## 2 Materials and Methods
### Turning Data Analysis  
Turning as a cyclic behavior: A 360\({}^{\circ}\) turn is composed of several units of turn cycles depending on the balance ability of the subject, usually with a minimum of three turn cycles in healthy adults. Each turn cycle has two turns: (1) spin turn and (2) step turn. Each turn has a single support (SS critical phase) (one foot on ground) and double support (DS) (both feet on ground). The time interval of SS critical phase is defined as critical time (with high instability) when the participant is on a single limb support (either ipsilateral or contralateral foot). Double support can be placed into two categories: (i) double support with feet apart (large base of support DS-LBOS), which occurs in the spin turn, and (ii) double support with feet together (small base of support DS-SBOS), which occurs in the step turn. Turning variables are defined in Table 1b. The direction of turning starts with the initiation foot (or leading/ipsilateral foot) undergoing a spin turn through foot off (FO) followed by ipsilateral foot strike (FS) leading to DS-LBOS. The time taken from the first FO to FS is defined as critical time-1 (CT-1). Similarly, the events are followed sequentially for the contralateral foot (trailing limb) from a position of DS-LBOS to SS critical phase and then back to DS-SBOS. Thus, all odd-numbered critical times (such as CT-1, CT-3, CT-5) are from ipsilateral (or leading) foot SS movement via spin turns and all even-numbered critical times (such as CT-2, CT-4, CT-6) are from the contralateral (trailing) foot SS movement via step turns. Figure 2 shows all these events in a sequence, with the right foot being the initiation foot (leading or ipsilateral foot) and the left foot being the contralateral foot (or trailing limb). Thus, a turn cycle (TC) starts with a spin turn of (a) FO of leading limb (SS) and (b) FS of leading limb (DS-LBOS), followed by a step turn of (c) FO of trailing limb (SS) and (d) FS of the trailing foot (DS-SBOS). Thus, each turn cycle consists of two FOs and two FSs for each leading and trailing limb. \begin{table}
\begin{tabular}{c c c c} \hline  & **Healthy Individuals** & **Stroke** & **Cohen’s d** \\ \hline Mean leading limb critical times (CTs) [seconds] & 0.47 \(\pm\) 0.17 & 0.44 \(\pm\) 0.12 & 0.20 \\ Standard deviation of leading limb critical times [seconds] & 0.13 \(\pm\) 0.06 & 0.11 \(\pm\) 0.10 & 0.24 \\ Mean trailing limb critical times [seconds] & 0.44 \(\pm\) 0.12 & 0.47 \(\pm\) 0.18 & 0.19 \\ Standard deviation of trailing limb critical times [seconds] & 0.08 \(\pm\) 0.06 & 0.11 \(\pm\) 0.08 & 0.42 \\ Number of critical time/single support (SS) [\(n\)] & 7.64 \(\pm\) 1.36 & 12.20 \(\pm\) 3.19 & 1.85 \\ Total critical time duration [seconds] & 3.45 \(\pm\) 1.18 & 5.49 \(\pm\) 1.77 & 1.35 \\ Mean critical time duration [seconds] & 0.91 \(\pm\) 0.28 & 0.91 \(\pm\) 0.22 & 0.0 \\ Standard deviation of critical time duration [seconds] & 0.21 \(\pm\) 0.09 & 0.21 \(\pm\) 0.12 & 0.0 \\ Mean double support feet apart (DS-LBOS) [seconds] & 16.94 \(\pm\) 7.49 & 98.38 \(\pm\) 209.3 & 0.54 \\ Standard deviation of double support feet apart [seconds] & 8.17 \(\pm\) 3.75 & 10.97 \(\pm\) 8.05 & 0.44 \\ Mean double support feet together (DS-SBOS) [seconds] & 20.64 \(\pm\) 6.98 & 118.5 \(\pm\) 196.0 & 0.70 \\ Standard deviation of double support feet together [seconds] & 10.48 \(\pm\) 4.61 & 19.21 \(\pm\) 30.64 & 0.39 \\ Total double support duration [seconds] & 1.27 \(\pm\) 0.44 & 8.74 \(\pm\) 12.00 & 0.87 \\ Mean double support duration [seconds] & 0.19 \(\pm\) 0.04 & 1.08 \(\pm\) 2.02 & 0.62 \\ Standard deviation of double support duration [seconds] & 0.11 \(\pm\) 0.03 & 0.24 \(\pm\) 0.21 & 0.86 \\ Number of turn cycles & 3.45 \(\pm\) 0.69 & 5.40 \(\pm\) 1.58 & 1.59 \\ Mean time taken in a turn cycle [seconds] & 1.08 \(\pm\) 0.28 & 1.88 \(\pm\) 2.05 & 0.54 \\ Standard deviation of time in a turn cycle [seconds] & 0.13 \(\pm\) 0.08 & 0.14 \(\pm\) 0.07 & 0.13 \\ \hline \end{tabular}
\end{table}