APPLICATION OF MATHEMATICAL AND STATISTICAL METHODS IN PSYCHOLOGY: POSSIBILITIES, LIMITATIONS, AND PROSPECTS FOR DEVELOPMENT

Abstract

The article is devoted to the theoretical and methodological analysis of the significance of mathematical and statistical methods in modern psychology and the justification of their role in the formation of evidence- based, scientifically verified practice. It shows that statistics ensure the objectivity and reliability of psychological conclusions, minimize subjective interpretations, standardize the measurement process, and improve the quality of research procedures. The paper reveals the functional capabilities of the main groups of statistical methods: descriptive, inferential, comparative, regression, multidimensional, and psychometric. It is emphasized that it is thanks to correlation, factor, cluster, and regression analyses that it is possible to identify latent structures, predict behavioral trends, determine predictors of psychological states, and construct typologies of personality traits. Particular attention is paid to the practical application of statistics in psychological counseling, educational activities, and organizational psychology, where quantitative methods are used to evaluate the effectiveness of programs, analyze the dynamics of the client's condition, select personnel, and predict professional risks. The article analyzes current trends in the development of statistical culture among psychologists, in particular the spread of structural modeling, neural network algorithms, Bayesian approaches, and the automation of statistical analysis in Python and SPSS environments. The importance of interpretive literacy, the formation of critical statistical thinking skills, adherence to the principles of research reproducibility, and the implementation of open science are emphasized. The article integrates the provisions of contemporary Ukrainian scholars, who emphasize the need to combine classical statistical methods with modern analytical technologies to increase the validity and reliability of psychological conclusions. It is concluded that the formation of statistical competence is a strategic direction for the development of psychological science, which determines the effectiveness of both academic research and the practical work of psychologists.