The role of the sample standard deviation in the analysis of measurement data

This paper builds on recent letters to the editor to consider different ways in which the 'sample standard deviation' of a set of repeated measurements might be used in the expression of accuracy or uncertainty. A distinction is made between using the sample standard deviation, s, to calculate a figure of merit for the measurement procedure and using s to express uncertainty in the estimate of a measurand. In particular, we consider whether s should be adjusted for bias. It is shown that most procedures involving s are valid without the application of any such adjustment. The paper emphasizes the importance of clear definitions and an unambiguous statement of purpose, and also emphasizes the need for a distinction in notation between a random variable and its observed value.