In uncertain terms

In this article we return to the proper treatment of data. We have previously seen how to apply descriptive statistics to multiple measurements, and how to ensure that quantities we calculate are expressed to appropriate numbers of significant figures. Here, however, we will discuss how to estimate the likely uncertainty in a single measurement or a small number of measurements.

But first there is an issue of terminology. An overwhelming majority of scientists use the term ‘experimental error’, whereas a minority including myself prefer the term ‘experimental uncertainty’. This is simply because the term ‘error’ implies a mistake, whereas ‘uncertainty’ allows for the fact that no experimental measurements will be exact.

Uncertainty is often introduced in introductory science courses using the concepts of significant figures and by analysing the uncertainty in measurements. It can be a challenging subject to teach, but studies suggest that the latter method is more likely to result in students understanding what their results mean.