Confidence intervals and other statistical intervals in metrology

Abstract

Typically, a measurement is regarded as being incomplete without a statement of uncertainty being provided with the result. Usually, the corresponding interval of measurement uncertainty will be an evaluated confidence interval, assuming that the classical, frequentist, approach to statistics is adopted. However, there are other types of interval that are potentially relevant, and which might wrongly be called a confidence interval. This paper describes different types of statistical interval and relates these intervals to the task of obtaining a figure of measurement uncertainty. Definitions and examples are given of probability intervals, confidence intervals, prediction intervals and tolerance intervals, all of which feature in classical statistical inference. A description is also given of credible intervals, which arise in Bayesian statistics, and of fiducial intervals. There is also a discussion of the term “coverage interval” that appears in the International Vocabulary of Metrology and in the supplements to the Guide to the Expression of Uncertainty in Measurement.