Re: [Phys-l] statistics [was projectile motion lab]

[Jack Uretsky <jlu@hep.anl.gov>]

Thank you, Karimn, for actually reading and answering the question. 
Truly, youd deserve the respect and admiration of your students and 
colleaguses.  Additionally, thanks for understanding the topic under 
discussion.  I was unfamiliar with the expression "standard deviation of
the mean", which is not used in probability texts that I'm familiar with.

Here's the correct mathematical formulation:
	Take N samplaes from an infinite population that is normally 
distributed with mean <x> and standard deviation s.  The probability p 
that a sample mean will differ from <x> by an amount u will be normally 
distributed with mean 0 and standard deviation s/sqrt(N).  The latter 
value is corresponds to what has been called "the standard deviation of 
the mean" in the earlier postings.
	The Burington/May Handbook (2d Ed.) at 13.36  also remarkds that 
if <x> or s is unknown, these may be estimated (see Sec. 13.62)

I refer to the <Handboook of Probability and Statistics (McGraw-Hill 
1970, p. 189).
					Regards,
						Jack).


On Wed, 11 Oct 2006, Karim Diff wrote:

> I don't have the references listed below, but the one I have,  (
> Practical Physics by G. L. Squires, 2nd edition, McGraw-Hill)  makes the
> distinction between the two.
> He first relates the standard error (the term he uses)  to the standard
> error  in the mean as:
> sigma_ m = sigma /sqrt (n)
>
> where sigma_m = standard error in the mean
> sigma = standard error (or standard deviation)
> n = number of measurements.
>
> But the knowledge of sigma is tied to the knowledge of the distribution
> function which may or may not be known (if it is known, then problem
> solved).
>
> If the distribution is not known then Squires goes on to
> sigma_m = <s^2> / sqrt(n-1)
>
> where s = rms value of the residuals  ( where residual d  = x_i -
> x_average)
> s^2 = (sum d_i ^2) /n
>
> Using the approximation <s^2> ~ s^2   (since the distribution is not
> known <s^2> is not known)
> he gets
>
> sigma_m ~ s / sqrt(n-1)
>
>
> From there he goes into a more specific discussion for the Gaussian
> distribution..
>
> Karim Diff
>
> Jack Uretsky wrote:
>
> > Hi Tim-
> > 	Does one of the references distinguish - I repeat - distinguish
> > between "standard deviation" and "standard deviation of the mean" ?
> > If so, could you kindly tell me which one?
> > 				Regards,
> > 					Jack
> >
> > On Tue, 10 Oct 2006, Folkerts, Timothy J wrote:
> >
> >
> >
> > > > Can someone direct me to an authoritative work on statistics
> > > > that distinguishes between "standard deviation" and
> > > > "standard deviation of the mean" ?
> > >
> > > How about NIST?  They have a great online applied stats references.
> > >
> > > Here is a general discussion of error analysis
> > > http://www.itl.nist.gov/div898/handbook/mpc/section5/mpc5.htm
> > >
> > > Here is a bit on confidence intervals for means, which mentions "standard error".
> > > http://www.itl.nist.gov/div898/handbook/eda/section3/eda352.htm
> > >
> > > Or read the glossary for a quick (although rather dense) definition for "standard error"
> > > http://www.itl.nist.gov/div898/handbook/glossary.htm
> > >
> > >
> > > Tim Folkerts
>
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