The effect of influential data, model and method on the precision of univariate calibration

Building a calibration model with detection and quantification capabilities is identical to the task of building a regression model. Although commonly used by analysts, an application of the calibration model requires at first careful attention to the three components of the regression triplet (data, model, method), examining (a) the data quality of the proposed model; (b) the model quality; (c) the LS method to be used or a fulfillment of all least-squares assumptions. This paper summarizes these components, describes the effects of deviations from assumptions and considers the correction of such deviations: identifying influential points is the first step in least-squares model building, the calibration task depends on the regression model used, and finally the least squares LS method is based on assumptions of normality of errors, homoscedasticity, independence of errors, overly influential data points and independent variables being subject to error. When some assumptions are violated, the ordinary LS is inconvenient and robust M-estimates with the iterative method of reweighted least-squares must be used. The effects of influential points, heteroscedasticity and non-normality on the calibration precision limits are also elucidated. This paper also considers the proper construction of the statistical uncertainty expressed as confidence limits predicting an unknown concentration (or amount) value, and its dependence on the regression triplet. The authors' objectives were to provide a thorough treatment that includes pertinent references, consistent nomeclature, and related mathematical formulae to show by theory and illustrative examples those approaches best suited to typical problems in analytical chemistry. Two new algorithms, calibration and linear regression written in s-plus and enabling regression triplet analysis, the estimation of calibration precision limits, critical levels, detection limits and quantification limits with the statistical uncertainty of unknown concentrations, form the goal of this paper.