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

["Krishna Chowdary" <professor.head@gmail.com>]

I think that this conversation is a great example of the "Who's on First"
syndrome mentioned in another thread.  Seems like a misuse of assumed common
language has led us to a miscommunication.  Also some sloppiness on my part.

On 10/9/06, John Denker <jsd@av8n.com> wrote:
> Well, I still think that the "nutshell" question is isomorphic to the
> sample_variance versus population_variance question.  Rereading the
> previous message tells me the same thing.
>
> At some very abstract level, asking whether you should propagate the
> standard deviation (i.e. sqrt of population variance) or propagate
> the standard deviation of the mean ( i.e. sqrt of sample variance)


I use these terms differently than you are using them.  I call one the
sample standard deviation (this is the square root of the sample variance);
actually in casual conversation I just call this standard deviation.  I call
the other the population standard deviation (this is the square root of the
population variance); I think I usually call this the standard deviation of
the population.  As you pointed out, the difference between dividing by
sqrt(N) and dividing by sqrt(N-1) is not terribly important for large N.

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).

I hope that _this_ attempt makes my "nutshell" question a better
representation of what I was trying to ask.  Tim F. has mostly addressed
that in the other thread, I think.

I do appreciate your concise example of the difference between the sample
standard deviation and the population standard deviation.  I've often
struggled with a good way to explain the distinction to students, and I'm
going to try your explanation.

--
regards
-Krishna

Krishna Chowdary
Department of Physics & Astronomy
Bucknell University