The quality coefficient as performance assessment parameter of straight line calibration curves in relationship with the number of calibration points

Abstract

Knowledge of the response function (y = f(x)) is essential in the validation of quantitative analysis methods as it describes the mathematical relationship between measurable responses and the concentrations or quantities of the analyte in the sample within a suitable range. The most common response function used is a straight line obtained by ordinary least squares (OLS) regression. Suitability of calibration lines obtained by OLS regression might be verified by calculation of a quality coefficient (QCmean). Mathematical modelling performed previously showed that with respect to critical limit values for g, which controls the symmetry of the prediction interval of the abscissa value obtained from the confidence intervals around the OLS calibration curve, a corresponding quality coefficient value exists as a quality performance parameter which is related to the spread of the abscissa values around their mean. In this paper, new mathematical models are developed to demonstrate to which extend also the number n of calibration points (xi,yi) defines the required value for the quality coefficient (QCmean) for different values of g. From these models, it could be established that the attribution of a critical limit value to QCmean as a performance parameter for straight line calibration cannot be arbitrary chosen but has to rely on the mathematical model relating QCmean, the g-value, the number n of calibration points and the spread of the xi-values around their mean. Practical measures for analysts are provided which tend to lower the g-value of straight calibration lines beneath critical values and enable to improve the quality of the calibration line applied for analysis, as demonstrated in an elaborated example.