Measurement replicates under the lens: evaluating NIR spectroscopic error quality through multivariate error analysis

The optimal number of replicates for reliable measurements is a recurring issue in analytical chemistry, particularly for inherently multivariate techniques (e.g. spectroscopy) often coupled with chemometrics. Replicates allow error estimation, incorporation of error into models, and quantification of the multivariate error structure, described by the Error Covariance Matrix (ECM). This study proposes an ECM-based approach to determine the optimal number of measurement replicates necessary for proper error estimation. A new, easy-to-compute index, ECM-SI (ECM similarity index), is introduced to study the effect of sample number and replicates on ECM estimation, demonstrated on real world datasets obtained with NIR portable sensors. The approach uses intuitive graphical representations without imposing strict rules, allowing flexible evaluation. Accurately characterizing measurement error is fundamental to understanding the data acquired but requires enough samples and replicates. In practice, the proposed methodology allows two objectives to be achieved simultaneously: determining the optimal number of measurement replicates through the best possible estimation of the ECM, while obtaining the most accurate estimate of the ECM itself. This study offers a methodological strategy framed into a practical perspective to determine replicates needed for describing data uncertainty in multivariate data, avoiding the assumption that a stable mean implies fully characterized data variability. Applicable to spectroscopic systems, the approach can also be extended to other multivariate analytical techniques and other sources of error, improving model reliability for both novices and experienced practitioners.