Asymmetric distribution of results in calibration curve and standard addition evaluations

Abstract

The inherent asymmetry in the application of linear regression analysis to the determination of sample analyte concentrations using calibration curve or standard addition evaluations gives rise to systematic errors. On the average, this always results in an overestimation of the true analyte concentrations in standard addition evaluations, while in calibration curve evaluations, the mean relative error depends on the value of sample concentration in relation to the analyte concentrations used for the calibration curve. In both evaluation techniques, the distribution of the results will deviate from a Gaussian distribution even if all analytical signals are normally distributed. It is shown that for the standard addition technique, and for samples with low analyte concentrations evaluated by the calibration curve technique, optimum precision and accuracy is obtained by using a minimum number of calibration points or standard additions, and performing multiple measurements on these. It is also shown that the linear regression correlation coefficient is a very poor indicator of the accuracy and precision in multiple-point standard addition evaluations. Weighted linear regression can be used to decrease the magnitudes of the systematic errors, but due to the inherent asymmetry, the distribution of the results will nevertheless be non-Gaussian. A publically available, in-house constructed Windows 3.1/Windows 95 program, capable of simulating all kinds of calibration curve and standard addition evaluations, was used for all calculations.