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Re: st: RE: AW: ratio function


From   Jeph Herrin <jeph.herrin@yale.edu>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: RE: AW: ratio function
Date   Fri, 02 Apr 2010 07:53:06 -0400

if you know the mean (E) and variance (V) of X and Y, you can calculate
the first order approximation:

  E(X/Y) = E(X)/E(Y)
  V(X/Y) = E(X/Y)^2 * (V(X)/E(X)^2 + V(Y)/V(Y)^2 + COV(X,Y)/E(X)E(Y))

at least, that's what they taught us in physics lab.

hth,
Jeph


Roman Kasal wrote:
I don't agree...so how to do it when you want to find out ratio between
years, male X female, ...? So there is no solution? Just to keep N,mean,
SE, degrees of freedom, N_strata, N_psu, .... and calculate it manually?
I think it is not appropriate solution, at least to have it as an
option. I think there is missing a lot with complex survey in Stata and
complex survey is needed for almost every survey research, even freeware
R-project is better equipped :(

so have a hope Stata will get it soon....immediately we are buying it
again :)


And it should.   Data (x,y) (1,2) (2,4) (3,6) (100,.)    will give an
entirely different view of the data if the unpaired observation is
included in a mean or ratio calculation.  Or consider data with x
missing in half the pairs and y missing in the other half; the ratio
of means would be meaningless.

The formulas for standard errors for ratios  assume that the data are
paired. Formally, they are based on the residual MSE of a regression
of y on x through the origin. You cannot do that regression with
unpaired data.

If your concern is missing data, the solution is to impute the missing
values before analysis.

Steve


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