Refined and supplemented author's criterion for the study of dependent and independent samples in the field of experimental sciences (with the focus on education)

Introduction. The article is devoted to the triune system: 1) the selection of primary information about the problem under study; 2) the principle of comparing pairs of samples; 3) the criterion for determining a promising technology among competing ones. It is a continuation of the author’s previous research. The work is directly related to the research of samples in the field of experimental sciences and deals with education. Materials and Methods. The methodology for solving the problem of creating a triune system (selection - comparison - criterion) is a systematic analysis of the shortcomings of functioning criteria and the use of a cluster approach. Results. A mathematical complex (MC) has been developed containing the following components: matrix models that take into account the academic performance and personal development of students and allow to collect first–hand information about students’ activities; a new system for comparing the results of the application of innovations and the criterion of the author of QL: free from all the shortcomings of the predecessor criteria, with no restrictions on the number of students and categories; contributing to the identification of the best technologies among competing; reducing the volume of theory tenfold, which gives significant savings in time and finances, and its consistency attracts professionals. All this is achieved due to the fact that the QL criterion is two-parameter, unlike the one-parameter criteria, they do not have access to about 50% of the information about the problem under study. Conclusions The implementation of a mathematical complex in the scientific and educational processes not only contributes to the selection of an appropriate technology among competing ones, but also solves the problem of predicting the direction of changes in "improvement – deterioration" system. The transition to a single and consistent quality of life criterion enhances the accessibility and attractiveness of this criterion, does not frighten or repel teachers and academic staff– who are the main consumers of research results and active participants in the process of improving the quality of education.