APPLICATION OF NUMERICAL OPTIMIZATION METHODS AND MATHEMATICAL STATISTICS IN PROCESSING THE RESULTS OF ENGINEERING–PEDAGOGICAL RESEARCH

Abstract

Modern engineering-pedagogical research is characterized by the complexity of educational systems, multidimensional learning outcomes, and the need for objective and reproducible data interpretation. In this context, descriptive approaches to data analysis are insufficient to ensure the scientific validity of research findings. This paper substantiates the application of numerical optimization methods and mathematical statistics for processing experimental data in engineering-pedagogical studies. Particular attention is given to the Newton–Raphson method as a numerical optimization tool for refining model parameters and identifying optimal conditions in engineering-oriented educational models, as well as to classical statistical techniques, including Student’s t-test and Pearson’s χ² test, used to verify statistical hypotheses and assess the significance of observed differences between experimental and control groups.