Determining Consensus Values in Interlaboratory Comparisons and Proficiency Testing

An important part of interlaboratory comparisons and proficiency testing is the determination of the reference value of the measurand and the associated uncertainty. It is desirable to have reference values with low uncertainty, but it is crucial that these values are reliable, i.e. they are correct within their stated uncertainty. In some cases it is possible to obtain reference values from laboratories that reliably can produce values with significantly lower uncertainty than the proficiency testing participants, but in many cases this is not possible for economical or practical reasons. In these cases a consensus value can be used as the best estimate of the measurand. A consensus value has the advantage that it often has a lower uncertainty than the value reported by the reference laboratory. There are well known and statistically sound methods available for combining results with different uncertainties, but these methods assume that the stated uncertainty of the results is correct, which is not a given. In fact, the very purpose of proficiency testing is to establish whether the participants can measure within their claimed uncertainty. The paper explores a number of methods for determining preliminary consensus values used to determine which participant values should be deemed reliable and therefore included in the calculation of the final consensus value and its uncertainty. Some values are based on impressive equations and others have curious names. The relative merits of these methods in various scenarios are discussed.