Taking the binary logarithm - error propagation?

Biochemist

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Aug 30, 2016
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Hi,

I have a set of data consisting of for example 10 numerical values. Let's call these x1 to x10. x1 to x10 have a certain standard deviation, which I calculate by using the general formula for the standard deviation for samples.

Then, I convert these values by taking the binary logarithm: log2(x)

From this, I get 10 new numerical values. I can calculate the new sample standard deviation for these based on the general formula for standard deviation and the individual values or I can use the rules for the Gaussian error propagation to calculate the new standard deviation (see formula below, here I named the new error delta(z)).

I get different results using one or the other method. Which way of calculating the standard deviation is correct (and why)?
 
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