Alexander Koldanov – Professor, Department of Applied Mathematics and Informatics, Faculty of Business Informatics and Applied Mathematics, National Research University Higher School of Economics.
Address: 25/12, Bolshaya Pecherskaya str., Nizhniy Novgorod, 603155, Russian Federation.
E-mail: akoldanov@hse.ru

Peter Koldanov – Assistant Professor, Department of Theory and Methodology of Distance Learning, Lobachevsky State University of Nizhniy Novgorod.
Address: 23, Prospekt Gagarina, 603950, Nizhni Novgorod, Russian Federation.
E-mail: kold@mail.ru

The study focuses on efficiency comparison for enlistment campaigns at University affiliates using small samples in aggregate. From engineering point, the actuality of such an objective will be governed by the necessity of sound management of affiliate activities specifically allocation of possibly capital investments in affiliates and taking other management decisions. From theoretical approach, actuality of objective under review as mathematical statistics objective will be determined by its multi-alternative nature and limited study.

The study’s goal is building up and investigation into statistical procedure of loose ordering of affiliates subject to their efficiency. To build up a statistical procedure for selecting a single out of multiple solutions, it has been suggested using a theory of procedures (Leman) with multiple solutions. The procedure consists in joint review of all pair-wise comparisons. Besides, there arises an issue of consistent combining the results. The study suggests a solution for inconsistency issue based on introduction of an additional uncertainty range, which, from engineering point, will not change the task nature.

The newness of the study results consists in the following: Optimum statistical procedures with multiple solutions have been built up per various classes; certain decision rules with desired accuracy have been elaborated; results for application of such rules to actual investigations were analyzed; possibility to improve statistical multiple solution procedures characteristics has been demonstrated due to efficient use of combined small samples. Such an improvement is based on using additional homogeneity hypotheses, which allows using observation results at all affiliates per each pair-wise comparison test.