[Test-Equipment] Corrected link

Tue Jun 1 06:40:10 EDT 2004

At 01:51 AM 6/1/2004, wolfbob wrote:

>They make no proof or present any
>evidence as to just what is the error distributions and why they should be
>random with a Gaussian distribution. The phenomena that is causing the
>variation could be defined and it is entirely possible that the errors are
>Gaussian, but I rather doubt it.

I see no reason to question an NBS assumption that the errors have a 
Gaussian distribution. Documenting an assumption of that nature would seem 
to be outside the scope of that particular paper. I doubt that you have 
access to measured voltages of as many saturated cells as NBS (and now 
NIST) has. If anyone in the world would have held a large enough sample of 
saturated cell measurements to justify an assumption of Gaussian 
distribution of errors it would have been NBS. Is there anything in the 
chemistry or physics of saturated cells that you can show would indicate a 
non-Gaussian stochastic process? Please leave out any comparison to the 
accuracy of a group of watches - we are dealing with entirely principles here.

 From the authors' statements on possible systematic error (pp. 9-10; pp. 
11-12 in the PDF file) it seems to me that the authors were familiar enough 
with error distribution in groups of saturated cells, and proficient enough 
in statistical analysis, that they would have known whether or not those 
errors have a Gaussian distribution.

I do not recall whether NBS Monograph 84, which I cited upstream, 
demonstrates Gaussian distribution of errors. Unfortunately the electronic 
archives on the NIST site reach back to only 1997, and that monograph is 
dated 1965. I do not have access to a printed copy of that monograph at the 
moment as I am about an hour's drive from the nearest location that 
probably holds a copy, and I won't have a chance to get to Virginia Tech to 
look for it for at least a few weeks. If I remember correctly it was 
available in the NBS Technical Notes series. If anyone on the list would 
like to try to find a copy sooner than that, visit:

http://worldcatlibraries.org/wcpa/servlet/WLAHoldingServlet;jsessionid=CE5CBF12B3F6480FF615581A5C190471.two?zip=24018&query=no%3A2016400&sessionid=CE5CBF12B3F6480FF615581A5C190471.two&recno=1

(watch out for line wrap) and enter your Zip code to display a list of 
libraries holding some or all of the NBS Technical Notes.

>Taking the average if a few things can be very misleading and fraught with
>statistical errors. If you run some basic probability test like Student T
>(again only applicable for Gaussian distributions as I recall) or what ever
>to see just what confidence there is that the average is any more accurate
>than any one of the cells.
>
>A very good example that all can appreciate is that of taking the reading of
>time from 6 watches and averaging them and expecting to get more accuracy in
>knowing what time it is. Here is a case where it is obvious that the error
>is not random but arbitrary, a really quite different thing. It should be
>obvious the average reading of the watches is no more accurate than any one
>of the watches as you do not have a clue as to the distribution of the
>errors or their cause, except the are not random, just different. Now if you
>have 10,000 watches, you have another hunk of mathematics coming in to play
>and that is the central limit theorem that says if you got enough
>independent samples of any distribution they will appear Gaussian and all
>the good math applies. Six is not a large enough to qualify under this
>caveat.
>
>Another way to see the error of this thinking is to make a simple
>assumption. One of the 5 cells is dead ass on the correct voltage and the
>other four are wrong. The average will also be wrong. just randomly picking
>one of the 5 cells for the standard will make you right 20% of the time
>whereas the average will make you wrong 100% of the time.
>
>WBob
>
>----- Original Message -----
>From: "Tom Dawson" <wb3akd at earthlink.net>
>To: <test-equipment at mailman.qth.net>
>Sent: Monday, May 31, 2004 8:59 AM
>Subject: [Test-Equipment] Corrected link
>
>
> > Sorry,
> >
> > Fumble fingered the previous post.
> >
> >
> > Follow the link to the following NBS Tech Note relating to measurements of
> > standard cells, and maintaining the volt with a small group of saturated
> > standard cells.
> >
> >
> > http://www.radio-science.com/std_cells/tn_430.pdf
> >
> > and a dos program to do the arithmetic.
> >
> > http://www.radio-science.com/std_cells/cells.exe
> >
> >
> > regards,
> >
> > Tom
> >
> >
> > _______________________________________________
> > Test-Equipment mailing list
> > Test-Equipment at mailman.qth.net
> > http://mailman.qth.net/mailman/listinfo/test-equipment
> >
> >
>
>
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Dale H. Cook, Chief Engineer, WWWR Roanoke VA, WCQV Moneta VA, WKBA WZZI 
Vinton VA, WKPA WLNI WZZU Lynchburg VA, WMNA/WMNA-FM Gretna VA
http://members.cox.net/dalehcook/starcity.shtml 