Thin layer chromatography, a case study

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 mwell‐studied substances in each of nsystems. Sections 2–5 are mainly devoted to the construction of The “best design(s)”{j1*…jk*} of ksystems from the navailable ones. The attention is restricted to the situation that an unidentified sample exclusively contains one of the msubstances covered by the data bank and produces the scores xj…xjkin the systems j,…jkrespectively. 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 (nk) designs (j1…jk}. The latter performance is maximized in order to determine {j1*.,., jk*}. 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.