What is the geometric standard deviation of a value, which is the result of dividing two independent values, each of which has its own geometric standard deviation ?
It is a frequent situation in science, that the the signal of the machines is in linear relationship to the logarithm of the analysed quantity, so it is appropriate to use geometric standard deviation to characterize the the error of the measured quantity. (I calculated geometric mean and geometric standard deviation from triplicate measurements for each value). Now I want to divide two such quantity values (one by another) to obtain a relative concentration. What will be the geometric standard deviation of the relative concentration ?
(I assume, that the two original values are independent - I do not want to deal with covariances etc.)