What are measurement errors (sometimes called “uncertainties”), and why are they important?
Except in straightforward counting situations, there is always a difference between the measured value of a variable and the true value. This difference is called the “error”. By the nature of an error, it must be an indeterminate quantity, or an “uncertainty”, for if we knew what it was precisely we could adjust for it and we would then know the true value precisely. The value of an error can therefore only be estimated; it cannot be known precisely. A measurement which does not report the likely range of possible errors contains limited information, for we can be quite sure that the true value differs from that reported and we have no idea of the possible size of this difference. Uncertainties are sometimes quoted as a fixed number at a 90% confidence level, or somesuch figure. There are established procedures for estimating such figures; a useful site is the National Institute of Standards and Technology (NIST) in the USA. An example. Consider the statement “Guildford is in the coun
