Selectivity and related measures for nth order data

Analytical figures of merit are often used as criteria to decide whether or not a given instrumental method is suitable for attacking an analytical problem. To date, figures of merit primarily exist for analytical instruments producing data indexed by one variable, i.e., first-order instruments and first-order data, Almost none exist for instruments that generate data indexed by two variables, i.e., second-order instruments and data, and none exist for instruments supplying data indexed by three or more variables, i.e., nth-order instruments and data. This paper develops practical mathematical tools that can be used to create several figures of merit for nth-order instrumentation, namely, selectivity, net analyte signal, and sensitivity. In particular, the paper fully develops a local selectivity measure for second-order instrumentation and tests its performance using simulated second-order data and real second-order data obtained by gas chromatography with Fourier transform infrared detection and liquid chromatography with photodiode array detection. Also included in the paper is a brief discussion on practical uses of nth-order figures of merit.