[time-nuts] σ vs s in ADEV
attila at kinali.ch
Wed Jan 4 15:12:42 EST 2017
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)?
It is upon moral qualities that a society is ultimately founded. All
the prosperity and technological sophistication in the world is of no
use without that foundation.
-- Miss Matheson, The Diamond Age, Neil Stephenson
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