Re: [Phys-l] sample variance versus population variance

[John Denker <jsd@av8n.com>]

On 10/09/2006 10:45 PM, Krishna Chowdary wrote:

> What I call the standard deviation of the mean is sometimes called the
> standard error (though I learned that this is also ambiguous nomenclature):
>
> http://mathworld.wolfram.com/StandardError.html
>
> It is the standard deviation _further_ divided by sqrt(N).

OK, that's clear.  I think I get it now.

Again the answer depends on what you're trying to do.
Cat food versus dog food.

Let us introduce the concept of /cluster/.  In this case
we have a cluster with 50 observations in it.  If you
are trying to predict the next observation, there is no
_further_ factor of N.  If OTOH you are trying to predict
the mean of the next /cluster/, then you do need a further
factor of N.

The notation and terminology are quite messy in this area,
especially if you are simultaneously interested in the
ensemble of observations *and* the ensemble of clusters.