ANALYTICAL FIGURES OF MERIT FOR TENSORIAL CALIBRATION

The subject of analytical figures of merit for tensorial calibration i s critically reviewed. Tensorial calibration derives its name from ten sor algebra, which provides a classification of calibration methods de pending on the complexity of the data obtained for one chemical sample , Expressions for net analyte signal, sensitivity (classical model for mulation), 'inverse sensitivity' (inverse model formulation), selectiv ity, signal-to-noise ratio and limit of detection (in signal space) ar e proposed for Nth-order data (N greater than or equal to 2) that are consistent with the accepted zeroth-order definitions and previously p roposed definitions for first-order data, Useful relationships between the proposed figures of merit and prediction error variance are descr ibed. A selectivity-based rule of thumb is derived to compare data ana lysis across orders, Central to the currently proposed framework for a nalytical figures of merit is the reduction of a complex data structur e to the scalar net analyte signal. This allows for the construction o f a univariate calibration graph (classical or inverse model), indepen dent of the complexity of the data. Enhanced visualization and interpr etation are obtained that may help to bridge the gap between Nth-order calibration and the intuitive understanding of zeroth-order data. (C) 1997 John Wiley & Sons, Ltd.