# Kinematic Analysis of Short and Long Services in Table Tennis
## 2 Materials and Methods
### The Statistical Procedures  
The Statistica(r) 14 (Tbco Software Inc., Santa Clara, CA, USA) package was used for the statistical calculations. The Shapiro-Wilk test was performed to check the normality of distribution. Descriptive statistics were calculated and the nonparametric Mann-WhitneyU test was used with a significance level of 0.05. The statistical analysis also included the calculation of effect sizes using Cohen's d to quantify the magnitude of the differences between short and long serves (paired comparisons). Effect sizes were interpreted as small (\(d<0.3\)), moderate (\(0.3>d>0.5\)), or large (\(d>0.5\)), providing an indication of the practical significance of the observed differences. Additionally, a post hoc power analysis was conducted using paired T-tests to evaluate the statistical power of the study. The power analysis incorporated the observed effect sizes, sample size (\(n=15\)), and an alpha level of 0.05 to calculate the probability of detecting true effects. Power values \(\geq\) 0.80 were considered adequate, indicating a low likelihood of Type II errors, while values below this threshold were noted as limitations in the study design. The post hoc power analysis was conducted using G*Power and the Excel Analysis ToolPack. The following data were subjected to statistical analysis: the course of changes in joint \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & \multicolumn{4}{c}{**ShS**} & \multicolumn{4}{c}{**LoS**} \\ \cline{2-10}
**Joint Movement** & **Median** & \begin{tabular}{c} **Quartile** \\ **Range** \\ \end{tabular} & \begin{tabular}{c} **Coef. Var.** \\ **(\%)** \\ \end{tabular} & **Median** & \begin{tabular}{c} **Quartile** \\ **Range** \\ \end{tabular} & \begin{tabular}{c} **Coef. Var.** \\ **(\%)** \\ \end{tabular} & \begin{tabular}{c} **\(p\)-** \\ **Value** \\ \end{tabular} & \
\begin{tabular}{c} **Cohen’s** \\ **d** \\ \end{tabular} &
\begin{tabular}{c} **Power** \\ **(1-b)** \\ \end{tabular} \\ \hline Shoulder Total Flexion (LT) & 35.0 & 25.4 & 52.8 & 38.3 & 26.2 & 40.1 & \(<\)0.01 & \(-\)0.13 & 0.95 \\ Shoulder Flexion (RT) & 16.5 & 21.8 & 147.0 & 5.1 & 32.7 & 305.8 & \(\leq\)0.01 & 0.40 & 0.72 \\ Shoulder Abduction (LT) & 31.8 & 25.3 & 56.5 & 35.9 & 22.4 & 42.1 & \(<\)0.01 & \(-\)0.20 & 0.91 \\ Elbow Flexion (RT) & 91.7 & 33.2 & 24.1 & 113.9 & 37.7 & 19.2 & \(\leq\)0.01 & \(-\)0.62 & 0.39 \\ Wrist Extension (RT) & \(-\)6.1 & 35.9 & \(-\)633.1 & \(-\)19.3 & 14.5 & \(-\)55.2 & \(\leq\)0.01 & 0.48 & 0.60 \\ Wrist Radial (RT) & 2.7 & 40.5 & \(-\)2461.0 & \(-\)9.7 & 20.6 & \(-\)217.6 & \(\leq\)0.01 & 0.37 & 0.76 \\ Wrist Supintation (RT) & 64.4 & 32.2 & 39.6 & 67.6 & 36.7 & 35.3 & \(<\)0.01 & \(-\)0.09 & 0.96 \\ Thoracic Flexion & 2.5 & 9.0 & 247.7 & 4.0 & 8.2 & 132.5 & \(\leq\)0.01 & \(-\)0.23 & 0.89 \\ Hip Abduction (RT) & 9.4 & 17.6 & 121.0 & 3.0 & 12.2 & 312.4 & \(\leq\)0.01 & 0.41 & 0.71 \\ Hip Rotation Ext (RT) & 6.1 & 13.9 & 109.5 & 14.0 & 11.9 & 63.8 & \(<\)0.01 & \(-\)0.66 & 0.34 \\ Knee Flexion (LT) & 47.5 & 21.2 & 30.9 & 43.4 & 20.7 & 31.5 & 0.02 & 0.20 & 0.91 \\ Knee Flexion (RT) & 50.1 & 22.0 & 27.2 & 45.5 & 27.5 & 35.6 & \(\leq\)0.01 & 0.19 & 0.92 \\ Knee Rotation Ext (LT) & \(-\)0.2 & 9.9 & \(-\)2456.5 & 3.3 & 10.5 & 462.0 & 0.03 & \(-\)0.34 & 0.79 \\ \hline \hline \end{tabular} Note: RT—right; LT—left.  
\end{table} 
Table 4: Angles values (in degrees) during Forward (Forw) event. Differences are significant when \(p\leq 0.05\).