If I have Q= ab/cd, with a,b,c and d representing means of independent abundance measurements and each with known SD, I want to calculate the SD in Q by adding the Coefficients of Variation in quadrature and multiplying with Q. I think this is standard practice when assuming independence of variables. What is counter-intuitive (to me) is to see that the error in Q depends on whether the ratio is taken as (ab/cd) or as (cd/ab) or any other combination of the same variables. I would expect that the resulting error should only depend on the four underlying errors and not on the way the means are combined, but this seems inevitable when fractional uncertainties are added in quadrature. Can anyone comment and perhaps advise?
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