Comparison of different statistical approaches to evaluate the orthogonality of chromatographic separations: Application to reverse phase systems

Selectivity of phase system is of primary concern when designing a bidimensional chromatographic system and looking for the highest degree of orthogonality between the two separations. Several statistical or geometrical criteria can potentially be used to measure the degree of orthogonality. A comparison of eight candidate criteria has been carried out in this study. Analysis of variance (ANOVA) was used to evaluate the relevance of each criterion and its ability to reveal the significance of the influence of factors like pH, stationary phase, and organic modifier. Experimentally, a set of 32 chromatographic systems was evaluated by the same generic gradient with 63 probe solutes, likely to be present in biological and/or environmental samples and covering a wide range of physico-chemical properties: acidic, basic and neutral compounds with different pKa, molecular mass and hydrophobicity (log P). Each chromatographic system was defined by the nature of the stationary phase (8 different silica or grafting chemistries), the pH of the aqueous fraction of the mobile phase (2.5 or 7.0) and the nature of the organic modifier (acetonitrile or methanol). The orthogonality of the 496 couples of chromatographic systems was evaluated and ranked using the eight different approaches: the three correlation coefficients (Pearson, Spearman and Kendall), two geometric criteria characterizing the coverage of the 2D separation space, Slonecker's information similarity and two chi-square statistics of independence between normalized retention times. In fact, there were only seven distinct criteria, since we established the analytical equivalence between the rankings with the likelihood ratio statistics and Slonecker's information similarity. Kendall's correlation coefficient appeared to be the best measure of orthogonality since, according to ANOVA, it exhibited the highest sensitivity to all experimental factors. The chi-square measures, and hence Slonecker's information similarity, performed equally well provided the discretization of the separation space was carried out appropriately. Finally, from the compared study of the factors acting upon orthogonality carried out by ANOVA, it is possible to draw the conclusion that the pH of the mobile phases has the highest impact on the selectivity followed by the type of stationary phase and finally by the organic modifier.