USING ANOVA TO EVALUATE AND ANALYZE THE IMPACT OF PREVIOUS SUCCESS ON THE RESULTS OF STUDYING MATHEMATICAL ANALYSIS

Abstract

Mathematical training occupies a special place in the educational process at higher military educational institutions, as it develops logical thinking and the ability to analyze and make decisions in conditions of uncertainty or risk to life. Probabilistic and statistical methods play a crucial role in ensuring objective data analysis, as do information technologies, which enhance the effectiveness of research and the educational process. The influence of studying linear and vector algebra on the academic performance of cadets of the Flight Faculty of the I. Kozhedub National Air Force University in Kharkiv utilizes modern mathematical IT tools. The use of Microsoft Excel (MS Excel) for statistical data processing provides cadets with a comprehensive picture ranging from theoretical foundations to the practical application of data analysis methods in the military and educational spheres. A one-way ANOVA was performed using the MS Excel Data Analysis add-in, and a post-hoc analysis was performed using Tukey's Honestly Significant Difference (HSD) test and Cohen's d effect size in the Real Statistics Resource Pack add-in. When considering the five levels of factor A based on the academic performance assessments for the first semester, it was found that Level 1 differs significantly from Levels 2 through 5. The Tukey HSD test did not reveal a significant difference for some pairs, although Cohen's d effect size indicates a practically large effect (large d, but not significant p), which may be due to insufficient test power. The most influential is the level with the lowest ratings. Ways to improve performance and further develop research methods in cases involving a large number of factors are proposed. The study's results confirm the importance of high-quality mathematical training in developing analytical thinking among flight faculty cadets, thereby enhancing their skills in the practical application of statistical methods in professional activities. Further research should focus on expanding the sample and incorporating multifactorial models, which will enable a more comprehensive assessment of the impact of various components of mathematical training on cadets' overall academic performance.