title: Evaluation of analytical performance based on partial order methodology.
abstract: Classical measurements of performances are typically based on linear scales. However, in analytical chemistry a simple scale may be not sufficient to analyze the analytical performance appropriately. Here partial order methodology can be helpful. Within the context described here, partial order analysis can be seen as an ordinal analysis of data matrices, especially to simplify the relative comparisons of objects due to their data profile (the ordered set of values an object have). Hence, partial order methodology offers a unique possibility to evaluate analytical performance. In the present data as, e.g., provided by the laboratories through interlaboratory comparisons or proficiency testings is used as an illustrative example. However, the presented scheme is likewise applicable for comparison of analytical methods or simply as a tool for optimization of an analytical method. The methodology can be applied without presumptions or pretreatment of the analytical data provided in order to evaluate the analytical performance taking into account all indicators simultaneously and thus elucidating a "distance" from the true value. In the present illustrative example it is assumed that the laboratories analyze a given sample several times and subsequently report the mean value, the standard deviation and the skewness, which simultaneously are used for the evaluation of the analytical performance. The analyses lead to information concerning (1) a partial ordering of the laboratories, subsequently, (2) a "distance" to the Reference laboratory and (3) a classification due to the concept of "peculiar points".
authors.affiliation: Awareness Center, Linkøpingvej 35, Trekroner, DK-4000 Roskilde, Denmark; Kazakh British Technical University, Department of Chemical Engineering, Almaty, Kazakhstan. Electronic address: LC@AwarenessCenter.dk.
authors.forename: Lars
authors.initials: L
authors.lastname: Carlsen
authors.affiliation: Leibniz - Institute of Freshwater Ecology and Inland Fisheries, Department Ecohydrology, Müggelseedamm 310, D-12587 Berlin, Germany.
authors.forename: Rainer
authors.initials: R
authors.lastname: Bruggemann
authors.affiliation: RSE Kazakh Institute of Metrology, Almaty, Kazakhstan.
authors.forename: Olga
authors.initials: O
authors.lastname: Kenessova
authors.affiliation: RSE Kazakh Institute of Metrology, Almaty, Kazakhstan.
authors.forename: Erkin
authors.initials: E
authors.lastname: Erzhigitov
mesh_terms: D002623:Chemistry Techniques, Analytical / Q000706:statistics & numerical data*; D006801:Humans; D059021:Laboratory Proficiency Testing / Q000706:statistics & numerical data*; D015588:Observer Variation; D012107:Research Design
keywords: Analytical performance; Hasse diagram; Multi-indicator systems; Partial order; Posets