Confidence-interval interpretation of a measurement pair for quantifying a comparison

Abstract

We present a method for applying the results from a pair of comparison measurements, made in two laboratories, to form a confidence interval needed to support equivalence statements. Only the usual assumptions indicated in the ISO Guide to the Expression of Uncertainty in Measurement about the interpretation of the means and combined standard uncertainties are required. The method is mathematically rigorous and can be used to calculate the interval to arbitrary precision for any confidence level. It can also include the effects of correlations and degrees of freedom. Simple graphical and numerical methods of practical accuracy are presented for commonly used confidence levels. The method permits statements for clients to be made of the form "On the basis of comparison measurements [reference] performed in the period of [date to date], the results of similar measurements made at [Laboratory 1] and [Laboratory 2] can be expected to agree to within (±d0.95), with 95% confidence". We derive and discuss the first rigorous justification for this type of statement.