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 analytical results and in assessing the compliance with legislative limits. An important component of the expanded uncertainty is obtained by analysing the results of calibration curves or standard addition methods. Linear Least Square Regression is widely used to this aim, but it requires repeated observations of standard solutions in order to properly verify homogeneity of variance and linearity. Sometimes, a different number of observations of tested solutions is available or retained. By revising the original formulations, a worksheet was obtained which makes it possible to test homogeneity of variance and linearity by proper F-tests and to evaluate slope and intercept of the calibration function, unknown concentrations and their uncertainties whatever5 the number of standards and the number 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 known calibration function and NIST reference data and ii) is applied to routine DPASV analysis of some heavy metals in tap water.