Certified reference materials and materials distributed in proficiency testing need to be 'sufficiently homogeneous', that is, the variance in the mean composition of the distributed portions of the material must be negligibly small in relation to the variance of the analytical result produced when the material is in normal use. The requirement for sufficient homogeneity suggests the use of a formal test. Such tests as have been formulated rely on the duplicated analysis of the material from a number of portions, followed by analysis of variance. However, the outcome is not straightforward. If the analytical method used is very precise, then an undue proportion of the materials will be found to be significantly heterogeneous. If it is too imprecise, the test may be unable to detect heterogeneity. Moreover, the Harmonised Protocol Procedure (M. Thompson and R. Wood, Pure Appl. Chem., 1993, 65, 2123) seems to be unduly prone to the rejection of material that is in fact satisfactory. We present a simple new statistical approach that overcomes some of these problems.