## 4 Discussion  
In our previous work [26], with the aim to validate the use of vision-based systems for measuring the Functional Reach Test (FRT), we compared FRT values obtained using Microsoft Kinect v1 with those measured manually. Participants performed the FRT interchangeably between the manual way and using the system. Results showed an average absolute difference of 2.84 cm and no statistical significant difference was found applying a paired t-student test to the data. These results suggested that Microsoft Kinect v1 can be used to measure the FRT. In this present work, two new experiments were conducted in order to improve and further validate the system using the Microsoft Kinect v2 for possible deployment at homes. Overall Kinect v2 outperforms Kinect v1 as it offers better robustness and accuracy when estimating joint positions except for the feet [47]. In fact, the Kinect v1 measures the depth with the Pattern Projection principle, where a known infrared pattern is projected into the scene and out of its distortion the depth is computed. The Kinect v2 contains a Time-of-Flight (ToF) camera and determines the depth by measuring the time emitted light takes from the camera to the object and back [48]. This time, measurements were extracted simultaneously by both methods. With the Microsoft Kinect v2, we found that the measurements obtained by the standard way and the experimental system in both experiments are linearly correlated and the absolute measurement error in both experiments was also less than the one obtained by Kinect v1. Applying paired \(t\)-test, we found that the data obtained was valid but needed to be corrected, hence a linear regression model was applied to correct the data acquired using the Microsoft Kinect v2. Examination of regression assumptions showed that the model \begin{table}
\begin{tabular}{l} \hline t = \(-\)0.92759 \\ \hline \(p\)-value = 0.3571 \\ \hline Difference = \(-\)0.06191252 \\ \hline \end{tabular}
\end{table} 
Table 6: Results of paired \(t\)-test applied to the data of Experiment 2 after correction. Figure 16: [PERSON]–Altman plot for experiment 2.  
explains well the data and applying the paired \(t\)-test to the data after correction indicated that there is no statistical significant difference between the measurements obtained by both methods. In a similar study to ours, [PERSON] et al. [34] sought the validity of an interactive Functional Reach Test. To achieve their aim, they used wrist joint data from Kinect v1 SDK with the camera set on the left of the user. They computed the reach distance and compared it with the outcomes obtained simultaneously by the Optotrak Certus 3D motion-capture system. They set the experiment with three different distances from the Kinect sensor: at 2 m, 2.5 m, and 3 m, with the best agreement was reported at 2.5 m. However, they noted that there was no optimal distance with minimal measurements errors. Even so, the mean measurement found at 2.5 m distance from the camera was 4.92 cm; a value that lays within the minimal detectable change values of the FRT in stroke and Parkinson's disease populations as reported by the authors. As for our experiments, we used the hand joint data provided by Kinect v2 to compute the FRT with the user facing the camera at 2.5 m distance; the user is best tracked while he is facing the sensor. As in [34], we compared the values returned by the system with those measured by the physiotherapist simultaneously. In both experiments, we found an average absolute difference smaller than found in the experiment of [34], though a larger sample is required to detect minor differences between the standard FRT and the experimental system. As for display interface, we used mirror feedback where the user can see herself/himself on the screen all time whereas in the work of [PERSON] et al. [34] they employed a wireframe skeleton avatar.