Evaluation of nonlinearity testing procedures on simulated data

When calibrating a method, use of a straight line is highly favorable because it is easy to compute sensitivity and the blank to be used to predict an unknown concentration. Therefore, when validating an analytical method, it is necessary to check whether linearity is acceptable over the method’s whole application range before trying another model. Available procedures for checking linearity are reviewed by using a simulation model that gives a complete family of curved calibration lines. From the simulated data, it is possible to compute the prediction error generated by the model curva ture as the relative difference between the linear extrapolated value and the observed value. It appears that the power of the classical “linearity test” depends on experimental design and that at least 25 measurements are necessary to detect curvature for an acceptable prediction error. An alternative model-fitting criterion, based on the χ2 probability law, also was evaluated. It is also applicable but seems less stable and more sensitive to data size. The question of the definition of nonlinearity is also raised because it is directly connected to the comparison of nonlinearity detection techniques.