Do small samples bias the correlation between strength and jumpperformance? Multivariate insights into age and sex amidststrength saturation: an analysis of 1,544 participants fromdifferent sports

Maximal strength is considered a fundamental aspect of athletic performance across a wide range of sports and is also needed for a range of activities of daily life. Yet, compared to males there are fewer publications examining females, with most showing similar coefficients of correlation between dynamic strength and different athletic performances. In both, males and females, results are biased by mostly small sample sizes (sample bias) leading to a fluctuation around the true correlation coefficient of the entire population. This crosssectional analysis involving 1544 participants employed multivariate and correlative analyses to clarify the importance of maximum strength in the parallel back squats on the jump performance controlling for variables such as type of sport, sex, age, and performance level. The analysis revealed two principal components that reflect distinct types of variability within the dataset: the first, primarily associated with performance capabilities, accounts for 58.45% of the variance, while the second, emphasizing demographic differences, accounts for a considerably lower variance of 25.08%. The correlation analyses in this study identified maximal strength as a significant factor influencing jumping performance, accounting for 48-53% of the variance in jump height. The analysis presents a saturation curve, with potential diminishing returns at higher strength levels. Age and sex had little to no effect on overall correlation coefficients. The overall correlation coefficients and the analyses for the subgroups (by sport and performance level) can differ considerably, which can be explained (mathematically) by the artificial formation of clusters, homogeneous subject groups, or small sample sizes.