David G Johnston schrieb am 2015-01-21:
> Andrew Dunstan wrote
> > On 01/20/2015 01:26 PM, Arne Scheffer wrote:
> >> And a very minor aspect:
> >> The term "standard deviation" in your code stands for
> >> (corrected) sample standard deviation, I think,
> >> because you devide by n-1 instead of n to keep the
> >> estimator unbiased.
> >> How about mentioning the prefix "sample"
> >> to indicate this beiing the estimator?
> > I don't understand. I'm following pretty exactly the calculations
> > stated
> > at <http://www.johndcook.com/blog/standard_deviation/>
> > I'm not a statistician. Perhaps others who are more literate in
> > statistics can comment on this paragraph.
> I'm largely in the same boat as Andrew but...
> I take it that Arne is referring to:
> http://en.wikipedia.org/wiki/Bessel's_correction
Yes, it is.
> but the mere presence of an (n-1) divisor does not mean that is what
> is
> happening. In this particular situation I believe the (n-1) simply
> is a
> necessary part of the recurrence formula and not any attempt to
> correct for
> sampling bias when estimating a population's variance.
That's wrong, it's applied in the end to the sum of squared differences
and therefore per definition the corrected sample standard deviation
estimator.
> In fact, as
> far as
> the database knows, the values provided to this function do represent
> an
> entire population and such a correction would be unnecessary. I
That would probably be an exotic assumption in a working database
and it is not, what is computed here!
> guess it
> boils down to whether "future" queries are considered part of the
> population
> or whether the population changes upon each query being run and thus
> we are
> calculating the ever-changing population variance.
Yes, indeed correct.
And exactly to avoid that misunderstanding, I suggested to
use the "sample" term.
To speak in Postgresql terms; applied in Andrews/Welfords algorithm
is stddev_samp(le), not stddev_pop(ulation).
Therefore stddev in Postgres is only kept for historical reasons, look at
http://www.postgresql.org/docs/9.4/static/functions-aggregate.html
Table 9-43.
VlG-Arne
> Note point 3 in
> the
> linked Wikipedia article.
> David J.
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