<p>When a reference value for the measurand in an interlaboratory study is unknown, the laboratory results may be used to estimate/build a consensus value instead of a reference value. Since no algebraic operations and mathematical functions exist among categorical (nominal and ordinal) values, a numerical consensus value cannot be formulated. 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 be interpreted as the degree to which the experts agree. Two-way factorial analysis of variation of nominal variables CATANOVA and of ordinal variables ORDANOVA answers the question ‘is a consensus of participating laboratories achieved or not?’ The answer is in testing hypotheses about the homogeneity of between- and within-laboratory variation components, as well as the variation components caused by other factors under study. The same technique is implemented in the assessment of risks of false decisions in chemical analysis caused by human errors, when expert responses on an ordinal scale characterize different error scenarios and different components of the quality system, intended to reduce the risks. The present paper is a brief review of the approach based on two-way factorial analysis of variation and its recent applications in an analytical chemistry/testing laboratory for comparison of categorical characteristics of a substance, material, or object.</p>