A concept of interlaboratory consensus for categorical characteristics of a substance, material, or object

Interlaboratory studies are widely used for: 1) evaluation of calibration and measurement capabilities of national metrology institutes and designated institutes participating in key and supplementary comparisons; 2) estimation of proficiency (competence) of calibration and testing laboratories; and 3) development of certified reference materials. When a reference value for the measurand is unknown, the laboratory results may be used to estimate (build) a measurand consensus value applicable instead of the reference value. The consensus value typically is: 1) an arithmetic mean of the measured values, when their associated measurement uncertainties are approximately equal; 2) a weighted mean with weights calculated considering the measurement uncertainties; 3) a Bayesian estimator; or another kind of mean. However, no algebraic operations and mathematical functions exist among categorical characteristics of a substance, material, or object. Therefore, a consensus numerical value (such as a mean) in an interlaboratory comparison of categorical properties cannot be formulated. In sociology, consensus of opinions within a given group of individuals is discussed as ‘cohesiveness’ or ‘closeness’, i.e., the degree to which the members of the group agree. Consensus of responses of experts of different laboratories participating in an interlaboratory comparison, classifying a substance, material, or object according to its nominal and ordinal characteristics, could also be interpreted as cohesiveness. The recently developed two-way factorial analysis of variation of nominal (categorical) variables CATANOVA and of ordinal variables ORDANOVA, included a detailed decomposition of the total variation, answers the question ‘is a consensus of participating laboratories achieved or not?’ The answer is based on testing hypotheses about homogeneity of the between-laboratory and within-laboratory variation components, as well as the components caused by other factors under study.