Posterior distributions, sampling distributions and inter-laboratory comparison data

Abstract

Weighted least-squares estimation methods are often used in the analysis of inter-laboratory comparison data. In classical statistics, least-squares methods can be justified in terms of properties of sampling distributions. However, not all distributions associated with laboratory results can be regarded sampling distributions and, for these cases, least-squares methods are a less straightforward to justify. Furthermore, they can give results that differ significantly from a Bayesian analysis. We illustrate these differences for the case in which the results of the laboratories are derived from repeated measurements.