Factor and correlation analysis of the interrelationships between physical and functional fitness of middle school-aged students

The study aimed to perform a factor and correlation analysis of the relationships between indicators of physical and functional fitness in 12–13-year-old students to identify the leading factors shaping the structure of their physical condition. Materials and Methods. Four subgroups were examined: boys aged 12 (n = 9), boys aged 13 (n = 23), girls aged 12 (n = 16), and girls aged 13 (n = 27). The assessment included anthropometric measurements (body height, body weight, Quetelet index/BMI), functional indicators (vital capacity, vital index, Stange and Genchi tests, heart rate, arterial blood pressure, Robinson and Ruffier indices), and results of physical fitness tests (pull-ups, push-ups, trunk lifts in 30 s, standing long jump, 4×9 m shuttle run, forward bend from a sitting position, jump rope test, and tapping test). Descriptive statistics, Pearson’s pairwise correlations, and factor analysis using the principal component method with Varimax orthogonal rotation were applied. Results. Stable and strong correlations were observed within the respiratory subsystem in all groups: vital capacity–vital index (r = 0.80–0.86; p < 0.01) and Stange–Genchi tests (up to r = 0.90; p < 0.01). Among 13-year-old boys, strength and speed-strength indicators were highly integrated (e.g., hand dynamometry–strength index r = 0.804; p < 0.01; long jump–dynamometry r = 0.706; p < 0.01), whereas shuttle run performance correlated negatively with strength endurance (r ≈ –0.58; p < 0.01). In 12-year-old girls, higher body mass/BMI was associated with lower relative strength (body mass–strength index r = –0.716; p < 0.01), while at 13 years, an integration of strength and coordination abilities was noted (long jump–rope jumping r = 0.76; p < 0.01; right–left tapping r = 0.86; p < 0.01). Factor analysis consistently identified three latent components: (1) strength-motor (hand dynamometry, push-ups, trunk lifts, long jump, rope jumping); (2) respiratory-functional (vital capacity, vital index, Stange and Genchi tests); and (3) cardiorespiratory (heart rate, blood pressure, Robinson and Ruffier indices). The structure was more ordered in 13-year-olds (particularly boys), while in 13-year-old girls, integration of strength and coordination parameters became more pronounced. Scientific Novelty and Practical Significance. The study demonstrated reproducibility of the main correlation patterns and their age- and sex-specific characteristics at 12-13 years. The identified latent factors can serve as criteria for differentiated assessment of physical and functional fitness and as methodological guidelines for regulating physical loads in school physical education. Conclusions. The obtained results form a methodological basis for developing differentiated assessment scales considering age and sex characteristics.