Global homogeneity index: An integrated approach for assessing multielement homogeneity in reference materials

Homogeneity assessment is critical in reference material preparation and characterization but is conventionally performed for each measurand individually. However, for multielement materials, this approach does not provide a single quantitative response describing the overall compositional homogeneity. In this study, a Global Homogeneity Index (GHI) is proposed as a complementary dimensionless metric for the integrated assessment of multielement homogeneity. A leafy candidate laboratory reference material was prepared, bottled into 100 units, and characterized for 19 elements (Al, As, Ba, Ca, Cd, Co, Cr, Cu, Fe, K, Mg, Mn, Na, Ni, P, Pb, Se, V, and Zn) by ICP OES. Homogeneity was investigated through minimum-mass, within-bottle, and between-bottle experiments using conventional one-way ANOVA and the proposed GHI. The minimum-mass experiment provided an experimental evaluation of the GHI response. Conventional ANOVA identified significant differences for Co, Cu, and Fe when 100 mg portions were included, whereas no significant differences were observed from 200 to 500 mg. Consistently, the GHI distinguished the 100 mg group from all higher masses (p = 0.0062), while 200-500 mg portions were statistically equivalent. Within-bottle and between-bottle GHI assessments showed no significant differences (p = 0.131 and 0.696, respectively), in agreement with element-specific ANOVA. The GHI thus provides a simple and integrated representation of global multielement variability while preserving conventional element-specific homogeneity assessment as an essential component of reference material characterization. The proposed approach offers a complementary strategy for reducing complex multielement homogeneity information to a single interpretable response.