## 2 Materials and Methods
### Data Analysis  
All of the collected data were analyzed using MATLAB (MathWorks, Natick, MA, USA). Previous studies have reported WBB data collection with different frequencies of acquisition (e.g., 30 [14], 40 [4],  
Figure 2: Experimental walkway including two Nintendo Wii Balance Boards (WBBs) and force plates. (a) Actual setup; (b) schematic walkway and walking directions of each task. 50 [6] and 100 Hz [9; 10; 11]), which were varied significantly throughout the data acquisition. Moreover, because the WBB has a low signal-to-noise ratio, data from the device has to be filtered. Therefore, we collected data from the WBB at 100 Hz, and then used a moving window filter to smooth the raw data and reduce the noise. A window size of 3 was chosen because it allowed us to average the data from one prior and one posterior frame for smoothing. This size was based on the average sampling frequency of the WBB, as recommended at 63 Hz in the previous study [11]. For the data analysis, a walking stance from both the WBB and the force plate was classified as the time from the heel of the foot's initial contact (IC) to the time when the toes of the foot came off the ground (TO). The IC and TO were defined as timings for which the force measurement (vGRF) exceeded 5% of each participant's body mass. Then, the difference in the durations from the two devices was evaluated for each stance. Next, the data were resampled to compare the vGRF and COP from the force plate with the measurements from the WBB. When there was a difference in the data length between the two devices, the frame numbers were fit to the shorter one. To determine the accuracy of the WBB compared with the force plate, the accuracy of the measured vGRF value was assessed using the %RMSE and Pearson's correlation coefficient (\(p<0.05\)); the %RMSE, which is the root-mean-square error of the WBB to the force plate divided by each participant's body mass, was calculated as follows:  
\[\%\text{RMSE}=\frac{\sqrt{\frac{\sum\limits_{\text{i=1}}^{N}\sum\limits_{i= 1}^{N}\left(F_{FPi}-F_{WBBi}\right)^{2}}{m}}}{m}\times 100 \tag{1}\]  
where \(N\) is a sample data size in a stance, and \(F_{FP}\) and \(F_{WBB}\) are the vGRF values measured by the force plates and the WBB, respectively. In addition, Bland-Altman plots (BAPs) were created for the vGRF in the stance. The BAP was created by plotting the difference in vGRF measurements between the two devices against the mean results to examine the relationship between the spread of the error to determine if there was systematic bias. In the study, we used all the sampling data from walking stances to obtain the BAPs. The COP generated from the WBB measurements was calculated using a weighted average of the location and the measured force value of the four force sensors of the WBB, as shown in the following formula:  
\[COP_{\text{X}}=\frac{\sum\limits_{\text{i=1}}^{n}X_{\text{i}}F_{\text{i}}}{ \sum\limits_{\text{i=1}}^{n}F_{\text{i}}}\,\ \ COP_{\text{Y}}=\frac{\sum\limits_{\text{i=1}}^{n}Y_{\text{i}}F_{\text{i}}}{ \sum\limits_{\text{i=1}}^{n}F_{\text{i}}} \tag{2}\]  
where \(n\) is the number of force sensors, \(F\) is a sensor force value, and \(X\) and \(Y\) are sensor coordinates on the WBB. The sensor coordinates (\(X\), \(Y\)) were set as (\(\pm 216.5\), \(\pm 119\)) (in mm), and the center of the WBB was regarded as the origin. These calculations were executed when the total force value of the four sensors exceeded 5% of a participant's body mass. The surface of the WBB was located at a height of 53.2 mm from the plane of the force plate. It is difficult to compare the COP trajectory between the two devices precisely because there is a larger horizontal GRF while walking than there is while standing still, and this applies different effects to the COP on the surfaces of the two devices. Thus, the COP trajectory from the force plates were transformed to the WBB's coordinate system using a transformation matrix generated from the four edge positions of the WBB and the iterative closest point (ICP) algorithm [24].