# Isometric Strength in Volleyball Players of Different Age: A Multidimensional Model
## 3 Results  
Tables 2 and 3 show descriptive statistics of all the variables obtained from the performed tests for both male and female age groups, respectively. \begin{table}
\begin{tabular}{c c c c c} \hline
**Variable** & **U15 (Mean \(\pm\) SD)** & **U17 (Mean \(\pm\) SD)** & **U19 (Mean \(\pm\) SD)** & **U21 (Mean \(\pm\) SD)** \\ \hline HGR F\({}_{\text{max}}\) (\(n\)) & 321.1 \(\pm\) 78.1 & 432.4 \(\pm\) 78.5 & 437.3 \(\pm\) 83.6 & 572.2 \(\pm\) 82.7 \\ HGR RFD\({}_{\text{max}}\) (\(n\)/s) & 2299.4 \(\pm\) 538.9 & 3018.0 \(\pm\) 559.1 & 3196.4 \(\pm\) 622.3 & 3976.9 \(\pm\) 423.8 \\ HGL F\({}_{\text{max}}\) (\(n\)) & 303.7 \(\pm\) 78.4 & 402.6 \(\pm\) 86.7 & 417.4 \(\pm\) 78.2 & 521.0 \(\pm\) 82.4 \\ HGL RFD\({}_{\text{max}}\) (\(n\)/s) & 2161.3 \(\pm\) 605.8 & 2798.7 \(\pm\) 600.5 & 2979.3 \(\pm\) 562.5 & 3605.2 \(\pm\) 571.6 \\ LB F\({}_{\text{max}}\) (\(n\)) & 814.7 \(\pm\) 234.9 & 1157.2 \(\pm\) 199.4 & 1249.1 \(\pm\) 167.4 & 1568.5 \(\pm\) 222.9 \\ LB RFD\({}_{\text{max}}\) (\(n\)/s) & 5328.5 \(\pm\) 1985.8 & 8251.7 \(\pm\) 2407.6 & 9736.2 \(\pm\) 1920.7 & 152538.3 \(\pm\) 2784.7 \\ AE F\({}_{\text{max}}\) (\(n\)) & 2736.3 \(\pm\) 788.1 & 3506.8 \(\pm\) 602.2 & 3540.2 \(\pm\) 634.8 & 4616.5 \(\pm\) 354.1 \\ AE RFD\({}_{\text{max}}\) (\(n\)/s) & 12650.5 \(\pm\) 3679.7 & 16458.7 \(\pm\) 2857.6 & 17409.7 \(\pm\) 2785.3 & 21384.7 \(\pm\) 3810.3 \\ \hline \end{tabular} Legend: HGR—isometric handgrip right; HGL—isometric handgrip left; LB—isometric lumbar extensors; AE—isometric ankle extensors; F\({}_{\text{max}}\)—maximal force; RFD\({}_{\text{max}}\)—maximal rate of force development.  
\end{table} 
Table 2: Descriptive statistics of male subjects’ isometric strength. Figure 1: Isometric ankle extensors strength measurement procedure. PCA results are presented in Table 4. Initial KMO analysis showed sufficient sampling adequacy (0.857 and 0.817 for male and female samples, respectively), indicating that the PCA was justified. Bartlett method indicator was statistically significant (Sig. \(<\) 0.001) for both male and female subject samples, confirming the sphericity of data for further analysis. Table 3 shows the component matrix results of both samples with a cumulative percentage of variability explanation. All components have had high participation (0.688-0.940) in the main factor extracted with PCA. Cumulative variance explained by the extracted factors was moderate to high (Table 3). Table 5 shows descriptive statistics of Score values for every age group, calculated with PCA multidimensional transformation. The table also shows ANOVA F values for both samples with statistical significance of differences (\(p\) value). Figure 2 depicts post hoc differences in Score values between age groups of male and female samples. Regression analysis results are shown with trend lines, which were significant predictors for both male (F = 36.897, R\({}^{2}\) = 0.947, \(p\) = 0.026), and female subjects' (F = 44.297, R\({}^{2}\) = 0.957, \(p\) < 0.022) age-related changes of Score values. \begin{table}
\begin{tabular}{c c c} \hline
**Variable** & **Male** & **Female** \\ \hline HGR \(\mathrm{F}\mathrm{D}_{\mathrm{max}}\) & 0.940 & 0.869 \\ HGR \(\mathrm{F}_{\mathrm{max}}\) & 0.939 & 0.877 \\ HGL \(\mathrm{F}_{\mathrm{max}}\) & 0.925 & 0.897 \\ HGL \(\mathrm{F}\mathrm{D}_{\mathrm{max}}\) & 0.916 & 0.884 \\ LB \(\mathrm{F}_{\mathrm{max}}\) & 0.913 & 0.818 \\ AE \(\mathrm{F}_{\mathrm{max}}\) & 0.879 & 0.736 \\ LB \(\mathrm{RFD}\) max & 0.798 & 0.688 \\ AE \(\mathrm{RFD}_{\mathrm{max}}\) & 0.784 & 0.767 \\ \hline
**Cumulative \%** & 78.984 & 67.284 \\ \hline \end{tabular}
\end{table} 
Table 4: Principal component analysis structure matrix.