Analytical figures of merit for tensorial calibration

Abstract

The subject of analytical figures of merit for tensorial calibration is critically reviewed. Tensorial calibration derives its name from tensor algebra, which provides a classification of calibration methods depending on the complexity of the data obtained for one chemical sample. Expressions for net analyte signal, sensitivity (classical model formulation), sensitivity' (inverse model formulation), selectivity, signal-to-noise ratio and limit of detection (in signal space) are proposed for Nth-order data (N≥2) that are consistent with the accepted zeroth-order definitions and previously proposed definitions for first-order data. Useful relationships between the proposed figures of merit and prediction error variance are described. A selectivity-based rule of thumb is derived to compare data analysis across orders. Central to the currently proposed framework for analytical figures of merit is the reduction of a complex data structure to the scalar net analyte signal. This allows for the construction of a univariate calibration graph (classical or inverse model), independent of the complexity of the data. Enhanced visualization and interpretation are obtained that may help to bridge the gap between Nth-order calibration and the intuitive understanding of zeroth-order data. © 1997 John Wiley & Sons, Ltd.