## 3 Results
### Analysis of Differences in Three Jumping Abilities  
The vertical, lateral, and horizontal jumps were analyzed using the same parameters, including jump distance (height), R-GRF, and T-PRF (\(\theta\)). The differences were analyzed as shown in Table 6. Through a three-factor ANOVA, it was found that the lateral jump distance was the longest, followed by the horizontal jump distance, with the vertical jump height being the shortest. The differences in the three jump distances indicated that lateral jumps generate more horizontal force. In contrast, vertical jumps do not produce horizontal force, requiring the lower limbs to generate a high-intensity GRF. Additionally, in terms of R-GRF ranking, vertical jumps require the most GRF, followed by lateral jumps, with horizontal (step-back) jumps requiring the least force. Finally, for the T-PRF (\(\theta\)) of vertical, lateral, and horizontal jumps, the study found that the angle for lateral jumps was \begin{table}
\begin{tabular}{c c c c c c} \hline \multirow{2}{*}{**Parameter**} & **EG (\(\mu\) = 15)** & **CG (\(\mu\) = 15)** & **F-Value** & \(p\)**-Value** & \(\eta^{2}\) \\  & **M \(\pm\) SD** & **M \(\pm\) SD** & **F-SD** & **\(p\)**-Value** & \(\eta^{2}\) \\ \hline JD (m) & & & & & \\ L-Pre & 0.86 \(\pm\) 0.07 & 0.87 \(\pm\) 0.06 & & & & \\ L-Post & 1.15 \(\pm\) 0.11 & 0.88 \(\pm\) 0.06 & 79.33 \({}^{*}\) & \(<\)0.05 & 0.739 \\ R-Pre & 0.89 \(\pm\) 0.07 & 0.90 \(\pm\) 0.05 & & & \\ R-Post & 1.14 \(\pm\) 0.09 & 0.88 \(\pm\) 0.06 & 36.71 \({}^{*}\) & \(<\)0.05 & 0.567 \\ \hline RFD (N/S) Left and right foot take-off & & & & & \\ L-Pre & 6386 \(\pm\) 291 & 6353 \(\pm\) 239 & & & & \\ L-Post & 6816 \(\pm\) 373 & 6349 \(\pm\) 233 & & & & \\ R-Pre & 6269 \(\pm\) 312 & 6268 \(\pm\) 298 & & & & \\ R-Post & 7160 \(\pm\) 311 & 5939 \(\pm\) 592 & & & & \\ \hline H-GRF (N) Step-back take-off & & & & & \\ L-Pre & 954 \(\pm\) 221 & 948 \(\pm\) 233 & & & & \\ L-Post & 1072 \(\pm\) 194 & 954 \(\pm\) 215 & & & & \\ R-Pre & 913 \(\pm\) 224 & 906 \(\pm\) 203 & & & & \\ R-Post & 1053 \(\pm\) 236 & 926 \(\pm\) 184 & & & & \\ \hline V-GRF (N) Step-back landing & & & & & \\ L-Pre & 1448 \(\pm\) 268 & 1443 \(\pm\) 269 & & & & \\ L-Post & 1606 \(\pm\) 204 & 1454 \(\pm\) 251 & & & & \\ R-Pre & 1422 \(\pm\) 281 & 1420 \(\pm\) 239 & & & & \\ R-Post & 1582 \(\pm\) 245 & 1430 \(\pm\) 218 & & & & \\ \hline R-GRF (N) Resultant force of step-back & & & & & \\ L-Pre & 1734 \(\pm\) 345 & 1728 \(\pm\) 350 & & & & \\ L-Post & 1932 \(\pm\) 276 & 1740 \(\pm\) 325 & & & & \\ R-Pre & 1690 \(\pm\) 356 & 1686 \(\pm\) 307 & & & & \\ R-Post & 1906 \(\pm\) 304 & 1704 \(\pm\) 279 & & & & \\ \hline T-PRF (\(\theta\)) Step-back resultant force trajectory & & & & & \\ L-Pre & 56.7 \(\pm\) 1.4 & 56.8 \(\pm\) 2.0 & & & & \\ L-Post & 56.3 \(\pm\) 1.8 & 56.7 \(\pm\) 1.9 & & & & \\ R-Pre & 57.2 \(\pm\) 2.0 & 57.2 \(\pm\) 2.4 & & & & \\ R-Post & 56.2 \(\pm\) 1.9 & 57.1 \(\pm\) 1.9 & & & & \\ \hline \end{tabular} \
\begin{tabular}{c c c c c} \hline Action time of step-back (s) & & & & \\ L-Pre & 1.38 \(\pm\) 0.09 & 1.36 \(\pm\) 0.07 & & & & \\ L-Post & 1.06 \(\pm\) 0.04 & 1.35 \(\pm\) 0.05 & 157.08 \({}^{*}\) & \(<\)0.05 & 0.849 \\ R-Pre & 1.19 \(\pm\) 0.07 & 1.18 \(\pm\) 0.06 & & & \\ R-Post & 1.03 \(\pm\) 0.06 & 1.19 \(\pm\) 0.06 & & & \\ \hline \end{tabular}
\begin{tabular}{c c c c c} \hline \multirow{2}{*}{EG represents the experimental group, and CG represents the control group. Abbreviations: The jump distance is JD. The maximum RFDs of the left and right foot take-off (m = N/s) are L-RFD (m = N/s) and R-RFD (m = N/s). The vertical ground reaction force of take-off (N) is V-GRF (N). The horizontal force of step-back take-off is H-GRF. The vertical force of step-back landing is V-GRF. The resultant force of the step-back is R-GRF. The take-off resultant force trajectory is T-PRF (\(\theta\)). The data are presented as the mean \(\pm\) standard deviation (M \(\pm\) SD), and were statistically analyzed using the F-test, with the significance level set at \({}^{*}p<0.05\).  
\end{table}