## 4 Discussion  
The objective of this study was to provide insight into the effects of including a penetration test, which is the main driver that determines helmet shell thickness and therefore of its stiffness, in order to improve the protective performance of helmets. To that end, the impact performance of 10 helmet models, which were sorted into either hard or soft shell groups, were compared at two impact speeds. PLA and HIC variables were selected to determine the protection capability of the helmets. Since three headform sizes were used in the impact absorption tests, the influence of the headform size on the PLA or HIC variables was analyzed prior to carry out the main statistical analysis of this study. In Appendix A, Tables 1 and 2 include the PLA and HIC mean and the SD for each headform group, together with the \(p\)-value for each impact \begin{table}
\begin{tabular}{c c c c c} \hline \multirow{2}{*}{**Impact Point**} & \multirow{2}{*}{**Variable**} & \multicolumn{2}{c}{**Hard Shell**} & \multicolumn{2}{c}{**Soft Shell**} \\  & & **Group (\(n\) = 4)** & **Group (\(n\) = 6)** & **\(p\)-Value** \\ \hline \multirow{2}{*}{B} & PLA (g) & 127 \(\pm\) 20 & 124 \(\pm\) 16 & 0.9143 \\  & HIC & 659 \(\pm\) 171 & 591 \(\pm\) 170 & 0.6095 \\ \hline \multirow{2}{*}{X} & PLA (g) & 135 \(\pm\) 13 & 136 \(\pm\) 8 & 0.6095 \\  & HIC & 609 \(\pm\) 81 & 639 \(\pm\) 82 & 0.4762 \\ \hline \multirow{2}{*}{P} & PLA (g) & 139 \(\pm\) 16 & 134 \(\pm\) 10 & 0.9143 \\  & HIC & 794 \(\pm\) 184 & 717 \(\pm\) 100 & 0.6095 \\ \hline \end{tabular}
\end{table} 
Table 1: Mean and SD of the PLA and HIC for each shell group with the Mann–Whitney \(U\) test results (\(p\)-value) for each impact point tested at 5 m/s. Significant values are shown in bold font. \begin{table}
\begin{tabular}{c c c c c} \hline \multirow{2}{*}{**Impact Point**} & \multirow{2}{*}{**Variable**} & \multicolumn{2}{c}{**Hard Shell**} & \multicolumn{2}{c}{**Soft Shell**} \\  & & **Group (\(n\) = 4)** & **Group (\(n\) = 6)** & **\(p\)-Value** \\ \hline \multirow{2}{*}{B} & PLA (g) & 207 \(\pm\) 13 & 241 \(\pm\) 72 & 0.1714 \\  & HIC & 2042 \(\pm\) 220 & 2138 \(\pm\) 517 & 0.9143 \\ \hline \multirow{2}{*}{X} & PLA (g) & 250 \(\pm\) 14 & 240 \(\pm\) 20 & 0.6095 \\  & HIC & 2377 \(\pm\) 264 & 2284 \(\pm\) 296 & 0.9143 \\ \hline \multirow{2}{*}{P} & PLA (g) & 211 \(\pm\) 11 & 230 \(\pm\) 12 & **0.0381** \\  & HIC & 2244 \(\pm\) 62 & 2431 \(\pm\) 255 & 0.3524 \\ \hline \end{tabular}
\end{table} 
Table 2: Mean and SD of the PLA and HIC for each shell group with the Mann–Whitney \(U\) test results (\(p\)-value) for each impact point tested at 8.2 m/s. Significant values are shown in bold font. point tested at 5 m/s and 8.2 m/s, respectively. The preliminary statistical hypothesis testing could not find any significant influence of the headform size on the PLA or HIC values at neither of the tested speeds. This result was expected because normally, the requirements of the helmet standards are the same for all headform sizes and therefore helmet manufacturers individually adjust the performance of each helmet size. Regarding the impact performance comparison, the main statistical hypothesis testing showed no significant differences between the hard shell group and the soft shell group on the results of the impact absorption tests at 5 m/s. Similar results were observed in the tests at 8.2 m/s, except for the impacts on the helmet P point, which, showing contrary results to what had been suggested in previous research [13; 14], resulted in significantly higher PLA for the soft shell group (\(p\)-value = 0.038), even if the HIC value was not significantly different (\(p\)-value = 0.352). These findings seem to be contradictory with the statement that including a penetration test in regulations causes helmets to be designed with a stiffer shell that behave very rigidly when striking flat surfaces [13; 14].