Probabilistic approach to confidence intervals of linear calibration

Abstract

It is demonstrated that the statistical reliability of experimentally determined confidence intervals in some linear calibration problems in instrumental analyses can greatly be enhanced if the standard deviation (s, σ_M) of measurements, which is a theoretical prediction of the instrumental response error, is incorporated into the usual statistical equation instead of the residual of least-squares fitting. The reliability of the calibration depends on not only the fluctuation of calibration lines due to the response error, σ_M, but also the error of parametrization associated with the a priori response error prediction, i.e., the variance of the response s, Var(σ_M). The error prediction requires the Fourier transform of an instrumental baseline, signal shape and others (e.g., sample injection error). The variability in the confidence interval from five calibration standards is as small in the probabilistic approach as that for 50 standards in the statistical method. Liquid chromatography and capillary electrophoresis are taken as examples.