19.6 Reporting Uncertainty

19.6 Reporting Uncertainty#

When reporting on your uncertainty all of the information needed to re-evaluate the measurement should be available (the more information the better). In this section we will provide a simplified, minimalistic approach to reporting the uncertainty. The GUM has a lot more to say on this matter, including more specialized advice.

Some key information to include with your standard uncertainty is:

  • The underling PDF of the measurand

  • If it is a combined uncertainty

If you quote the expanded uncertainty, then the coverage factor and confidence level should be quoted as well. For example, a combined standard uncertainty quoted with a coverage factor of 2:

``The reported uncertainty is an expanded uncertainty calculated using a coverage factor k = 2, providing a confidence level of approximately \(95\%\). The combined standard uncertainty was determined in accordance with the principles of the Guide to the Expression of Uncertainty in Measurement (GUM).’’

It is good practice to quote the uncertainty to 2 significant figures, and to quote the best approximation of the measurand to match this. Both the best approximation of the meausurand and the standard uncertainty should be quoted in the same units and to the same order of magnitude (if using scientific notation).

Worked Example - Quoting a best approximation and standard uncertainty

In this example, we have measured a mass with best approximation \(m = 100.02147g\) with an estimated standard uncertainty of \(u = 0.35\) mg. Some options for how this can be quoted (as recommended by the GUM) are:

  • “\(m = 100.021 47\)g with \(u = 0.35\) mg”

  • “\(m = 100.021 47(35)\)g”, where the number in parentheses is the numerical value of \(u\) referred to the corresponding last digits of the quoted result.

  • “\(m = 100.021 47(0. 000 35)\)g”, where the number in parentheses is the numerical value of \(u\) expressed in the unit of the quoted result.

  • “\(m = 100.021 47 \pm 0. 000 35\)g”, where the number following the symbol \(\pm\) is the numerical value of \(u\) and not a confidence interval.