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.