Kay, the usual propagation-of-uncertainty formulae are based on a first-order approximation of the Taylor series expansion, i.e. assuming that 2nd and higher order terms in the series are can be neglected. This is clearly not the case if B is small relative to its uncertainty: you would need to include higher order terms. See the 'Caveats and Warnings' section in the Wikipedia article that Bernhard quoted.
Cheers -- Ian On Tue, Jun 7, 2011 at 8:59 AM, Kay Diederichs < kay.diederi...@uni-konstanz.de> wrote: > what I'm missing in those formulas, and in the Wikipedia, is a discussion > of the prerequisites - it seems to me that, roughly speaking, if the > standard deviation of B is as large or larger than the absolute value of the > mean of B, then we might divide by 0 when calculating A/B . This should > influence the standard deviation of the calculated A/B, I think, and seems > not to be captured by the formulas cited so far. > > best, > > Kay > > Am 20:59, schrieb James Stroud: > >> The short answer can be found in item 2 in this link: >> >> http://science.widener.edu/svb/stats/error.html >> >> The long answer is "I highly recommend Error Analysis by John Taylor:" >> >> http://science.widener.edu/svb/stats/error.html >> >> If you can find the first edition (which can fit in your pocket) then >> consider yourself lucky. Later editions suffer book bloat. >> >> James >> >> >> On Jun 4, 2011, at 10:44 AM, capricy gao wrote: >> >> >>> If means and standard deviations of A and B are known, how to estimate >>> the variance of A/B? >>> >>> Thanks. >>> >>> >> > > -- > Kay Diederichs http://strucbio.biologie.uni-konstanz.de > email: kay.diederi...@uni-konstanz.de Tel +49 7531 88 4049 Fax 3183 > Fachbereich Biologie, Universität Konstanz, Box 647, D-78457 Konstanz > > This e-mail is digitally signed. If your e-mail client does not have the > necessary capabilities, just ignore the attached signature "smime.p7s". > >
