Applied statistics to evaluate the quality of education

The application of statistical methods and machine learning to analyze the data describing the education process are considered. The solution of two problems typical of the educational process but different in the organization is shown. The first problem is to analyze the results of students' tests who study Russian as a foreign language to enter the university in Russia. The purpose of the analysis is to evaluate the adequacy of the teaching methods, in particular, the consistency of results gained for the elementary and intermediate tests with the result obtained for the advanced test. Data is transformed firstly, then the analysis of variance is conducted, finally, the clustering is built. Found structure shows that students successfully coping with elementary and intermediate tests are likely to pass the advances level test. In the second problem, the results of studying mathematics by junior pupils are analyzed. Classification of pupils is made based on their marks gained for the answer in the lesson. The classifier determines the pupil mark for the final control work. The predictive model is built as the ensemble of random forests trained on four samples: the first is a sparse matrix of estimates, the others are the transformation of the first obtained by principal component analysis within a nuclear structure.