```Date: Fri, 23 Jan 2004 14:17:40 -0500 Reply-To: "Elmaache, Hamani" Sender: "SAS(r) Discussion" From: "Elmaache, Hamani" Subject: Re: confidence interval for a quotient of two means Comments: To: julie 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 ```

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