Statistical determination of a comparison reference value using hidden errors

A statistical method is given for the combination of measurement results in an interlaboratory comparison to obtain a summary reference value and its uncertainty. The method allows objective treatment of measurements suspected of being outliers and objective treatment of measurements with individual uncertainties that appear overly optimistic. This is achieved by assuming that the measurement procedure of each laboratory is subject to a hidden error, and not just the procedures of those laboratories whose results appear to be outliers. The basic method can be extended to allow these errors to be drawn from different distributions for well-defined subsets of laboratories, and to allow the errors within these subsets to be correlated. Examples are given using actual data.