Selection of orthogonal chromatographic systems based on parametric and non-parametric statistical tests

The generalized pairwise correlation method (GPCM) with different statistical tests was applied to examine the similarity/orthogonality of the tested systems. Beside this, the Pearson's (product moment) correlation coefficient, the Spearman's rho and the Kendall's tau were also used as conventional correlation parameters. The Williams't-test (as a parametric statistical test), and the Conditional Fisher's, the McNemar's and the Chi-square tests (as non-parametric statistical tests) were used for hypotheses testing. Except for the selection using correlation coefficients all other measures are non-parametric. A new procedure was applied to establish orthogonality of the chromatographic systems. From the different correlation measures so-called orthogonality ratios were calculated. The ratios originating from GPCM with McNemar's test was found to be the best to select orthogonal (dissimilar) and similar systems. The method was compared with various alternatives to validate the findings (among others with the ratios from Pearson's correlation coefficients). The non-parametric options for correlation coefficients (Spearman's rho and Kendall's tau) are found not to be sensitive enough to define the orthogonality of these chromatographic systems.