[RASMB] An early Christmas puzzle

[Arthur Rowe]

Greeting RASMBers -

Here is a puzzling little matter on which 
comments are invited. It's hardly a new point 
being made, so much as an old one wrapped up in 
AUC paper.

We all know that the cheerful assumption that 
errors in measured quantities are normally 
distributed is a hazardous one. In the extreme 
case of 'rounding error' (in computational work) 
a simple range defines the region in which values 
may lie, as compared to a bell-shaped curve with 
(increasingly less likely) values going off to 
infinity either side. For physical 
instrumentation with quality control defining 
limits, a bell-shaped curve is also unlikely to 
be a good representation of distribution of 
errors.

Now, the temperature control in an AUC is the 
most important factor limiting the estimation of 
absolute s values, its magnitude equalling all 
other factors put together (Errington & Rowe, 
2003). The Beckman XL instruments have a stated 
accuracy of ±0.5º in temperature. For which 
assurance one devoutly trusts there is evidence, 
with a QA backing. In other words, we can be 
confident that if we accept the actual 
temperature as being equal to that stated, then 
we will not be more than 0.5º in error. Walter's 
temperature measurement method does not suggest 
otherwise, although obviously a significant 
number of XLs was not sampled.

So here is the question. We have 3 XL's running 
here, and the range in s values when we estimate 
s for the identical samples in different 
instruments suggests that two of them differ by 
an amount which is approaching 1º. Which is 
perfectly consistent with the machine spec. Bad 
news? Well, maybe not. If we accept that ±0.5º as 
an outer limit, then for each estimate from one 
XL we can discount that half of the potential 
variation which lies outside the bounds specified 
by the other estimate. Indeed, if we push this 
argument to its limit,  we can discard all values 
for the 'true' temperature which lie at all 
significantly away from the mean of the two 
values!

So - is this a paradox? Given the type of error 
distribution expected, can we really accept that 
it is better, using 2 instruments, to get 2 
estimates for an s value that dis-agree than 2 
which agree? Or is this believing in Santa Claus?

Regards to all

Arthur

N Errington, A J Rowe (2003)  "Probing 
conformation and conformational change in 
proteins is optimally undertaken in relative 
mode" European Biophysics Journal 32 (5) 511-517
--
*******************************************************
Arthur J Rowe
Professor of Biomolecular Technology
NCMH Business Centre
University of Nottingham
School of Biosciences
Sutton Bonington
Leicestershire LE12 5RD   UK

Tel:        +44 (0)115 951 6156
           +44 (0)116 271 4502
Fax:        +44 (0)115 951 6157
email:      arthur.rowe at nottingham.ac.uk
Web:        www.nottingham.ac.uk/ncmh/business
*******************************************************


--
*************************
Arthur Rowe
Lab at Sutton Bonington
tel: +44 115 951 6156
fax: +44 115 951 6157
*************************

This message has been scanned but we cannot 
guarantee that it and any attachments are free 
from viruses or other damaging content: you are 
advised to perform your own checks. Email 
communications with the University of Nottingham 
may be monitored as permitted by UK legislation.
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://list.rasmb.org/pipermail/rasmb-rasmb.org/attachments/20041116/6d393fe1/attachment.htm>