[R] variance of combinations of means - off topic

[Kent Holsinger]

Bill Shipley wrote:
> Hello, and please excuse this off-topic question, but I have not been
> able to find an answer elsewhere.  Consider a value Z that is calculated
> using the product (or ratio) of two means X_mean and Y_mean:
> Z=X_mean*Y_mean.  More generally, Z=f(X_mean, Y_mean).  The standard
> error of Z will be a function of the standard errors of the means of X
> and Y.  I want to calculate this se of Z.  Can someone direct me to a
> reference (text book or other) that gives the solution to this *general*
> problem?
> 

Kendall's Advanced Theory of statistics (sect. 10.6, p. 324 in the 5th 
edition) provides an approximate expression for the variance of a ratio 
(based on the delta method already mentioned).  Sect. 11.9 and following 
provides a general discussion of the distribution of a ratio, and some 
special cases (F-ratio, ratio of standard normals).

Kent

-- 
Kent E. Holsinger                kent at darwin.eeb.uconn.edu
                                  http://darwin.eeb.uconn.edu
-- Department of Ecology & Evolutionary Biology
-- University of Connecticut, U-3043
-- Storrs, CT   06269-3043