In this article an accurate confidence interval is derived when the results of a small number of different experimental methods are combined for the determination of an unknown quantity. ANOVA and a simple hierarchical Bayesian analysis of variance result in confidence intervals too wide for precision metrology. In choosing methods, scientists often have a priori knowledge of where the truth lies with respect to the means of the methods. Combining this supplementary information with experimental data, an interval more accurate than the ANOVA and the simple hierarchical Bayesian intervals is obtained. Using a fully Bayesian procedure conflicts with the official industrial guide for expressing uncertainty, the ISO Guide. The estimate obtained falls within the ISO guidelines, and the mean and standard deviation used to derive the confidence interval are shown to be the posterior mean and variance of a fully Bayesian procedure.
48 No 2
anova, bayesian, combining data, multiple methods, type b
and Guthrie, W.
Combining Data in Small Multiple Method Studies, Technometrics
(Accessed May 29, 2023)