[BioC] standard deviation from log to normal scale???

[Wolfgang Huber]

Hi Jesper,

the asymmetry only becomes appreciable when SD(X)/X = SD(A) (btw this is
called the coefficient of variation) becomes big; say, much bigger than
0.1 (=10%). You can see this from the power series of the exponential
function. e^x = 1 + x + O(x^2), and the quadratic and higher order terms
that cause the asymmetry become non-negligible when |x|>>0.

 Hope this helps
 Wolfgang



> Here is just a lil "trivia" statistic question for the forum:-) I  
> apologize for my clumsy annotation but i hope I get the question  
> through anyhow:-)
> 
> 
> For ratios I take it its normal procedure to calculate the average as  
> the geometric mean. That is easiest done with log transformed values,  
> giving something like
> 
> <R> = mean(Ratio=a/b)=2^ (<log2(a)> - <log2(b)> + - SD)
> 
> Its the SD thats giving me a little headache as i go back to normal  
> (un-transformed, i use ** for annotating normal) values. SD in log  
> space is not symmetric in normal space, so SD** != 2^(SD)? or?
> 
> To illustrate my clumsy annotation, if : < log2(R) > + - SD(log2(R))  
> =  4+-1 in log space it becomes (2^4- 2^3) and 2^4+2^5 ~ 16-8 and 16  
> + 32. so SD** is not symmetric.
> 
> 
> I found 2 suggestions in the litterature that doesnt seem to account  
> for this asymmetry. One was giving the standard deviation of the  
> geometric mean to be SD**=2^(SD) just as i reasoned was inappropriate?
> 
> Another suggestion I found was for propagating errors for exponential  
> transformation :
> 
> X = e^A, 	SD(X)/X = SD(A)
> 
> So should i do SD**(X) = mean(X) * SD(A)  ---  X ~ Ratio and A ~ log 
> (R) ???? again i dont see how this solved the asymmetric SD from the  
> log space???
> 
> Maybe i missed something basic with log-normal distributions, in any  
> case any help will be highly appreciated:-)  I have the feeling its  
> rather trivial but I would really like to know how to put  
> (assymetric?) error bars on my (normal scale) ratios correctly. This  
> goes for both Affymterix summary ratios  and RT-PCR ratios. What's  
> the correct procedure???
> 
> 
> cheers:-)
> jesper ryge
> Karolinska Institutet
> Dep. of Neuroscience
> 
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Wolfgang Huber  EBI/EMBL  Cambridge UK  http://www.ebi.ac.uk/huber