[Numpy-discussion] non-standard standard deviation
Christopher Barker
Chris.Barker@noaa....
Fri Dec 4 11:12:23 CST 2009
This is getting OT, as I'm not making any comment on numpy's
implementation, but...
yogesh karpate wrote:
> # As far as normalization by(n) is concerned then its common assumption
> that the population is normally distributed and population size is
> fairly large enough to fit the normal distribution. But this standard
> deviation, when applied to a small population, tends to be too low
> therefore it is called as biased.
OK.
> # The correction known as bessel correction is there for small sample
> size std. deviation. i.e. normalization by (n-1).
but why only small size -- the "beauty" of the approach is that the "-1"
makes less and less difference the larger n gets.
> " . Its shown that for N=16 the std. deviation normalization was (n-1)=15
> # While I was learning statistics in my course Instructor would advise
> to take n=20 for normalization by (n-1)
Which introduces an incontinuity -- I never like incontinuities -- why
bother? for large n, it makes no practical difference, for small n you
want the -1 -- why arbitrarily decide what "small" is?
From an engineering/applied science point of view, I take the view
expressed in the Wikipedia page on Unbiased estimation of standard
deviation:
"...the task has little relevance to applications of statistics..."
-Chris
--
Christopher Barker, Ph.D.
Oceanographer
Emergency Response Division
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Chris.Barker@noaa.gov
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