## 3 Results
### Two-Way Analysis of Variance (ANOVA) Results  
As shown in Table 4, the trunk angle affected all responses (TES, LES, HMS and LSA; all \(p\) < 0.001). Because all interactions were nonsignificant (all \(p\) > 0.05), the main effects were confirmed. The significance of muscle activities and LSA varied according to the flexibility measurement. TTT and SRT revealed a similar result, indicating that all muscle EMGs and LSA were significantly affected by the flexibility group, whereas MST exhibited differences only in LES and HMS activations. Table 5 presents the Duncan MRT grouping results for responses under varying trunk angles. Because these were averaged across the other variable, the results are shown regardless of which flexibility measurement was grouped. Figure 4 illustrates the alterations in the muscle EMG values of each trunk position. When participants flexed their trunk forward from upright to 45\({}^{\circ}\), the activations of all three muscles increased. As trunk flexion continued, the LES EMG began to decrease first, followed by TES EMG after 60\({}^{\circ}\) and the HMS EMG after 75\({}^{\circ}\). Table 5 also shows the changes in LSA during trunk flexion, indicating that LSA was close to 40\({}^{\circ}\) when the participant was standing upright, and then gradually decreased with more trunk flexion, becoming negative when the trunk was flexed at 90\({}^{\circ}\). Table 6 presents the Duncan grouping results for each variable under different flexibility levels. As shown, \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Variables**} & \multirow{2}{*}{**Responses**} & \multicolumn{2}{c}{**TTT**} & \multicolumn{2}{c}{**SRT**} & \multicolumn{2}{c}{**MST**} \\ \cline{3-7}  & & **F** & **Significance** & **F** & **Significance** & **F** & **Significance** \\ \hline \multirow{4}{*}{\
\begin{tabular}{c} Trunk \\ angle \\ \end{tabular} } & TES & 11.06 & \(p\) < 0.001 & 10.7 & \(p\) < 0.001 & 11.55 & \(p\) < 0.001 \\  & LES & 47.43 & \(p\) < 0.001 & 49.01 & \(p\) < 0.001 & 49.50 & \(p\) < 0.001 \\  & HMS & 30.14 & \(p\) < 0.001 & 29.5 & \(p\) < 0.001 & 28.92 & \(p\) < 0.001 \\  & LSA & 220.65 & \(p\) < 0.001 & 208.1 & \(p\) < 0.001 & 159.62 & \(p\) < 0.001 \\ \hline \multirow{4}{*}{
\begin{tabular}{c} Flexibility \\ \end{tabular} } & TES & 4.81 & \(p\) < 0.01 & 4.33 & \(p\) < 0.05 & 1.56 & \(p\) = 0.214 \\  & LES & 3.95 & \(p\) < 0.05 & 9.09 & \(p\) < 0.001 & 7.43 & \(p\) < 0.01 \\  & HMS & 5.52 & \(p\) < 0.01 & 4.19 & \(p\) < 0.05 & 5.11 & \(p\) < 0.01 \\  & LSA & 13.98 & \(p\) < 0.001 & 12.12 & \(p\) < 0.001 & 0.94 & \(p\) = 0.391 \\ \hline \hline \end{tabular} Notes: TTT—toe-touch test, SRT—sit-and-reach test, MST—modified Schober’s test, TES—thoracic erector spinae, LES—lumbar encoder spinae, HMS—hamstring, LSA—lumbosacal angle.  
\end{table} 
Table 4: Main effects of the variables for three flexibility measurements based on a 2-way ANOVA. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Flexibility** & **TTT (cm)** & **n** & **SRT (cm)** & **n** & **MST (cm)** & **n** \\ \hline High & 3.2–30.0 & 15 & 5.1–21.6 & 15 & 7.5–9.2 & 12 \\ Middle & \(-\)2.5—2.1 & 12 & \(-\)0.5–4.6 & 13 & 6.3–7.0 & 14 \\ Low & \(-\)26.0—3.0 & 13 & \(-\)24.0—3.5 & 12 & 4.5–6.2 & 14 \\ \hline \hline \end{tabular} Notes: TTT—toe-touch test, SRT—sit-and-reach test, MST—modified Schober’s test, n—sample size.  
\end{table} 
Table 2: Criteria for classifying the flexibility levels. different flexibility groups (i.e., high, middle and low) cause different degrees of LES activations. TTT can significantly discriminate the difference in LES activations between groups with high and low flexibilities, whereas MST and SRT can discriminate between groups with high and non-high flexibilities. Figure 5 further illustrates LES EMG alterations at varying trunk flexions for three flexibility grouping methods. Differences in the EMG alterations were more notable among the measurements when the trunk was fixed between 45\({}^{\circ}\) and 75\({}^{\circ}\).