Re: [ccp4bb] Question about the statistical analysis-might be a bit off topic
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 Diederichshttp://strucbio.biologie.uni-konstanz.de > email: kay.diederi...@uni-konstanz.deTel +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". > >
Re: [ccp4bb] Question about the statistical analysis-might be a bit off topic
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 Diederichshttp://strucbio.biologie.uni-konstanz.de email: kay.diederi...@uni-konstanz.deTel +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". smime.p7s Description: S/MIME Cryptographic Signature
Re: [ccp4bb] Question about the statistical analysis-might be a bit off topic
Just so that an actual answer appears in the archives of the CCP4BB: If you define C = A/B and also define sig(X) as the standard deviations of "X", where X can be A,B or C, then you can get sig(C) from: (sig(C)/C)^2 = (sig(A)/A)^2 + (sig(B)/B)^2 Note the subtle difference from the rule for propagating errors through addition and subtraction! Basically, when you are adding or subtracting, the total error is: sig(A+B)^2 = sig(A)^2 + sig(B)^2 or: the square root of the sum of the squares of all the individual "sigmas". But, when multiplying or dividing it is the "percent error" rather than the "sigma" itself that you run through the root-sum-square calculation. It is interesting I think that you get the SAME rule for multiplying or dividing. Errors always increase. As usual, all this assumes that the errors come from a Gaussian (normal) distribution and that fluctuations in A are "uncorrelated" to fluctuations in B. Other distributions or correlated errors will have different propagation rules, and for those you might want to actually read a statistics book. -James Holton MAD Scientist On Sat, 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. >
Re: [ccp4bb] Question about the statistical analysis-might be a bit off topic
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.
Re: [ccp4bb] Question about the statistical analysis-might be a bit off topic
http://en.wikipedia.org/wiki/Propagation_of_uncertainty From: CCP4 bulletin board [mailto:CCP4BB@JISCMAIL.AC.UK] On Behalf Of capricy gao Sent: Saturday, June 04, 2011 10:45 AM To: CCP4BB@JISCMAIL.AC.UK Subject: [ccp4bb] Question about the statistical analysis-might be a bit off topic If means and standard deviations of A and B are known, how to estimate the variance of A/B? Thanks.
[ccp4bb] Question about the statistical analysis-might be a bit off topic
If means and standard deviations of A and B are known, how to estimate the variance of A/B? Thanks.
