[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.
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