EVALUATION OF UNCERTAINTY BY ORDINARY LINEAR LEAST-SQUARE REGRESSION OF REPLICATED DATA - A REVISED FORMULATION TO DEAL WITH UNBALANCED DATA SETS

Uncertainty is a critical estimate in evaluating the quality of analyt ical results and in assessing the compliance with legislative limits. An important component of expanded uncertainty is obtained by analysin g the results of calibration curves or standard addition methods. Line ar Least Square Regression is widely used to this aim but it requires repeated observations of standard solutions in order to properly verif y homogeneity of variance and Linearity. Sometimes, a different number of observations of tested solutions is available or retained. By revi sing original formulations, a worksheet was obtained which makes it po ssible to test homogeneity of variance and linearity by proper F-tests and to evaluate slope and intercept of the calibration function, unkn own concentrations and their uncertainties whatever the number of stan dards and the numbers of their replicates. The formulation proposed i) is validated by analysing data whose signal-to-noise ratio is known a priori, obtained by adding randomly generated gaussian noise to a kno wn calibration function and NIST reference data and ii) is applied to a routine DPASV analysis of some heavy metals in tap water.