Statistical Tools of Pedagogical Research

Due to the active development of scientific and technological progress, mathematical science has impacted on all scientific fields, including pedagogy. A crucial element is enhancing the quality of pedagogical research through the organization of experiments, the evaluation of acquired scientific data, and the validation of these results employing methods of mathematical statistics. The complexities involved in the proper implementation of statistical methods in pedagogical research arise from the necessity to investigate qualitative attributes of phenomena and events, requiring the alignment of research objectives and content with the appropriate mathematical and statistical techniques. Statistics seeks to provide relevant evidence to the claims of experts in various fields using mathematical methods to reach a consensus on making appropriate decisions based on statistical information. The article theoretically highlights mathematical and statistical methods in pedagogical research when organizing an experiment, evaluating acquired scientific data and verifying the reliability of these results usingmethods of mathematical statistics. It defines the main concepts of the research, namely: mathematical statistics, problems of mathematical statistics, methods of mathematical statistics, statistical literacy, statistical hypothesis, criteria of agreement, e-resources for statistical analysis. The main mathematical methods used in pedagogical research have been selected, and the algorithm for testing statistical hypotheses in pedagogical research has been provided. The statistical criteria of agreement have been identified for testing the hypothesis about the type of distribution of a random variable (Pearson, Fisher, Student), and modern e-resources for calculating the criteria of agreement (JASP, PSPP, DataMelt, Sisense and others), as well as some online calculators, have been discussed