Quantitative Evaluation of Method-Dependent Variability and Multivariate Structure in ICP-OES, AAS and XRF Analyses of Lead Smelting Slag

Knowledge of the heterogeneous composition of mineral substances and technogenic materials is vital in the development of technological designs and in environmental impact assessments. However, the simultaneous application of analytical methods often reveals discrepancies between different methods that cannot be explained by the commonly used scalar agreement metrics. The current study suggests the possibility of evaluating inter-methodical agreement in the compositional data of heterogeneous substances using the example of lead smelting slag compositional data. The compositional data of 96 samples of lead smelting slag were analyzed using independent methods of XRF, ICP-OES and AAS. The agreement between the obtained results was evaluated at three levels of hierarchy: element-wise bias and dispersion, structured variability between methods and preservation of covariance structure; PCA was used as the tool for the evaluation. High agreement between the ICP-OES and AAS methods was found for the transition metals (r ≈ 0.97–0.99), with negligible bias. The presence of increased dispersion and deviations in the inter-methodical agreement was found in the case of the methods compared with the XRF method, especially for the matrix components such as Si (r ≈ 0.92). Coefficients of variation for metallic elements stay between 12 and 15%, but XRF has shown consistently higher variability for certain elements. PCA results show that despite local differences, the main covariance structure was kept across methods, with the first two components explaining about 40–45% of total variance. These results clearly indicate that high correlation does not necessarily ensure methodological interchangeability. The hierarchical framework proposed here will provide a reproducible basis for cross-method validation and support reliable data integration in complex mineral systems.