Re: st: RE: AW: ratio function

[Jeph Herrin <jeph.herrin@yale.edu>]

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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