Statistical tests for the selection of the optimum parameters set in models describing response surfaces in reversed-phase liquid chromatography

Abstract

An appropriate procedure based on statistical criteria is suggested for the determination of the optimum set of model parameters for a given chromatographic system. The criteria employed are the t-ratio test, the rate of change in the sum of squares of residuals, the standard error of the fit, the F-test, and the CP-test. The suggested procedure has been evaluated using two different models, one based on partition and the other on adsorption mechanisms, which describe the combined effect of pH and organic modifier content on the retention of ionogenic solutes in reversed-phase liquid chromatography. It is shown that all the criteria give almost converged results and therefore we may simply use the F-test, which seems to be the most sensitive and reliable criterion excluding any personal judgement. It is also found that the retention models tested show a different behavior towards their simplification. In particular, the use of a reduced equation of the partition model, selected on the basis of the suggested procedure, is necessary for the prediction of meaningful retention surfaces, whereas the decrease in the number of the adjustable parameters in the adsorption model offers only noise reduction and fitting simplicity, because no version of this model predicts abnormal retention surfaces.