Criteria for studying dependent and independent samples in the field of education

Introduction. The article is devoted to monitoring the quality of education and continues the research presented in the author’s previous article. The goal of this work is to improve the author's criterion presented in the above mentioned work in two directions: the first is to strengthen its practical applicability; the second is to deepen research, covering all possible manifestations of problems in the field of quantitative characteristics within the education system (academic performance). Materials and Methods. The methodology of solving this problem and achieving the goal is based on the integration of two important areas of science – mathematics and pedagogy, as well as on the new results obtained by the author in the field of research of dependent and independent samples, which together form the basis of the theory of measuring academic performance. Results. The author has formulated the criterion in order to increase its practical applicability. Consequently, half of the tasks on the problem under study are solved by direct application of the criterion. In the field of deepening the research, a second special class of problems has been found which, together with the first, exhausts all the variety of manifestations of the problem under study in the field of dependent and independent samples. In addition, a two-parameter criterion is introduced, contributing to a more objective way of determining a promising educational technology among competing ones and taking into account the chronology of events. The latter is very important due to the fact that many well–known and widely used criteria (Wilcoxon –Mann - Whitney) are "blind", give the same result for different pairs (X, Y) and (Y, X) and do not follow the chronological order. The recommendation provided by incompetent researchers to rearrange the samples in pairs is very harmful and leads to falsification of results. Conclusions. The introduction of the author's criterion not only contributes to the selection of a decent educational technology, but also reduces the volume of scientific and methodological material on mathematical statistics serving the education system tenfold. It is justified by the fact that instead of 12-15 criteria containing about 100 rules and formulas, only one criterion can be used. In addition, this criterion does not contain contradictions, restrictions on the number of students and categories, etc.