Combining Data in Small Multiple-Method Studies

Abstract

In this article an accurate confidence interval is derived when the results of a small number of possibly biased experimental methods are combined for the determination of an unknown quantity called the consensus mean. ANOVA and a simple hierarchical Bayesian analysis of variance with locally uniform priors result in confidence intervals too wide for precision metrology. Often when deciding on experimental methods, scientists choose methods in such a way that the truth lies between the extremes of the method means. Combining this additional information with experimental data, an interval more accurate than the ANOVA interval and the simple hierarchical Bayesian interval is obtained. 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.

KEY WORDS :

• Analysis of variance
• Bayesian
• Consensus value
• Standard reference materials