## 3 Results  
Table 1 reports mean \(\pm\) standard deviations of working volume, weight support, clinical scale scores and the relevant correlations at baseline (T1). Correlation was also tested with respect to the upper limb ranges of motion, finding that the working volume significantly correlated with the shoulder ab-adduction (R = 0.594, \(p\) < 0.001), flexo-extension (R = 0.361, \(p\) = 0.023), internal/external rotation ROMs (R = 0.364, \(p\) = 0.021) and the elbow flexo-extension ROM (R = 0.491, \(p\) = 0.001), but not with the forearm pronsupination (R = 0.166, \(p\) = 0.304) or arm aperture (R = \(-\)0.120, \(p\) = 0.458). Weight support was found significantly correlated only with shoulder ab-adduction (R = \(-\)0.365, \(p\) = 0.021) and internal/external rotation ROMs (R = \(-\)0.506, \(p\) < 0.001). At T2, the working volume was increased, and the weight support was reduced, and all the clinical scale scores significantly improved in terms of deficits reduction. Table 2 shows the percentage changes between T1 and T2 for the parameters also reported in Table 1. The \(p\)-values refer to the pairwise comparison of the values between the two assessments. Despite the common trends related to a general amelioration, neither the percentage changes in working volume nor weight support significantly correlated with the changes in clinical scale scores. Figure 2 shows the significant relationships of the working volume with spasticity at T1 (R = \(-\)0.0395, \(p\) = 0.012) and T2 (R = \(-\)0.319, \(p\) = 0.04). Despite these correlations, the change in volume was not significantly correlated with the change in spasticity (R = \(-\)0.094, \(p\) = 0.564). The correlations between working volume and weight support were statistically significant at T1, as reported in Table 1, but neither at T2 (R = 0.118, \(p\) = 0.469) nor between their percentage changes (R = \(-\)0.046, \(p\) = 0.779). Figure 1: Representation of the working areas on the anatomical planes that formed the working volume and define the space for interacting with the video game-based exercises during the therapy sessions. All the ranges of motion significantly increased from T1 to T2 (Table 3), but of angles ranging from 1.5\({}^{\circ}\) (for the shoulder flexo-extension) to 7\({}^{\circ}\) (for the shoulder ab-adduction), with small effect sizes. A statistically significant correlation related to improvements in ROM and in clinical scale score was found only for the percentage change in forearm prono-supination and that of the FMA-UE score (R = 0.455, \(p\) = 0.003). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Percentage Changes (\(\Delta\))** & **Mean \(\pm\) SD** & \begin{tabular}{c} _p-Value_ \\ **T1 vs. T2** \\ \end{tabular} & **Effect Size** & \
\begin{tabular}{c} **Correlation** \\ **with \(\Delta\)WV\%** \\ \end{tabular} &
\begin{tabular}{c} **Correlation** \\ **with \(\Delta\)WV\%** \\ \end{tabular} \\ \hline \(\Delta\) Working volume (WV) & 45.0 \(\pm\) 98.3\% & **<0.001** & 0.722 & - & R = \(-\)0.046, \(p\) = 0.779 \\ \(\Delta\) Weight support (WS) & \(-\)32.0 \(\pm\) 30.7\% & **<0.001** & 0.876 & R = \(-\)0.046, \(p\) = 0.779 & - \\ \(\Delta\) MRC score & 30.9 \(\pm\) 32.4\% & **<0.001** & 0.999 & R = 0.212, \(p\) = 0.190 & R = 0.050, \(p\) = 0.758 \\ \(\Delta\) FMA-UE score & 24.3 \(\pm\) 23.5\% & **<0.001** & 0.999 & R = 0.007, \(p\) = 0.967 & R = 0.052, \(p\) = 0.752 \\ \(\Delta\) VAS score & \(-\)31.1 \(\pm\) 40.6\% & **<0.001** & 0.880 & R = \(-\)0.159, \(p\) = 0.329 & R = 0.065, \(p\) = 0.691 \\ \(\Delta\) MAS total score & \(-\)19.8 \(\pm\) 27.0\% & **<0.001** & 0.954 & R = \(-\)0.094, \(p\) = 0.564 & R = 0.220, \(p\) = 0.172 \\ \(\Delta\) NIH-SS score & \(-\)7.0 \(\pm\) 18.1\% & **0.003** & 0.733 & R = \(-\)0.059, \(p\) = 0.716 & R = \(-\)0.138, \(p\) = 0.397 \\ \(\Delta\) BI score & 1.0 \(\pm\) 2.1\% & **0.008** & 0.999 & R = 0.191, \(p\) = 0.238 & R = 0.078, \(p\) = 0.634 \\ \hline \hline \end{tabular}
\end{table}