Comparison of multianalyte proficiency test results by sum of ranking differences, principal component analysis, and hierarchical cluster analysis

Sum of ranking differences (SRD) was applied for comparing multianalyte results obtained by several analytical methods used in one or in different laboratories, i.e., for ranking the overall performances of the methods (or laboratories) in simultaneous determination of the same set of analytes. The data sets for testing of the SRD applicability contained the results reported during one of the proficiency tests (PTs) organized by EU Reference Laboratory for Polycyclic Aromatic Hydrocarbons (EU-RL-PAH). In this way, the SRD was also tested as a discriminant method alternative to existing average performance scores used to compare mutlianalyte PT results. SRD should be used along with the z scores-the most commonly used PT performance statistics. SRD was further developed to handle the same rankings (ties) among laboratories. Two benchmark concentration series were selected as reference: (a) the assigned PAH concentrations (determined precisely beforehand by the EU-RL-PAH) and (b) the averages of all individual PAH concentrations determined by each laboratory. Ranking relative to the assigned values and also to the average (or median) values pointed to the laboratories with the most extreme results, as well as revealed groups of laboratories with similar overall performances. SRD reveals differences between methods or laboratories even if classical test(s) cannot. The ranking was validated using comparison of ranks by random numbers (a randomization test) and using seven folds cross-validation, which highlighted the similarities among the (methods used in) laboratories. Principal component analysis and hierarchical cluster analysis justified the findings based on SRD ranking/grouping. If the PAH-concentrations are row-scaled, (i.e., z scores are analyzed as input for ranking) SRD can still be used for checking the normality of errors. Moreover, cross-validation of SRD on z scores groups the laboratories similarly. The SRD technique is general in nature, i.e., it can be applied to any experimental problem in which multianalyte results obtained either by several analytical procedures, analysts, instruments, or laboratories need to be compared.