## 4 Discussion  
This study used an objective method to compare measurements, namely variance and ZCR; the method entailed using a gyroscope and accelerometer to compare between children with ADHD and controls. A significantly higher variance value across the \(y\)-axis and ZCR values across all three axes of the gyroscope and significantly higher variance values across the three axes and ZCR values across the \(z\)-axis of the accelerometer were observed. The ZCR is used to analyze the rate of zero-crossing in a given period. In the smart watch, it was used to detect the frequency of moving or rotating back and forth. The ZCR was greater when the hand moved or rotated back and forth faster. Due to the human skeletal structure, rotating the hand back and forth tends to be more frequent than moving the hand back and forth. Moreover, the gyroscope was used to measure the orientation and angular velocity. Therefore, the signal obtained using the gyroscope was more suitable for the ZCR analysis. The results of the present study revealed that the ZCR values across all three axes of the gyroscope were significantly higher in the ADHD group than in the control group. However, only the variance across the \(y\)-axis was significantly different between the children with ADHD and controls. The variance was used to analyze the variability in the signal. In the smart watch, variance was used to detect movement amplitude variability. Greater hand movements resulted in greater values. Therefore, the accelerometer signal was more suitable for the variance analysis. In contrast to the ZCR obtained using the gyroscope, in the present study, a significantly higher variance across the three axes was obtained using the accelerometer in the children with ADHD than in the controls. However, only the ZCR values across the \(z\)-axis significantly differed between the children with ADHD and controls. The amplitude of arm sweeping was mainly expressed by the Ay and Az signals because of the vertical and horizontal posture of the palm. Therefore, the Ay and Az analytic results were similar and different from the Ax results obtained in the accelerometer recordings, respectively. The measurements in this study were acquired from children taking language or mathematics classes. Students' activities were limited to those in their desks and chairs. Although we did not use video to record the movements of the children with ADHD because of the applicable human privacy policy, the most frequent movement in patients with ADHD as reported by [PERSON] et al. tends to be hand-tapping [26]. The hand-tapping increased the Gy value of the gyroscope and the Az  
Figure 3: An example of one patient’s and one control’s variance in the accelerometer measurements in the three axes. Data indicate higher variance values of the accelerometer measurements in the \(x\)-, \(y\)-, and \(z\)-axes in the child with attention-deficit hyperactivity disorder (ADHD) than in the matched control. value of the accelerometer more than did other parameters in our recordings (Figure 1). As presented in Tables 2 and 3, Gy and Az were significantly different in variance and ZCR. An increase in Gy and Az corresponded to an increase in the bend/stretch (sweep) of the arm when the palm was in the horizontal position. Our study results showed detailed movements and are compatible with other studies of children with ADHD at school. The optimal location of the motion sensor on the body is dependent on the nature of the motion being monitored. In patients with ADHD, [PERSON] et al. used two sensors to record the movement data of each individual--one attached to a belt worn at the waist and the other fixed by a velcro star to the ankle of the dominant leg [21]. In other ADHD studies, actigraphy has been used on the non-dominant wrist to detect activity in patients with ADHD [14; 16; 17]. The children in the present study used their dominant hand for activities in class.