&N,(&M-1));
> if (alpha<=cutoff) then output;
> end;
> run;
> proc sort; by cntr cutoff alpha; run;
>
> *--{LOWER LIMIT: that closest estimates the limit}--;
> data Lower;
> set Lower;
> by cntr cutoff alpha;
> if (last.cutoff=1);
> drop alpha;
> run;
>
> *--{FINAL DATASET: label and confidence interval}--;
> data CI_Prop;
> merge lower upper;
> by cntr cutoff;
> length _label_ $6 CI_Prop $14 CI_pct $12;
> _label_=trim(left(put(100*(1-&alpha),8.)))||'% CI';
> CI_Prop='('||trim(left(put(ll,8.3)))||', '||trim(left(put(ul,8.3)))||')';
> CI_Pct ='('||trim(left(put(round(100*ll),3.)))||'%,
> '||trim(left(put(round(100*ul),3.)))||'%)';
> drop cntr;
> label _label_='Description of CI_Prot and CI_Pct'
> CI_Prop='Confidence Interval for Proportions'
> CI_Pct ='Confidence Interval for Percentages';
>
> put '$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$>';
> put '$$$';
> put "$$$ Alpha=&alpha., N=&N., M=&M";
> put '$$$';
> put '$$$ ' _label_ '= ' CI_Prop;
> put '$$$ ' _label_ '= ' CI_Pct;
> put '$$$';
> put '$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$>';
>
> run;
>
> *--{CLEANUP:}--;
> proc datasets nolist;
> delete upper lower /memtype=data;
> run;
> quit;
>
> %Mend ci_prop;
>
> At 03:14 PM 1/24/01 -0500, Victor Kamensky wrote:
> >Hi,SAS-L-ers!
> >I am looking for the way(s) to calculate
> >confidence intervals for proportions,
> >(i.e. percents in contingency tables).
> >PROC FREQ is most probable place for it,
> >but looks like it is not in the documentation
> >(did I miss it in ONLINE DOCS and books?).
> >(As much as I know, the formula is
> > the following:p+(-) 1.96*sqrt(p*(1-p)/n)).
> >I think it could be implemented as a macro
> >(based on PROC FREQ output data sets).
> >Did someone do it already?
> >Victor Kamensky
> >Programmer
> >Albert Einstein College of Medicine
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