By Hening Huang
A variety of statistical methods are available for estimating consensus values in interlaboratory studies (including key comparisons). These methods, although developed based on different approaches and ranging from simple to complex, produce largely compatible estimates of consensus values. However, the formulas or methods for estimating the standard uncertainty (SU) associated with the consensus value estimators are different and may produce incompatible results. This causes confusion among practitioners about the performance of consensus value estimators. To resolve the incompatibility problem and to eliminate potential confusion, we propose using a unified formula for estimating the SU. The unified formula is an unconditional SU estimator that accounts for both within- and between-laboratory variances. It is applicable to all weighted-average (WA) type estimators. The unified formula makes it possible to evaluate the performance of WA-type consensus value estimators on the same methodological basis. A case study of estimating the Newtonian constant of gravitation is presented to demonstrate the effectiveness of the unified formula.
