Audrey Bluomsohn explained how 'errors' are propagated in
various mathematical operations. I would prefer, though, to talk about
'uncertainties'.
Although the formulas that Audrey Blumsohn uses are
quite correct, the conclusions are not entirely so. Since squares are always
positive, the variance of a sum of variances will always be larger than any of
the individual variances.
To use this simple relation it is most important that the
variables are uncorrelated.
The second relation that Audrey Blumsohn quotes is an
approximation that, however, is most useful. Relations 1 and 2 can be
conveniently combined to tackel more complex funtions.
A more detailed approch requires partial derivatives.
All this is nicely described in a joint publication of IUPAC,
IFCC, ISO, BIPM and others. It has become a standard publication and is commonly
known as GUM, 'Guide to the interpretation of uncertainties of measurements'. It
is highly recommended. The concept of uncertaity, as defined by ISO and expanded
in this publication, simplifies much of the problems of random and systematic
'errors'.
Among other interesting things it contains a very useful
spreadsheet template to come closer to a partial derivative approach to estimate
the propagation of uncertainies. Another example is that this approach opens an
interesting new possibility to define 'detection limit'!
Anders Kallner
Dept Clin Chem, Karolinska
hospital, Stockholm Sweden
E-mail address:
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phone:
+46 (0)8 5177 49 43
fax:+46 (0)8 5177 28 99