## 2 Materials and Methods  
This study used the within-subject design in which the same group of subjects was subjected to more than one treatment. A within-subject design was chosen because it requires fewer participants, making the process much more streamlined and less resource-heavy, and because it can control for the individual differences in each participant that can affect the outcomes of treatments (that is, the changes in the independent variables).  
The study activities were performed on a volunteer basis by 10 outpatients, including 5 men and 5 women, at the rehabilitation treatment center of a tertiary hospital in northern Taiwan. However, 1 male subject had to exit the training due to hospitalization. Therefore, the subjects in this study ultimately consisted of 9 stroke patients with a mean age of \(56\pm 2.8\) years. The subjects were recruited from the rehabilitation center of Far Eastern Hospital. All of the patients signed Institutional Review Board (IRB) approval agreements and informed consent before participating in the study, and the study was conducted in accordance with relevant guidelines and regulations. Ethical approval was received from the Research Ethics Review Committee of Far Eastern Memorial Hospital (New Taipei, Taiwan), and IRB approval was also received (no: FEMH-IRB-103034-F, v.05, Board Meeting/Approval Date: 30 June 2015), including approval of the recruitment posting, agreement text, and questionnaire. Furthermore, clinical trial registration (27 October 2019) and a PPS receipt (ClinicalTrials.gov ID: NCT04141384) were obtained. The following inclusion criteria were used: stroke with hemiparesis (with the stroke having occurred at least 12 months earlier); stable medical condition; ability to walk over five meters (able to use assistive devices); ability to tandem stand independently for more than ten seconds; and ability to understand and cooperate with the experimental procedures [7]. Our exclusion criteria included the inability to stand or walk as indicated by a modified Rankin Scale (mRS) score \(>\) 3. The exclusion criteria also included having Alzheimer's, heart failure, eye disorders, and taking certain medications. Table 1 shows the subjects' characteristics, as well as the specific inclusion criteria and exclusion criteria. The inclusion and exclusion criteria were rigorously reviewed by the IRB committee twice before finally being approved for this study.  
\begin{table}
\begin{tabular}{l c} \hline Age (years) & \(56\pm 2.8\) \\ Time from stroke (months) & 17.3 \\ Men/women & 4/5 \\ Hemiparesis (R/L) & 5/4 \\ Height (cm) & 161.2 \(\pm\) 5.4 \\ Weight (kg) & 69.9 \(\pm\) 10.5 \\ \hline \multirow{4}{*}{The inclusion criteria} & (1) & The first onset of stroke with hemiparesis occurred at least six months. \\  & (2) & Stable medical condition. \\ \cline{1-1}  & (3) & Ability to walk over five meters with or without assistive device. \\ \cline{1-1}  & (4) & Ability to tandem stands independently for more than ten seconds. \\ \cline{1-1}  & (5) & Ability to understand and cooperate with the experimental procedures. \\ \hline \multirow{4}{*}{The exclusion criteria} & (1) & mRS = 4, moderately severe disability; unable to walk and attend to bodily needs without assistance. \\ \cline{1-1}  & (2) & mRS = 5, severe disability; bedridden, incontinent, and requiring constant nursing care and attention. \\ \cline{1-1}  & (3) & Other central or peripheral types of neurological diseases affecting balance control such as diabetic polyneuropathy, Alzheimer’s disease, heart failure, and eye disorders. \\ \cline{1-1}  & (4) & Musculoskeletal deficits affecting the lower extremities such as osteoporosis or history of fracture. \\ \cline{1-1}  & (5) & Medication or mental status affecting posture or balance control. \\ \hline \end{tabular}
\end{table}
Table 1: Subjects’ characteristics and the inclusion criteria (n = 9).