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Measurement errors and measurement
uncertainty
One might assume that the concepts of error and uncertainty
are well enough known to be not worth discussing.
Nevertheless a
few comments are needed
(although for more details
the DIN[1] and ISO[3,4] recommendations
should be consulted).
- The first concerns the terminology. In fact the words
error and uncertainty are
currently used almost as synonyms:
- ``error'' to mean both error
and uncertainty (but nobody says ``Heisenberg
Error Principle'');
- ``uncertainty'' only for the uncertainty.
``Usually'' we understand
what each is talking about, but a more precise
use of these nouns would really help. This is strongly
called for
by the DIN[1] and ISO[3,4] recommendations.
They state in fact that
- error is ``the result of a measurement minus a
true value of the measurand'' - it follows that
the error is usually
unkown;
- uncertainty is a ``parameter, associated with the result
of a measurement, that characterizes the dispersion of the values that could
reasonably be attributed to the measurand'';
- Within the High Energy Physics community
there is an established
practice for reporting the final uncertainty of a measurement in the form
of standard deviation.
This is also recommended by the mentioned standards.
However, this should be done
at each step of the analysis, instead of estimating
``maximum error bounds'' and using
them as standard deviation in the
``error propagation''.
- The process of measurement is a complex one and it is difficult
to disentangle the different contributions which cause the total
error. In particular,
the active role of the experimentalist
is sometimes overlooked.
For this reason it is
often incorrect to quote the (``nominal'') uncertainty due to the
instrument as if it were the uncertainty
of the measurement.
Next: Statistical inference
Up: Bayesian inference applied to
Previous: Bayesian inference applied to
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Giulio D'Agostini
2003-05-15