Date:         Fri, 23 Jan 2004 14:17:40 -0500
Reply-To:     "Elmaache, Hamani" <Hamani.Elmaache@CCRA-ADRC.GC.CA>
Sender:       "SAS(r) Discussion" <SAS-L@LISTSERV.UGA.EDU>
From:         "Elmaache, Hamani" <Hamani.Elmaache@CCRA-ADRC.GC.CA>
Subject:      Re: confidence interval for a quotient of two means
Comments: To: julie <catttss@YAHOO.COM>
Content-Type: text/plain; charset="iso-8859-1"

Hi julie.

/*
  The delta method provides a method of approximating Var[g(X, Y)]
where X and Y are random variables with means EX and EY respectively
and their variance as well as the covariance of A and B are known.
The Taylor series for g(X,Y) about (EX, EY), truncated after the linear
terms,
can be written
g(X, Y)~ g(EX,EY) + (X -EX)dg(EX,EY)/dX + (Y -EY)dg(EX,EY)/dY.
Thus
Var[g(X, Y)] ~ [dg(EX,EY)/dX]**2[Var(X)] +[dg(EX,EY)/dY]**2[Var(Y)] +
2[dg(EX,EY)/dX][dg(EX,EY)/dY]Cov(X, Y).

 Here the d-/dX  and d-/dY refer to partial derivatives according to X and
Y.
*/
proc corr data=sashelp.class cov ;
var weight height;
run;
/*
Variable         N        Mean     Std Dev

Weight=X          19   100.02632    22.77393
Height=Y          19    62.33684     5.12708

and covariance = 26.2869006

*/

Here  g=X/Y

==>dg(X,Y)/dX=1/Y  so  dg(EX,EY)/dX=1/62.33684 =0.016041878
==>dg(X,Y)/dY=-X/Y**2  so
dg(EX,EY)/dY=-100.02632/(62.33684**2)=-0.025740959
and Cov(X, Y)=26.2869006.

So
Var[g(X, Y)] ~ (0.016041878**2)*(22.77393)**2 +((-0.025740959)**2)*(5.12708
)**2 +
- 2*0.016041878*0.025740959*26.2869006 =0.12918.

So Std Dev of g is 0.35941


-----Original Message-----
From: julie [mailto:catttss@YAHOO.COM]
Sent: January 23, 2004 11:52 AM
To: SAS-L@LISTSERV.UGA.EDU
Subject: confidence interval for a quotient of two means


I will like to know How I can get the confidence interval of a ratio of two
means

Let's say I have two independent group with

group1 N=100, mean=10 , std=1.5
group2 N=150, mean=8 , std=2

The ratio of that is 10/8=1.25 How I can get the confidence interval of
that?

Thank you for the help