## 1 Introduction  
Attention-deficit hyperactivity disorder (ADHD) is one of the most common childhood psychiatric disorders and affects 3%-10% of children [1; 2; 3]. Currently, ADHD diagnoses are mostly dependent on criteria based on the Diagnostic and Statistical Manual of Mental Disorders, Fifth Edition (DSM-V). In addition to these criteria, some physicians use checklists to diagnose ADHD. However, many authors have indicated that the criteria and checklists used to diagnose ADHD are subjective, and objectively diagnosing ADHD is thus difficult [4]. For example, [PERSON] et al. found that using the ADHD Rating Scale IV led to overdiagnosis compared with using clinical interviews and that the diagnosis varied by procedure [5]. Although some behavioral and neuroscientific measures such as Conners' Continuous Performance Test (CPT) have been used to diagnose ADHD, correlations between CPT parameters and parent and teacher ratings of inattentive and hyperactive impulsive behavior have been reported to be weak in some studies [6; 7], which limits the clinical reliability of the CPT. In recent years, sensor technology has advanced to the extent that a wearable device as small as a watch can record data for long periods. These devices have been used to study many diseases, such as osteoarthritis, cerebral palsy, Parkinson disease, and stroke [8; 9; 10; 11]. In patients with ADHD, a computer-based infrared motion-tracking system and actigraphy have been used to differentiate children with ADHD from healthy controls [12]. However, the infrared motion-tracking system can only be used together with the CPT [13]. Through actigraphy analysis, movement counts from actigraphs in patients with ADHD must be converted into kilocalories (kcal) [14]. The calculation method is thus indirect. Other actigraphy studies have only classified performance between patients with ADHD and controls or presented an increased mean activity in children with ADHD, but they have lacked a detailed movement analysis of children with ADHD [15; 16; 17]. In the present study, we used a direct and convenient method to objectively detect detailed movements in children with ADHD. Studies have reported that increased activity compared with controls is characteristic in patients with ADHD [18; 19]. Intensity of movement is a better metric for distinguishing children with ADHD from controls than the number of movements measured through actigraphy [19]. Furthermore, two studies have used an accelerometer as an objective tool for diagnosing ADHD [15; 20]. The authors observed a small difference in the mean and variance in activity between ADHD and non-ADHD groups in language and math courses; however, in an art course, large differences in the mean and variance in activity between the two groups appeared [20]. In addition, two other studies have used a gyroscope with an accelerometer to distinguish patients with ADHD from controls during various activities during a visit to a psychiatric consultancy [21] and when performing nine motor tasks [22]. Both studies presented satisfactory performance in distinguishing between patients with ADHD and controls. However, these studies were task-oriented and did not measure natural/ambient movements. In the DSM IV Text Revision, ADHD is characterized by persistent inattention or hyperactivity-impulsivity on a more frequent or severe scale than expected at a particular level of development, and this adversely affects at least two areas of life (e.g., home and school) regarding social, academic, or occupational functioning. Based on clinical observation, compared with controls, children with ADHD presented hand actions with more variant speeds and higher frequency, such as movement back and forth along a spatial direction and rotation around a spatial direction back and forth, than did controls. The magnitude of the variation in motion can be quantified using a simple variance measure, and the speed of motion can be quantified using frequency domain analysis.