Estimating measurement uncertainties

Presentation of measurement results

In general, a measurement result consists of four elements:

  • a numerical value which corresponds to the measurand's value and may be corrected if an accuracy error has been noticed,

  • an expanded uncertainty associated with a confidence interval,

  • a measurement unit guaranteeing the traceability with the International System of Units (S.I.),

  • a coverage factor of the standard uncertainty.

The expression of the measurement result is then under the following form:

Besides, the following question must be asked when expressing the measurement result:

«Has enough information been provided in order to be able to update the result later if new information or data were to be made available? »

An excess of information is always better than a lack of it. For example, we must make sure that we :

  • give a clear description of the methods used to calculate the measurement result and its uncertainty on the basis of the experimental information and the input data,

  • list all the components of the uncertainty and provide documentation describing thoroughly how they have been evaluated,

  • present the analysis of the result in such a way that each major step can be easily retraced and that the provided result might be calculated again if necessary,

  • give all the corrections and the constants used for the analysis, along with their sources.

The numerical values of the estimate y and of its standard uncertainty uc(y) or its expanded uncertainty U must not be given with an excessive number of figures. It is usually enough to give uc(y) et U and all the standard uncertainties u(xi) with two significant figures. However, it might be necessary to mention more figures for the different u(xi) in order to avoid the propagation of rounding errors in intermediate calculations. The table below sums up the general principles that must be respected when presenting numerical values.


    Table 6 : Writing rules of a measurement result
Table 6 : Writing rules of a measurement result [zoom...]
AccueilOutils transversesNouvelle pageInformations sur le cours (ouvrir dans une nouvelle fenêtre)Number of degrees of freedomProcedure of evaluation of measurement uncertainty: summary