Thin layer chromatography, a case study

Abstract

Abstract This paper gives an account of the collaboration between two mathematical statisticians and a toxicologist (the second author) interested in thin layer chromatography (TLC). A TLC “system” consists of a medium through which a solvent is transported. If a solution of some (toxic) sample is applied to the medium, then the components are carried forward by the solvent over different distances. Section 1 describes the concept of a data bank which provides standard values for the degrees of migration characteristic for each of m well‐studied substances in each of n systems. Sections 2–5 are mainly devoted to the construction of The “best design(s)”{ j 1 *… j k * } of k systems from the n available ones. The attention is restricted to the situation that an unidentified sample exclusively contains one of the m substances covered by the data bank and produces the scores xj … x j k in the systems j,… j k respectively. Three different approaches to the identification problem were successively considered. Each approach leads to a class of procedures and their performances. The performance of the optimum procedure can be used to define the performance of any of the ( n k ) designs ( j 1 … j k }. The latter performance is maximized in order to determine { j 1 *.,., j k * }. In practice usually data is obtained for mixtures instead of single. pure substances. Section 6 gives some tentative theory for the evaluation of such data.