[time-nuts] σ vs s in ADEV

Scott Stobbe scott.j.stobbe at gmail.com
Mon Jan 9 13:41:34 EST 2017

I could be wrong here, but it is my understanding that Allan's pioneering
work was in response to finding a statistic which is convergent to 1/f
noise. Ordinary standard deviation is not convergent to 1/f processes. So I
don't know that trying to compare the two is wise. Disclaimer: I could be
totally wrong, if someone has better grasp on how the allan deviation came
to be, please correct me.

On Wed, Jan 4, 2017 at 3:12 PM, Attila Kinali <attila at kinali.ch> wrote:

> Hi,
> A small detail caught my eye, when reading a paper that informally
> introduced ADEV. In statistics, when calculating a variance over
> a sample of a population the square-sum is divided by (n-1)(denoted by s in
> statistics) instead of (n) (denoted by σ) in order to account for a small
> bias
> the "standard" variance introduces
> (c.f. https://en.wikipedia.org/wiki/Unbiased_estimation_of_
> standard_deviation )
> In almost all literature I have seen, ADEV is defined using an average,
> i.e. dividing by (n) and very few use (n-1).
> My question is two-fold: Why is (n) being used even though it's known
> to be an biased estimator? And why do people not use s when using (n-1)?
>                         Attila Kinali
> --
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> use without that foundation.
>                  -- Miss Matheson, The Diamond Age, Neil Stephenson
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