Clusterization of directions of training at russian technical college in factorial space of entrance examenations

In this work one of the problems of modern Russian reforming of higher engineering education in the transition to an innovative model of economic development - the problem of improving the quality of education and assessment of higher education reforming in the Russian Federation is discussed. One of the basic indicators of the effectiveness assessment of university learning is an average score of USE (Unified State Exam), that is an entry criterion, one of the indicators of quality of recruitment (IQR). Taking Tomsk Polytechnic University (TPU) by the example, we have carried out a multivariate statistical analysis of entrants IQR in various directions of training (DT) at Russian higher educational institutions on basis of entrance examination results in 2013. The components of the statistical method of the study are correlation, factor, cluster and variance analyses. As an IQR, the following three groups of input indicators were used: rating calculated index USE TPU DT among other universities, indicators of student recruitment in TPU DT (admission plan for the state-funded places, competition, passing score, total score of the applicant, scores in mathematics, number of accepted students in each DT and indicators of the entrance test (scores in maths and number of participated in DT). The statistical analysis of 25 main DT for the most typical IQR revealed the following features: main DT have diverse (from multimodal to normal) distribution laws, they are generally small in number, are often characterized by low competition and involve a strong pair correlation. Four IQR groups were identified on the correlation basis, and with the help of the factor analysis the 4-factor IQR model was built, which explains the overall variability by the first three factors in 87.4%, and by the fourth - 96.3%. In this case, the new variables are interpreted as factors of federal quality, university quality, competition and quantity. In the framework of the factor space of IQR developed the tree-like DT clusterization was performed, which makes it possible to receive the appropriate number of clusters depending on choice of association distance. To evaluate the quality of DT cluster model selected we used criteria of both parametric and rank variance analyses. The 8-cluster qualitative model of technical DT TPU was proposed that allows us to distinguish DT groups which are uniform in overall factor indicators. Using a posteriori multiple comparison criterion, uniform groups of clusters are identified for each factor. In the framework of the model proposed the DT classification in the nominal scale of measurements was carried out. The results of the statistical analysis may be taken into account when making management decisions within the ongoing reform in higher education. The analyses made may be taken into account in choice decision for distribution of the admission quotas students in majors, as well as for adjustment of directions of activity to ensure a high quality set of entrants and the formation of equalization and adaptive courses for university students.

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