When components of a substance or material are subject to a mass balance constraint, test results of the components' contents are intrinsically correlated because of the constraint. That is in addition to possible metrologically-related correlation of test results, and natural and/or technological correlation of the components' contents. Such correlations may influence understanding of compositional data and evaluation of risks in conformity assessment of the substance or material due to measurement uncertainty. A Bayesian multivariate approach to evaluate the conformance probability of multicomponent materials or objects and corresponding risks of false decisions, able to take into account all observed correlations including spurious, is discussed for different scenarios of compositional data. A Monte Carlo method, which includes the mass balance constraint, written in the R programming environment is provided for the necessary calculations. A technique for separation of spurious correlations from experimental (natural and/or technological) correlations is proposed.